A 1000-fold Acceleration of Hidden Markov Model Fitting using Graphical Processing Units, with application to Nonvolcanic Tremor Classification
Marnus Stoltz, Gene Stoltz, Kazushige Obara, Ting Wang, David Bryant
AA 1000-fold Acceleration of Hidden Markov Model Fittingusing Graphical Processing Units, with application toNonvolcanic Tremor Classification.
Marnus Stoltz Gene Stoltz , Kazushige Obara Ting Wang David Bryant . Department of Mathematics and Statistics, University of Otago, New Zealand . Council for Scientific and Industrial Research of South Africa, Pretoria, South Africa . Department of Electronic Engineering, University of Johannesburg, South Africa . Earthquake Research Institute, University of Tokyo, Japan ∗ Corresponding author. [email protected]
March 10, 2020
Abstract
Hidden Markov models (HMMs) are general purpose models for time-series datawidely used across the sciences because of their flexibility and elegance. Howeverfitting HMMs can often be computationally demanding and time consuming, par-ticularly when the the number of hidden states is large or the Markov chain itself islong. Here we introduce a new Graphical Processing Unit (GPU) based algorithmdesigned to fit long chain HMMs, applying our approach to an HMM for nonvol-canic tremor events developed by Wang et al. (2018). Even on a modest GPU,our implementation resulted in a 1000-fold increase in speed over the standard sin-gle processor algorithm, allowing a full Bayesian inference of uncertainty related tomodel parameters. Similar improvements would be expected for HMM models given a r X i v : . [ s t a t . C O ] M a r arge number of observations and moderate state spaces (<80 states with currenthardware). We discuss the model, general GPU architecture and algorithms andreport performance of the method on a tremor dataset from the Shikoku region,Japan. Keywords—
Bayesian inference, Computational hardware, Seismology, Algorithm design.
Slow slip events (SSEs), a type of slow earthquakes, play an important role in releasingstrain energy in subduction zones, the region where one tectonic plate moves underneath anothertectonic plate and sinks. It is currently understood that SSEs occur as shear slips on the bottomtip of subduction zones that transition between a fixed region above and slipping region below(Beroza and Ide, 2011). Recent evidence suggest that nonvolcanic tremors are observed in closeassociation with SSEs, however the causal relationship between the two phenomena is not yetwell understood. Classifying nonvolcanic tremors helps to better understand this link but canbe time consuming when typically done by hand.Recently, an automated procedure was developed by Wang et al. (2018) to classsify spatio-temporal migration patterns of nonvolcanic tremors. The procedure classifies tremor sourceregions into distinct segments in 2-D space using a Hidden Markov Model. The model is fittedusing the Expectation Maximisation algorithm. Here we implement a Bayesian approach. How-ever, fitting the model in either a frequentest or Bayesian framework is extremely demandingcomputationally, often taking days or weeks for large dataset with moderate state space. Fortu-nately, technological advances in hardware have the potential to solve this issue. Specifically, wemake use of fast and affordable graphic processing units (GPUs).In recent years HMM algorithms on GPUs have been implemented in various fields. A non-exhaustive list includes implementations in bioinformatics (Yao et al., 2010), speech recogni-tion (Yu et al., 2015), a registered patent in speech matching (Chong et al., 2014) and workloadclassification (Cuzzocrea et al., 2016), as well as HMMer (Horn et al., 2005) an open-sourceproject for use with protein databases. The HMM implementations are application specific often ith large number of states and mostly focused on increasing throughput of the Verterbi andBaum-Welch algorithms (Zhang et al., 2009; Li et al., 2009; Liu, 2009). This leads to a range ofconcurrent approaches. Here we focus on the efficient implementation of the forward algorithmof an HMM model given a large number of observations and a moderate number of states.The outline of the paper is as follows: In Section 2 we describe the HMM for classifying non-volcanic tremors and discuss the likelihood algorithm in a serial and parallel context. Thereafterwe give details on the OpenCL implementation of the parallel likelihood algorithm. In Section 3we discuss performance of the OpenCL implementation and compare it to the standard Forwardalgorithm. In Section 4 we report our analysis on a large tremor dataset from the Shikoku region,Japan. Nonvolcanic tremor activity is clustered spatially and each spatial cluster seems to recur episod-ically. To represent this phenomenon using an HMM, Wang et al. (2018) introduce one hiddenstate for each spatial cluster. The tremors themselves (including the absence of a tremor) are theobservations. The frequency and spatial distribution of tremors changes according to the hiddenstate.More formally, we suppose that the observations of nonvolcanic tremors are a sample pathof a stochastic process { X i } i =0 ,...,N with observations represented in the state space I = {∅ , R } generated under an HMM with K numbered hidden states. For each hidden state k = 1 , . . . , K we introduce parameters p k , µ ( k ) and Σ ( k ) , where p k is the probability of observing a tremorand µ ( k ) , Σ ( k ) are the mean and variance of a bivariate normal distribution modelling where atremor is likely to occur, if it does occur.To simplify notation we introduce for each observation x a K × K diagonal matrix P ( x ) , lso called the emission matrix , with the k th diagonal element corresponding to the probabilityof observing x given state k P ( x ) kk = p k φ ( x | µ ( k ) , Σ ( k ) )1 − p k . (1)Here φ ( . ) is the density function of bivariate normal distribution. Let Γ = (Γ ij ) denote the K × K transition matrix of the HMM, where Γ ij indicate the the transition probability fromhidden state K = i to K = j . Also, let δ = δ , . . . , δ K denote the vector of probabilities for theinitial state.Now the likelihood function for the parameters given the observed data can be written as L (cid:0) Γ , δ , { p k , µ ( k ) , Σ ( k ) } k =1 ,...,K | x , . . . , x N (cid:1) = δ T ΓP ( x ) . . . ΓP ( x N ) . (2) GPUs have had a large impact across statistical and computing sciences due to cost-effectparallelism (Kindratenko, 2014). However in order to translate an algorithm from CPU to GPUsome careful consideration is needed in terms of1. Reducing latency (how to concurrently execute instructions on GPU in order to optimisedata throughput.)2. Managing memory (how to effectively distribute and utilise memory across processors toavoid bandwidth bottlenecks).3. Designing robust algorithms with respect to varying GPU architecture between modelsand vendors as well as the rapidly changing landscape of computational hardware.Frameworks like OpenCL and CUDA, allow programmers to implement GPU algorithms withsome level of generality. The implementation we describe here was carried out in the OpenCLframework. OpenCL is an open standard maintained by the non-profit technology consortiumKhronos Group, see for more details on the non-profit organisation. he OpenCL framework consists of a host (CPU; terms in brackets relate to computationon GPU architecture) controlling one or more compute devices (We just used one GPU). Eachcompute device (GPU) is divided into compute units (streaming multiprocessors). Computeunits are further divided into compute elements (microprocessors or cores). Each compute unithas access to global memory of the compute device. This access though is slow. Each computeunit also has a shared memory to allow efficient data exchange between compute elements. Eachcompute element has exclusive access to private memory (registers) for computation. Our implementation will work well on a range of GPU models. For our studies we used a NVIDIAGeForce GTX 1080 Ti GPU with 28 compute units (streaming multiprocessors) each with 48KBof shared memory, 128 compute elements (cores) and a register file that can contain up to 32,76832-bit elements distributed across the compute elements (cores). For the host we used an IntelCore i7-7700K CPU at 4.20GHz. There are two main limitation for the OpenCL algorithm interms of hardware specifications1. The number of registers per compute element.2. The size of shared memory on a compute unit.For example given the hardware described above we have (32,768/128)=256 registers per computeelement. This implies that we can store up to roughly 200 32-bit matrix elements on a computeelement (we also need some registers left to store counters and other meta variables). Ourimplementation assumes that at least two matrix rows can fit into the registers of a computeelement. This gives an upper limit for the number of hidden states of
K < . In order toefficiently distribute rows of a matrix and update matrix elements we need space for two matricesin the shared memory of the compute unit. Our configuration has 48KB of shared memory percompute unit. Implying that we can fit a total of (48 · ) / K < . To andle a large number of states, alternative parallel computing strategies should be used (Hornet al., 2005; Yu et al., 2015).First we consider how the algorithm for the likelihood (2) would be implemented on a singleprocessor unit. To avoid matrix-matrix multiplications we would start with the stationary vector δ on the left, and then sequentially multiply that by transition matrices and emission matrices: Algorithm 1
The Forward algorithm on a CPU procedure Compute-likelihood ( { p k , µ ( k ) , Σ ( k ) } k =1 ,...,K , { x , . . . , x N } ) v ← δ T for k from to N do Compute P ( x k ) v ← v Γ v ← vP ( x k ) return v Running time will be dominated by the matrix-vector multiplication in steps 5 and 6, taking O ( K ) time per iteration. Hence the running time, or work, for this implementation is O ( N K ) .Next we compare it with the parallel implementation.The overview of our implementation is as follows:1. We compute all of the emission matrices P ( x ) , . . . P ( x N ) in parallel2. We then multiply the emission matrices by the transition matrices, all in parallel storingN matrices Γ P ( x ) , . . . , Γ P ( X N ) .3. Instead of computing Γ P ( x ) , . . . , Γ P ( X N ) as a single sequence of vector-matrix multi-plications, we multiply the matrices ( Γ P ( x )) , . . . , ( Γ P ( X N )) together.This increases the work done: we are carrying out matrix-matrix multiplications instead ofmatrix-vector multiplications, but it allows us to spread the computation over multiple proces-sors. We now discuss steps (1) to (3) in greater detail. The goal in this step is to compute the emission matrices P ( x i ) for each observation x i . Theemission probability is defined by (1) and makes use of the parameters p k , Σ k , µ k for each hiddenstate k . These parameters are initially copied to the registers of each core and remains there ntil all the datapoints have been evaluated. The compute elements work in parallel. Each isallocated a data point x i , uses the stored values to compute P ( x i ) and copies the diagonal matrixcomputed to global memory. Note that a compute element can request and copy the next datapoint at the same time as it processes the current data point.For this step there is no data sharing between compute elements, allowing for data-levelparallelism. Therefore it is more efficient to allow compute device compiler to optimise the work-load scheduling and data transfer between compute units in order to fully utilise SIMD (Singleinstruction multiple data) instructions. Output from compute elements are collected and copiedto global memory to form the list of new inputs { Γ , P ( x ) , . . . , P ( x N ) } for the next kernel. During the next step we compute Γ P ( x i ) for all data points x i , again in parallel. At this pointwe run into limitations with memory. While the register of a single compute element is largeenough to store the diagonal matrix P ( x i ) , it is not large enough to store the full transitionmatrix Γ nor the product matrix Γ P ( x i ) . The solution is to break down the multiplication of Γ and P ( x i ) by computing only a few rows at once.We query the register size for each compute element to determine how many rows of Γ canbe copied. The rows remain in the register until all data points have been evaluated. Thereafterthe next set of rows is copied into the registers and the data points is evaluated again until allthe rows of ΓP r for r = 0 , . . . , N have been computed. As P ( x i ) is diagonal, the product ofrows of Γ with P ( x i ) is computed by simply rescaling the corresponding columns.The next diagonal matrix subset is requested while scaling subset for current data point.Again, there is no data sharing between compute elements, allowing for optimal data-levelparallelism. Output from compute elements are collected and a new list of inputs, namely { ( ΓP ) , . . . , ( ΓP N ) } is compiled for the final GPU kernel. tep 3: The Square Matrix-Chain Multiplication on GPU The third step is the most time-consuming, and also the most involved. The general idea is toavoid the long sequence of matrix vector calculations δ T ΓP ( x ) . . . ΓP ( x N ) which cannot be readily parallelized, by instead multiplying the matrices together in parallel.Our algorithm here roughly follows (Masliah et al., 2016).Recall the general hierarchical structure of a GPU calculations, as described above. The CPUcontrols the GPU. Each compute GPU is divided into compute units (streamline multiprocessors).Compute units are further divided into compute elements (microprocessors or cores). The CPUis actually faster than the compute units for individual computations, the speed of GPUs beingdue to parallelism. Our algorithm takes advantage of all three levels: The sequence of matrices(known in computer science as a matrix chain ) is divided into multiple segments, one for eachcompute unit. The compute units then carry out matrix multiplication directly, making use ofmultiple compute elements to share out the rows in each matrix-matrix computation. We thenuse the CPU to carry out the final sequence of matrix-vector computations, using the matricesreturned by the computational units of the GPU.Note that in practise we compute log L rather than L and shift the registers either up ordown using the scale coefficients from compute units to avoid underflow.
One of the factors that influence the use of an algorithm on GPUs is whether it is actually fasterthan a Forward algorithm. To check this we compare computational times of the GPU algorithmwith the Forward algorithm from the software library Tensor flow. First we fixed the number ofHMM states to K = 25 while increasing the number of datapoints over a range of magnitudeorders N = 10 , . . . , . Thereafter we fixed the number of datapoints to N = 100 , and − Number of Datapoints E x ec u t i o n T i m e [ m s ] Execution Time for 25 StatesForwardOpenCL-GPUFigure 1: We compare computational time of OpenCL algorithm on GPU with a Forwardalgorithm on CPU. Computational time is indicated on the y-axis and number of data-points are indicated by the x-axis. We see that with datapoints, the GPU algorithmruns ∼ times faster. increased the number of HMM states for K = 5 , , . . . , . In each case model parameterswere drawn from the prior disribution (discussed in the next section) and thereafter data wassimulated using the R software package in Wang et al. (2018). The results are shown in Figure 1and Figure 2. We see that the GPU algorithm executes orders of magnitude faster then a Forwardalgorithm. Here we specifically compare computation time of step 3 in the OpenCL algorithm with matrix-chain multiplication using popular GPU BLAS (Basic Linear Algebra Subprograms) libraries.We use subroutines from the CLBlast library as well as the MAGMA BLAS libary to do thematrix-chain multiplication. CLBLast is a general BLAS library in OpenCL that automaticallytunes subroutines for specific hardware based on compile time. MAGMA BLAS is a CUDAlibrary exclusively available for NVIDIA GPUs. We followed the same procedure as in theprevious two experiments except that we fixed the number of HMM states to K = 50 . We showresults in Figure 3 and Figure 4. Using the MAGMA library gives roughly the same performance Matrix Size E x ec u t i o n T i m e [ m s ] Execution Time for 100,000 Data pointsForwardOpenCL-GPUFigure 2: We compare computational time of OpenCL algorithm on GPU with a For-ward algorithm on CPU. Computational time is indicated on the y-axis and number ofHMM states are indicated by the x-axis. We see that the GPU algorithm slows down asthe register capacity of compute elements is reached. However it still outperforms theForward algorithm by orders of magnitude. as the OpenCL algorithm for small matrices. We note that using these libraries in the OpenCLalgorithm is not straightforward due to small tweaks and scaling coefficients that we keep trackof in addition to performing the matrix-chain multiplication. The algorithm became very slowwhen the HMM had more than 100 states due to memory limitations previously discussed.
Bayesian techniques have become a popular method of statistical inference across a broad rangeof sciences (Jóhannesson et al., 2016; Kruschke, 2010; Moore and Zuev, 2005; Stoltz et al., 2019;Turner et al., 2016; Woolrich et al., 2009). This is due to advances in numerical techniques andthe affordability of powerful computers (Andrieu et al., 2004). In a Bayesian analysis the aimis to compute the joint posterior distribution of model parameters, simply referred to as theposterior distribution. The posterior distribution summarizes the uncertainty related to modelparameters. − Data Points E x ec u t i o n T i m e [ m s ] Speed Comparison for 50 StatesCLBlastMAGMAOWNFigure 3: For this computational comparison (in miliseconds) with the BLAS librarieswe fix the number of HMM states to K = 50 and increase the number of datapoints overa range of magnitude orders.
10 20 30 40 5010 − Matrix Size E x ec u t i o n T i m e [ m s ] Speed Comparison for 100000 Data PointsCLBlastMAGMAOWNFigure 4: For this computational comparison (in miliseconds) with the BLAS librarieswe fix the number of datapoints to N = 100 , and increase the number of HMM statesfor K = 5 , , . . . , . 11 ypically due to model complexity the posterior distribution is an analytically intractablefunction. However methods such as Monte Carlo Markov Chains (MCMCs) use random walksto estimate the posterior distribution. The basic concept behind MCMCs is that a Markov chaincan be constructed with a stationary distribution, where the stationary distribution is in factthe posterior distribution.An MCMC is initialized by choosing a random state, typically by drawing a sample fromthe prior distribution (we discuss prior distributions below). The MCMC is then simulated byaccepting or rejecting proposed MCMC states based on a ratio of the likelihood function andprior distribution of both the current and proposed MCMC state. The MCMC is simulated untilafter the stationary distribution is reached. Stationarity of an MCMC is assessed by lookingat trace plots of parameters as well as computing the number of effective independent samples.Samples of the stationary MCMC is then used to approximate the posterior distribution. Using ratios of the likelihood and prior distributions is an elegant way of sampling from theposterior distribution. It sidesteps some nasty calculations if we were to compute the poste-rior distribution directly instead. Roughly speaking prior distributions is a way to incorporateknowledge about model parameters before looking at the data. However prior distributions caneasily be neglected but they are in fact an important part of the model. Therefore choosing priordistributions needs to be carefully considered and requires some justification. For instance, it isknown that tremors occur in sequence bursts that cluster around the same area (Wang et al.,2018). This observation we translate into the model by specifying a model prior centred aroundsparse transition matrices. More formally, we specify a symmetric Dirichlet prior with concen-tration parameter 0.01 on Γ (formulas for prior densities are given in Appendix A). Furthermorewe expect that for some hidden states we are more likely to observe tremors than others. There-fore we specify independent gamma distributions on state probabilities { p k } k =1 ,...,K , half ofthe state probabilities with mean 0.1 and variance 0.001 and the other half with mean 0.9 andvariance 0.001. Also, we specify a uniform prior on hidden state means { µ ( k ) } k =1 ,...,K restrictedto a rectangular domain that contains all observations. We have no prior information on theshape of the hidden states therefore we specify an uninformative Inverse-Wishart prior on the ovariance matrices { Σ ( k ) } k =1 ,...,K with degrees of freedom equal to the number of states K andscale matrix set to a K × K identity matrix. In order to simulate MCMCs for the model, we incorporated the GPU likelihood algorithm alongwith the prior distributions into a general purpose MCMC sampler (Christen et al., 2010). This Rpackage bundle is freely available at https://github.com/genetica/HMMTremorRecurrencePatterns .Note that OpenCL 1.2 and Python 3.6 (or later versions) needs to be separately installed on asystem in order to support the back-end of the R package. The R package also contains a simpleexample using simulated data from the HMM described in Section 2. Additionally we provideinstructions on how to modify the OpenCL code if an HMM with a different emission functionis required. In order to assess convergence of the MCMC chains we used Tracer. For a brieftutorial on how to use Tracer to assess convergence, see https://beast.community/analysing_beast_output . Furthermore if some problems are encountered with convergence of the simulatedMCMCs see https://beast.community/tracer_convergence for some recommendations.
We use a large tremor dataset from the Shikoku region, Japan to demonstrate the sort of Bayesiananalysis that can be done with GPUeR-hmmer. The Shikoku region is one the three majorregions in Japan (the other two being the Tokai region and Kii region) in which nonvolcanictremor occurrences have been repeatedly detected. Tremor activity spans along the strike ofthe Phillipines Sea plate for about 600km and the depth ranges from 30 to 45 km on the plateinterface. The original waveform data is supplied by the High Sensivity Seismograph Networkof the National institute for Earth Sciences and Disaster prevention in Japan. The datasetanalysed by Wang et al. (2018) was extracted from the waveform data. It consists of , data point measurements between and . It is hourly control measurements determinedusing clustering and correlation methods described in Obara et al. (2010). .5 Model fitting A full Bayesian analysis of the model will sample the number of hidden states along with the restof the model parameters. However sampling from different parameter spaces is quite challengingand is an active and ongoing area of research (Lunn et al., 2009). Instead we incorporate thechoice of number of hidden states K into the model fitting process.We start with a small number of hidden states and incrementally increase the number ofhidden states, while doing so we assess the posterior distribution for each case. The posteriordistribution of each model is estimated by running the MCMC sampler for 1,000,000 iterations.Running each chain took approximately ∼ hours.In Figure 5 we summarize the posterior distributions for model fitted with number of hiddenstates K = 5 , , . . . , . Typically, the background states (i.e states that cover large areas)have the highest variance in posterior distribution. Whereas states covering smaller areas haveconsiderably less variance in posterior distribution of parameters. We also see in Figure 5(d)that parameters used in Wang et al. (2018) are recovered by the posterior distribution. Typicallyas we increase the number of states some states are divided into two, with rare new clusters.Furthermore we see for K = 30 that some additional hidden states ( k = 4 , , ) doesn’t fit overone particular cluster of points, covers a large area, has a low probability of observing tremorsand a low stationary probability (i.e time spent in state). Thereafter we also fitted models withhidden states for K = 26 , (see Appendix B) and we find that additional hidden states havethe same undesirable properties and therefore use K = 25 as our choice for number of hiddenstates for the model (see MCMC summary statistics in Appendix C). We carry out a Bayesian forecast from the model for a 5 day period (from December 11, 2012to December 16, 2012). Note that the data for this period was excluded in the model fittingprocess. In order to forecast tremors we simulated 120 hourly datapoints (i.e for 5 days) from themodel (with fixed number of hidden states K = 25 ) for every 1000th MCMC sample (total of 500simulations) of the approximate posterior distribution. Note that we used the same realizationof the MCMC that was generated in the model fitting process (see previous section). We usedthe HMM simulator in the R package HMMextra0s (freely available at https://rdrr.io/cran/ (a) K = 5 (b) K = 10 (c) K = 15 (d) K = 20 (e) K = 25 (f) K = 30 Figure 5: Posterior distributions of fitted models with number of hidden states K =5 , , . . . , for tremor occurrences in Shikoku region. Ellipses each map represent the2D normal density of one hidden state for one sample from the posterior distribution.States are numbered in red. Colour of an ellipse indicate how likely a tremor will occurgiven the process is in the hidden state. In the bottom right corner of each map wegive the mean transition matrix of the posterior distribution. Transition probabilities(array entries) and state probabilities (colour of ellipse) both use same colormap given inbottom right corner. Furthermore grey dots represent the Shikoku tremor data points.Black ellipses and -dots represent mean parameters.17 Time (hours) V (a)
20 0 20 40 60 80 100 120
Time (hours) V (b) Figure 6: We summarize the forecast simulations as two density plots. (a) Latitudepredictions and data plotted against time (in hours). (b) Longitude predictions and dataplotted against time (in hours). The red dots in both figures are the hourly Shikoku datafor the time period from December 11, 2012 to December 30, 2012 (not included in dataused for model fitting). Furthermore black dots in both figures are the hourly Shikokudata for the time period December 10, 2012 (included in data used for model fitting).
HMMextra0s/man/HMMextra0s-package.html ).We summarize the 500 forecast simulations as a density in a longitude plot over time and alatitude plot over time (Figure 6). Furthermore we plot the actual data as a scatterplot with reddatapoints. We also include the last day (December 10, 2012) of the data used for model fitting(as a scatterplot with black datapoints).We see that the model works well for the first two days. It captures nicely in which areathe tremors occur. We also see that see that we get coverage from the forecast (density plot) forall the data points except for one outlier. Furthermore we see that the variance in the modelpredictions increase with time. This is not unexpected since the further away our forecasts arefrom the present the less information our data contains about the future states of the process.It would be very unlikely to make an accurate forecast of more than a week.
In this paper we present an algorithm for evaluating HMM likelihoods that can run severalorders of magnitude faster than the traditional Forward algorithm. Our algorithm requires morework, but the high level of parallization of the likelihood calculation translates into high data hroughput.We have implemented the algorithm for an HMM model that categorises nonvolcanic tremordata. Furthermore we have integrated the algorithm as part of an R package for Bayesiananalysis using the OpenCL framework with Python under the hood. It is however expected thata CUDA implementation for NVIDIA GPUs will achieve higher data throughput but this limitsthe algorithm to a single vendor. OpenCL on the other hand allows execution of the algorithm onany OpenCL compliant device such as Intel CPUs, AMD CPUs and GPUs, Qualcomm processors,Xilinx FPGAs (Field-programmable gate array) and even NVIDIA GPUs.We have reported some runtime comparisons with implementations of the Forward algorithm.The efficieny gains in computation of the likelihood allowed us to conduct a detailed Bayesiananalysis for tremor data of Shikoku region of Japan.Lastly, the OpenCL algorithm can be easily modified for other HMM models. In some casesonly the evaluation function of the emission matrix needs to be updated. Marnus Stolz received a doctoral scholarship from the NZ Marsden Fund (PIs David Bryant andSteven Higgins).
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Symmetric Dirichlet distributions f ( γ , . . . , γ K , α ) = Γ( αK ) α K K (cid:89) i =1 γ α − i , for α < , we note that probability mass is sparsely distributed among γ , . . . , γ K if α < . Inverse-wishart distributions
Suppose Ψ is the scale matrix and ν the degrees of freedom then f ( x , Ψ , ν ) = | Ψ | ν/ νp/ Γ K ( ν ) = | x | − ( ν + K +1) / e − tr (Ψ x − ) , where Γ K is a multivariate gamma function Γ K (cid:16) ν (cid:17) = π ( ν )( ν − / K (cid:89) j =1 Γ (cid:16)(cid:16) ν (cid:17) + (1 − j ) / (cid:17) . Gamma distribution f ( x, α, β ) = β α x α − ) e − βx Γ( α ) , for x > α, β > . PPENDIX B: ADDITIONALS MODEL FITTED FOR NONVOLCANICTREMOR DATA (a) K = 26 (b) K = 27 Figure 7: Posterior distributions of fitted models with number of hidden states K = 26 , for tremor occurrences in Shikoku region. Ellipses each map represent the 2D normaldensity of one hidden state for one sample from the posterior distribution. States arenumbered in red. Colour of an ellipse indicate how likely a tremor will occur given theprocess is in the hidden state. In the bottom right corner of each map we give the meantransition matrix of the posterior distribution. Transition probabilities (array entries)and state probabilities (colour of ellipse) both use same colormap given in bottom rightcorner. Furthermore grey dots represent the Shikoku tremor data points. Black ellipsesand -dots represent mean parameters. 23 PPENDIX C: TABULATED POSTERIOR STATISTICS FOR NUMBEROF HIDDEN STATES K=25
Table 1: Combined GPU-hmmer parameter summary after 5,000,000 MCMC iterationsfor soybean dataset hmmer mean variance HPD ACT ESS posterior -1.0987E+03 7.6624E+04 -1.6110E+03 -4.0624E+02 35830.8997 239.5444Gamma1 8.6710E-01 2.4186E-04 8.3770E-01 8.9248E-01 29571.9564 169.0791Gamma2 1.6289E-02 4.7111E-05 3.8358E-03 2.8083E-02 14455.9226 345.8790Gamma3 1.8235E-03 8.1549E-06 5.3391E-06 5.9633E-03 31080.9139 160.8704Gamma4 1.8604E-03 9.1692E-06 8.0933E-06 6.5181E-03 23964.1982 208.6446Gamma5 1.4205E-03 1.2756E-06 4.4740E-05 3.3164E-03 14213.5729 351.7764Gamma6 3.4741E-03 7.6753E-06 2.8037E-05 8.2833E-03 21277.4832 234.9902Gamma7 2.9676E-03 3.5263E-06 4.7983E-05 5.7603E-03 15272.0127 327.3963Gamma8 1.9523E-03 5.1619E-06 1.8840E-05 4.8152E-03 27378.2848 182.6265Gamma9 8.8053E-04 1.4839E-06 6.1831E-07 2.6187E-03 15509.9601 322.3735Gamma10 4.0934E-03 1.6603E-05 8.1382E-15 1.2107E-02 57380.8895 87.1370Gamma11 9.3274E-03 1.4699E-05 1.9398E-03 1.5410E-02 45068.2804 110.9428Gamma12 6.1730E-04 3.1284E-07 4.1541E-07 1.7926E-03 14440.9950 346.2365Gamma13 3.5715E-03 5.4052E-05 1.2686E-04 8.2704E-03 24168.9799 206.8767Gamma14 9.6052E-04 7.1797E-07 8.2637E-06 2.5498E-03 18857.9341 265.1404Gamma15 1.3255E-03 1.4142E-06 4.1034E-06 4.0367E-03 31384.2830 159.3154Gamma16 1.5935E-03 1.1240E-05 7.3288E-06 4.9660E-03 20798.4511 240.4025Gamma17 3.8764E-02 3.7291E-05 2.6857E-02 4.8477E-02 48946.9321 102.1514Gamma18 1.0956E-03 1.9142E-06 7.6476E-06 3.7071E-03 45031.8581 111.0325Gamma19 1.0625E-03 4.7366E-06 5.9749E-06 2.6002E-03 17168.5493 291.2302Gamma20 2.6584E-03 5.6930E-06 2.0232E-05 6.8404E-03 35644.4221 140.2744Gamma21 2.9296E-02 2.9234E-05 1.9465E-02 4.0877E-02 42258.6322 118.3190
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Gamma22 1.9319E-03 3.1337E-06 8.6148E-05 6.0423E-03 16100.7869 310.5438Gamma23 2.3521E-03 3.8152E-06 3.0464E-05 6.1173E-03 22249.4145 224.7250Gamma24 2.8243E-03 7.0229E-06 1.4940E-04 7.1177E-03 15713.5026 318.1977Gamma25 7.5430E-04 1.2261E-06 0.0000E+00 2.8100E-03 33773.0435 148.0471Gamma26 7.5800E-04 9.2460E-07 2.7447E-06 2.1539E-03 19423.7468 257.4169Gamma27 9.7455E-01 1.8772E-05 9.6572E-01 9.8144E-01 16385.9590 305.1393Gamma28 1.1656E-03 5.5348E-07 3.8569E-06 2.4886E-03 433749.2599 11.5274Gamma29 2.6091E-04 1.4724E-07 6.0330E-07 5.3802E-04 34952.5560 143.0511Gamma30 1.1413E-03 2.5184E-07 3.8769E-04 1.6722E-03 12690.4915 393.9958Gamma31 2.5300E-03 2.2597E-07 1.7208E-03 3.7603E-03 62747.9452 79.6839Gamma32 7.2782E-04 6.3201E-07 8.2677E-05 1.5357E-03 22661.4152 220.6394Gamma33 4.7610E-03 2.8677E-06 2.1785E-03 7.5344E-03 128377.9942 38.9475Gamma34 1.4483E-04 3.3611E-07 0.0000E+00 4.4469E-04 18494.6559 270.3484Gamma35 8.8254E-04 9.1352E-06 1.1430E-179 2.6530E-03 17104.6382 292.3184Gamma36 2.2049E-04 5.6664E-07 3.2433E-07 8.8779E-04 13504.7449 370.2402Gamma37 2.8423E-04 1.8785E-06 1.3566E-07 5.3904E-04 16705.1430 299.3090Gamma38 1.8184E-03 8.9467E-07 1.0682E-03 2.9130E-03 12987.5478 384.9841Gamma39 1.5827E-04 3.8431E-07 8.2793E-240 5.5617E-04 10408.8774 480.3592Gamma40 1.5324E-04 5.9919E-08 1.7997E-06 3.9441E-04 35391.8500 141.2755Gamma41 1.1195E-04 6.7680E-07 4.5519E-07 1.0529E-04 6175.3438 809.6715Gamma42 1.6970E-04 5.8092E-08 2.3201E-68 4.8800E-04 19975.0180 250.3127Gamma43 5.4145E-04 1.7014E-06 8.0357E-07 1.2248E-03 12214.7293 409.3419Gamma44 9.4007E-05 1.2845E-07 0.0000E+00 3.0288E-04 15527.8979 322.0011Gamma45 5.8817E-04 2.5773E-06 2.6848E-07 1.7851E-03 16773.6991 298.0857Gamma46 2.7130E-04 1.6124E-06 0.0000E+00 9.7746E-04 12013.6336 416.1938Gamma47 8.3608E-04 8.7118E-07 8.1343E-06 1.6621E-03 25000.7219 199.9942Gamma48 6.1769E-03 1.6042E-06 3.7912E-03 8.2029E-03 72454.3676 69.0090
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Gamma49 1.3814E-03 1.2691E-07 8.2454E-04 1.8834E-03 16414.5669 304.6075Gamma50 2.7088E-04 1.8704E-07 1.9386E-06 8.3363E-04 20676.1070 241.8250Gamma51 3.8265E-03 1.4101E-05 1.5164E-06 1.1256E-02 54832.1289 91.1874Gamma52 4.1702E-02 2.7147E-04 1.4143E-02 7.0675E-02 177277.4811 28.2044Gamma53 6.5895E-01 1.1852E-02 5.3762E-01 8.6165E-01 179266.1419 27.8915Gamma54 5.2686E-02 1.3514E-04 3.0989E-02 7.5725E-02 20727.5986 241.2243Gamma55 3.7342E-03 8.7625E-06 4.2153E-06 8.8395E-03 35075.5349 142.5495Gamma56 3.7250E-03 1.4367E-05 2.1957E-05 1.0399E-02 13703.4629 364.8713Gamma57 3.4035E-03 7.6310E-06 1.1752E-06 9.5530E-03 60398.7204 82.7832Gamma58 1.1569E-02 5.7239E-05 1.4684E-03 2.6915E-02 126050.2525 39.6667Gamma59 8.3384E-03 5.0755E-05 2.4430E-05 1.9246E-02 108972.2649 45.8832Gamma60 7.5111E-03 1.8539E-05 1.3374E-03 1.5506E-02 35526.5778 140.7397Gamma61 2.4433E-03 5.7828E-06 3.7794E-05 7.1885E-03 23869.7025 209.4706Gamma62 2.9865E-03 1.1750E-05 0.0000E+00 9.4605E-03 24301.5009 205.7486Gamma63 4.6511E-03 1.1309E-05 4.0228E-04 1.1406E-02 17927.0292 278.9085Gamma64 3.4551E-03 1.0811E-05 8.0421E-06 9.2846E-03 60480.2163 82.6717Gamma65 1.7704E-03 2.9336E-06 2.0011E-05 5.5824E-03 31567.4252 158.3911Gamma66 1.8257E-03 5.5040E-06 4.8305E-06 6.7129E-03 21359.3236 234.0898Gamma67 4.4132E-03 1.0302E-05 2.3097E-04 1.0175E-02 30529.5466 163.7758Gamma68 3.3537E-03 1.3710E-05 4.6203E-06 1.1097E-02 47189.7634 105.9552Gamma69 2.5590E-03 1.2021E-05 1.6972E-05 8.6447E-03 17168.6412 291.2286Gamma70 3.6075E-03 2.1892E-05 1.3317E-05 1.4296E-02 51779.6476 96.5630Gamma71 2.7341E-03 1.0429E-05 6.6654E-05 9.0064E-03 50454.1729 99.0998Gamma72 1.6084E-01 8.9549E-03 1.7265E-04 2.6376E-01 52563.5955 95.1229Gamma73 4.7693E-03 1.3051E-05 9.0943E-04 1.3995E-02 31721.7813 157.6204Gamma74 3.2346E-03 1.1070E-05 2.3274E-05 8.6432E-03 32056.6747 155.9738Gamma75 1.9117E-03 3.3446E-06 0.0000E+00 5.6489E-03 15101.7754 331.0869
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Gamma76 4.0374E-03 1.3862E-05 5.6963E-06 1.1135E-02 17448.4236 286.5588Gamma77 1.8735E-02 1.3793E-04 1.4735E-03 3.7747E-02 153773.7616 32.5153Gamma78 5.2840E-02 1.4351E-03 8.7997E-03 1.2569E-01 109036.5946 45.8562Gamma79 7.7194E-01 4.7660E-04 7.3193E-01 8.1135E-01 97858.7582 51.0940Gamma80 2.3710E-03 6.3079E-06 8.1711E-209 6.0531E-03 40191.5185 124.4044Gamma81 9.8015E-03 2.1754E-05 2.7665E-03 1.9849E-02 14021.4458 356.5966Gamma82 8.0723E-03 1.8660E-05 1.5913E-03 1.6722E-02 13912.5818 359.3869Gamma83 4.2189E-03 1.5787E-05 5.4825E-05 1.2599E-02 17447.4497 286.5748Gamma84 1.5088E-02 5.6666E-05 2.5035E-03 3.0542E-02 25580.4554 195.4617Gamma85 9.6710E-03 1.6331E-05 2.9544E-03 1.8682E-02 31452.3565 158.9706Gamma86 1.6917E-03 2.8601E-06 8.1084E-06 5.7956E-03 8240.6163 606.7507Gamma87 5.7498E-03 2.7984E-05 2.2783E-04 1.5747E-02 21734.0305 230.0540Gamma88 6.3461E-03 1.9530E-05 4.5535E-04 1.4662E-02 26108.6270 191.5076Gamma89 5.2471E-03 1.3105E-05 2.0134E-04 1.0240E-02 13017.1322 384.1092Gamma90 2.0111E-03 4.2089E-06 1.1327E-05 5.9145E-03 25705.1264 194.5137Gamma91 1.0309E-03 1.6301E-06 0.0000E+00 3.8256E-03 28956.6968 172.6716Gamma92 2.2777E-03 3.1269E-06 1.0209E-05 5.9816E-03 14923.2556 335.0475Gamma93 2.1677E-03 9.3605E-06 0.0000E+00 5.6929E-03 23761.2254 210.4269Gamma94 1.0397E-03 3.5146E-06 4.8823E-06 4.4321E-03 23742.1096 210.5963Gamma95 3.3163E-03 5.2410E-06 1.4686E-04 7.9886E-03 30114.5464 166.0327Gamma96 2.5090E-03 1.6163E-05 2.7992E-05 7.1467E-03 41015.2414 121.9059Gamma97 5.8867E-02 1.3932E-03 2.0425E-05 1.0662E-01 31943.0005 156.5288Gamma98 5.7913E-03 2.4696E-05 4.1050E-50 1.4469E-02 35391.9791 141.2749Gamma99 1.4880E-03 2.3845E-06 0.0000E+00 4.5140E-03 25023.0598 199.8157Gamma100 3.6941E-03 6.4817E-06 3.0497E-04 7.7939E-03 20250.6950 246.9051Gamma101 1.0241E-02 7.2072E-05 1.0568E-04 2.7836E-02 20759.9054 240.8489Gamma102 1.0804E-01 4.6584E-04 6.1602E-02 1.4489E-01 14058.9871 355.6444
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Gamma103 5.6760E-03 2.0145E-05 5.4058E-06 1.4865E-02 82129.7028 60.8793Gamma104 2.8431E-03 6.8754E-06 1.2424E-04 8.9155E-03 34299.2175 145.7759Gamma105 7.1477E-01 7.0890E-04 6.6167E-01 7.6297E-01 11826.7772 422.7694Gamma106 6.5209E-03 1.7024E-05 1.5508E-04 1.4459E-02 18234.4629 274.2060Gamma107 2.8461E-02 2.2138E-04 7.8455E-03 5.4417E-02 17921.7664 278.9904Gamma108 3.3291E-03 8.5009E-06 1.2591E-05 9.5390E-03 26847.8163 186.2349Gamma109 1.0648E-02 4.2232E-05 3.1849E-04 2.3514E-02 37656.6887 132.7785Gamma110 1.4558E-02 9.6667E-05 1.4384E-03 3.0609E-02 19327.2137 258.7026Gamma111 2.6155E-03 1.2609E-05 0.0000E+00 1.0664E-02 35246.2265 141.8592Gamma112 3.1530E-02 9.3212E-05 1.5939E-02 5.2513E-02 21814.3469 229.2070Gamma113 3.0332E-03 9.1017E-06 2.1723E-05 8.8238E-03 21228.0396 235.5375Gamma114 2.8459E-03 5.0074E-06 8.5689E-05 8.0017E-03 20882.2793 239.4375Gamma115 3.2308E-03 1.2224E-05 5.1372E-05 9.8159E-03 26005.5177 192.2669Gamma116 1.7967E-03 3.4193E-06 5.5578E-06 5.4687E-03 14293.7529 349.8032Gamma117 5.1239E-03 2.2861E-05 7.6876E-06 1.4478E-02 14718.0883 339.7180Gamma118 3.9297E-03 1.7284E-05 0.0000E+00 1.0973E-02 30107.3335 166.0725Gamma119 2.4660E-03 6.7519E-06 3.6767E-05 8.8143E-03 39887.9865 125.3510Gamma120 5.9192E-03 2.0708E-05 2.1575E-05 1.4863E-02 41440.4025 120.6552Gamma121 3.3092E-03 7.1388E-06 1.2865E-04 9.1760E-03 19966.6857 250.4171Gamma122 1.4188E-02 1.4186E-04 1.0583E-04 3.8582E-02 29696.9340 168.3675Gamma123 6.1469E-03 3.7944E-05 3.5337E-103 2.0600E-02 14266.5070 350.4712Gamma124 5.3542E-03 6.3464E-05 2.1460E-05 1.3922E-02 16095.5744 310.6444Gamma125 3.4203E-03 2.1335E-05 0.0000E+00 1.0130E-02 45807.5273 109.1524Gamma126 1.4618E-02 1.1325E-04 2.8701E-04 3.6125E-02 13691.7749 365.1827Gamma127 3.2206E-01 1.0197E-03 2.6087E-01 3.7722E-01 49086.4278 101.8612Gamma128 7.2857E-03 3.1361E-05 1.3948E-04 1.8385E-02 42005.7489 119.0313Gamma129 1.6891E-02 9.2670E-05 6.3445E-04 3.3494E-02 7378.6105 677.6344
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Gamma130 4.6442E-03 1.3438E-05 1.1728E-04 1.1089E-02 13249.6606 377.3682Gamma131 4.9890E-01 1.3868E-03 4.2268E-01 5.6160E-01 22054.7456 226.7086Gamma132 8.1591E-03 2.6096E-05 2.4168E-04 1.6574E-02 11093.0986 450.7307Gamma133 5.9883E-03 2.4691E-05 0.0000E+00 1.6412E-02 26398.9966 189.4011Gamma134 7.2804E-03 2.6287E-05 8.8405E-05 1.8001E-02 18358.7256 272.3501Gamma135 8.7256E-03 2.1526E-05 2.2706E-04 1.7155E-02 23918.9752 209.0391Gamma136 2.9880E-03 7.3198E-06 2.0184E-06 7.9991E-03 19008.6479 263.0382Gamma137 4.1896E-03 1.5155E-05 0.0000E+00 1.0915E-02 25792.6040 193.8540Gamma138 4.0759E-03 1.7561E-05 0.0000E+00 1.2611E-02 26961.9908 185.4462Gamma139 1.9013E-03 2.7532E-06 3.6100E-06 5.6579E-03 24439.0003 204.5910Gamma140 3.0420E-03 9.0646E-06 0.0000E+00 9.7842E-03 13533.4384 369.4553Gamma141 5.9292E-03 9.9349E-05 0.0000E+00 1.8168E-02 26232.0800 190.6063Gamma142 3.5377E-03 9.6379E-06 0.0000E+00 1.0215E-02 23203.7127 215.4828Gamma143 1.5168E-02 6.2250E-05 1.9025E-03 3.0656E-02 15722.1103 318.0235Gamma144 5.7933E-03 4.4980E-05 1.7462E-289 1.6168E-02 22946.4046 217.8991Gamma145 5.7463E-03 3.2700E-05 2.3855E-05 1.7080E-02 21825.2432 229.0925Gamma146 2.6456E-03 1.2255E-05 2.5832E-06 9.3531E-03 24569.0253 203.5083Gamma147 1.4579E-02 1.2048E-04 0.0000E+00 3.9936E-02 16737.9921 298.7216Gamma148 8.6204E-03 5.7072E-05 2.7282E-06 2.0417E-02 38093.7914 131.2550Gamma149 1.6937E-02 6.7864E-05 4.1349E-03 3.4704E-02 17925.6478 278.9299Gamma150 1.0294E-02 4.6247E-05 1.4572E-03 2.1769E-02 18136.6081 275.6855Gamma151 1.3152E-02 7.3651E-05 4.6341E-05 3.0154E-02 15556.8030 321.4028Gamma152 3.7244E-02 2.8304E-04 2.8950E-03 6.5610E-02 33478.3899 149.3501Gamma153 1.3758E-02 6.6246E-05 4.0890E-04 3.0621E-02 29346.9173 170.3756Gamma154 5.9445E-03 2.1308E-05 1.4043E-04 1.5699E-02 32066.2635 155.9271Gamma155 2.8742E-02 1.1982E-04 7.3737E-03 5.2091E-02 33898.0279 147.5012Gamma156 2.5899E-03 7.0253E-06 7.4161E-06 7.8707E-03 18689.6816 267.5273
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Gamma157 7.4292E-01 1.0465E-03 6.7896E-01 7.9747E-01 17523.3619 285.3334Gamma158 3.7707E-03 1.0295E-05 0.0000E+00 8.9664E-03 39356.2073 127.0448Gamma159 4.6426E-02 1.6495E-04 1.9526E-02 6.8351E-02 20248.3966 246.9331Gamma160 9.4584E-03 2.2591E-05 2.0420E-03 1.9575E-02 15479.8442 323.0007Gamma161 2.4250E-03 6.0102E-06 2.2032E-05 6.5940E-03 24814.9610 201.4914Gamma162 1.1943E-02 5.1395E-05 1.7040E-03 2.6546E-02 19386.5635 257.9106Gamma163 2.5954E-03 5.8674E-06 1.6756E-05 7.9368E-03 48028.9088 104.1040Gamma164 2.1189E-03 4.6098E-06 6.1450E-06 5.7563E-03 21749.6357 229.8889Gamma165 2.2330E-03 1.8865E-05 8.4136E-06 6.9105E-03 32478.0637 153.9501Gamma166 3.6582E-03 8.4473E-06 9.5463E-05 9.4273E-03 22048.8286 226.7694Gamma167 3.6427E-03 1.1416E-05 1.0440E-05 9.4321E-03 28140.4471 177.6802Gamma168 1.1421E-02 6.9643E-05 4.6150E-04 2.6784E-02 25694.6466 194.5931Gamma169 5.1223E-03 4.4866E-05 1.0712E-04 1.6117E-02 24383.3685 205.0578Gamma170 4.9605E-03 2.9550E-05 1.9398E-05 1.4858E-02 19684.0267 254.0131Gamma171 2.9722E-03 1.0856E-05 0.0000E+00 7.2370E-03 19550.7361 255.7448Gamma172 1.9379E-02 2.5865E-04 2.0458E-04 5.2602E-02 42800.9521 116.8198Gamma173 1.3881E-02 7.6848E-05 6.7001E-04 3.1088E-02 23168.4207 215.8110Gamma174 6.8947E-03 1.6571E-05 1.2776E-03 1.5726E-02 18513.8606 270.0679Gamma175 2.7526E-03 4.9136E-06 1.9243E-63 7.1387E-03 36917.1373 135.4385Gamma176 2.6324E-02 2.7210E-04 8.3009E-04 5.7787E-02 34809.0990 143.6406Gamma177 5.5414E-01 2.2137E-03 4.7383E-01 6.4615E-01 47621.5790 104.9944Gamma178 2.5632E-02 2.7222E-04 3.2199E-03 6.4055E-02 63701.0484 78.4916Gamma179 1.3130E-02 9.7449E-05 8.0479E-04 3.2826E-02 19797.6125 252.5557Gamma180 5.8898E-03 2.2534E-05 1.5316E-04 1.6794E-02 45691.9265 109.4285Gamma181 7.4855E-03 2.9769E-05 7.2334E-04 1.9642E-02 46600.4791 107.2950Gamma182 4.8547E-03 1.6843E-05 0.0000E+00 1.3644E-02 15670.4387 319.0721Gamma183 8.8900E-02 1.2533E-03 2.7782E-02 1.5979E-01 55484.9668 90.1145
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Gamma184 6.7210E-03 6.9651E-05 3.3967E-06 2.5447E-02 22950.5821 217.8594Gamma185 6.8905E-03 2.4856E-05 2.6100E-05 1.6220E-02 23021.4924 217.1884Gamma186 1.0912E-02 1.1490E-04 1.9169E-05 2.9730E-02 24510.3336 203.9956Gamma187 7.3192E-03 7.6226E-05 8.4817E-07 2.4485E-02 59524.0225 83.9997Gamma188 1.2526E-02 5.8547E-05 7.1780E-04 2.5975E-02 18057.2891 276.8965Gamma189 7.0914E-03 4.2373E-05 0.0000E+00 1.9989E-02 26258.6102 190.4137Gamma190 5.6499E-03 2.0119E-05 3.7507E-04 1.5291E-02 18594.2158 268.9008Gamma191 5.3477E-03 5.5532E-05 1.4105E-214 2.0262E-02 27848.3877 179.5436Gamma192 1.1914E-02 1.2016E-04 4.8203E-04 4.0740E-02 42037.8420 118.9405Gamma193 8.6947E-02 1.2275E-03 2.4052E-02 1.4001E-01 65323.2487 76.5424Gamma194 4.3828E-03 1.4208E-05 5.8816E-05 1.2065E-02 24807.7751 201.5497Gamma195 6.2229E-03 4.6592E-05 1.5081E-126 2.0269E-02 19968.8234 250.3903Gamma196 3.9935E-03 1.6995E-05 5.8948E-06 1.1468E-02 22964.2384 217.7298Gamma197 4.8131E-02 1.0506E-03 1.8951E-03 1.1265E-01 61968.1768 80.6866Gamma198 3.8953E-02 4.6221E-04 4.3143E-03 7.6449E-02 103496.0248 48.3110Gamma199 6.8304E-03 3.0269E-05 0.0000E+00 1.6100E-02 23752.2087 210.5067Gamma200 3.8137E-03 1.2918E-05 0.0000E+00 1.1751E-02 29431.9507 169.8834Gamma201 2.2061E-03 2.8632E-05 5.1399E-06 4.8039E-03 19079.3054 262.0640Gamma202 3.9100E-03 1.0463E-05 1.0212E-05 1.0611E-02 42334.9988 118.1056Gamma203 1.3941E-02 5.6850E-05 4.6010E-03 3.2667E-02 73870.7415 67.6858Gamma204 8.8065E-03 4.3442E-05 2.1139E-04 1.6809E-02 25373.7124 197.0543Gamma205 3.5903E-03 6.3083E-06 1.0064E-04 8.4176E-03 26858.5310 186.1606Gamma206 1.8215E-03 3.9859E-06 0.0000E+00 5.5891E-03 21877.8619 228.5415Gamma207 2.7125E-02 5.0313E-05 1.2766E-02 3.8572E-02 18578.7242 269.1250Gamma208 4.5804E-03 1.6699E-05 1.4838E-05 1.1127E-02 36375.1408 137.4565Gamma209 8.0613E-01 1.7607E-03 7.3269E-01 8.7467E-01 124530.5793 40.1508Gamma210 8.4669E-03 1.9079E-05 2.2761E-03 1.5011E-02 20560.2395 243.1878
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Gamma211 2.4497E-03 1.0519E-05 0.0000E+00 9.1696E-03 13154.7921 380.0896Gamma212 2.7867E-02 8.6381E-05 1.1267E-02 4.2506E-02 27908.3662 179.1577Gamma213 1.4054E-03 2.2605E-06 1.4660E-24 4.9417E-03 18466.9677 270.7537Gamma214 1.2470E-02 4.7618E-05 1.3578E-03 2.4040E-02 57251.1230 87.3345Gamma215 1.9740E-03 3.5207E-06 2.6479E-05 5.2427E-03 13247.3981 377.4326Gamma216 2.5117E-03 2.6384E-05 2.9458E-05 6.2596E-03 19544.4539 255.8271Gamma217 2.2047E-03 3.0671E-06 2.7441E-05 5.7185E-03 21443.2562 233.1735Gamma218 2.1137E-02 1.0274E-04 3.6511E-03 3.9757E-02 32932.5392 151.8255Gamma219 2.2999E-03 1.0651E-05 4.5831E-06 9.0745E-03 42058.9521 118.8808Gamma220 2.8658E-03 2.5555E-05 1.5123E-05 9.6544E-03 22096.7836 226.2773Gamma221 1.2031E-03 1.5336E-06 1.4189E-05 4.1287E-03 19430.3636 257.3292Gamma222 3.4537E-02 5.9361E-04 1.6772E-04 7.8791E-02 189963.0833 26.3209Gamma223 3.0790E-03 7.7608E-06 1.2559E-05 7.7606E-03 20839.1635 239.9329Gamma224 1.6715E-03 1.8892E-06 4.5916E-05 4.3769E-03 15313.2087 326.5155Gamma225 1.7481E-03 7.3093E-06 2.5438E-159 5.0969E-03 12502.8650 399.9083Gamma226 3.6707E-02 9.9152E-04 3.0241E-04 1.1157E-01 47271.4019 105.7722Gamma227 6.2283E-02 3.8712E-03 2.9392E-05 2.0028E-01 94429.1491 52.9498Gamma228 2.7096E-02 2.2985E-04 4.3516E-03 5.4892E-02 26164.9348 191.0955Gamma229 3.2028E-02 1.4356E-04 1.2579E-02 5.5498E-02 29452.0847 169.7673Gamma230 1.0139E-02 5.1313E-05 4.9129E-04 2.3844E-02 65162.2063 76.7316Gamma231 2.1222E-02 2.0195E-04 3.6462E-03 4.7430E-02 22587.0898 221.3654Gamma232 3.0705E-02 1.8114E-04 8.2274E-03 5.9118E-02 36407.2808 137.3352Gamma233 1.5053E-02 3.4100E-04 0.0000E+00 4.8016E-02 80339.2098 62.2361Gamma234 3.7322E-02 1.6725E-04 1.0257E-02 5.9128E-02 12156.2454 411.3112Gamma235 2.1579E-01 3.2940E-03 1.0663E-01 3.2862E-01 73331.2251 68.1838Gamma236 1.2151E-02 9.8877E-05 8.8663E-05 3.5255E-02 23871.2828 209.4567Gamma237 1.8690E-02 7.5997E-05 3.7458E-03 3.5588E-02 13149.2648 380.2494
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Gamma238 6.3248E-03 4.0885E-05 2.4533E-07 2.1520E-02 31778.5257 157.3390Gamma239 4.9375E-02 6.0725E-04 1.1591E-02 9.9927E-02 45728.0585 109.3421Gamma240 6.7224E-03 4.2430E-05 0.0000E+00 1.8560E-02 36849.3569 135.6876Gamma241 9.4317E-02 6.8467E-04 5.8860E-02 1.4398E-01 31663.8131 157.9090Gamma242 1.7808E-02 2.4746E-04 3.8456E-06 5.3202E-02 45864.0363 109.0179Gamma243 1.5343E-02 1.2346E-04 1.0887E-03 3.9775E-02 25997.7812 192.3241Gamma244 5.1805E-02 2.3883E-04 2.8589E-02 8.9097E-02 14533.6772 344.0286Gamma245 2.0058E-02 3.1468E-04 1.1706E-04 5.0474E-02 42293.9325 118.2203Gamma246 7.4123E-02 5.8961E-04 3.8454E-02 1.3592E-01 35161.7526 142.2000Gamma247 1.9739E-02 2.0427E-04 1.2378E-04 4.3046E-02 18502.4938 270.2338Gamma248 4.6480E-02 7.2386E-04 1.1234E-02 1.0265E-01 31479.8738 158.8316Gamma249 1.9907E-02 1.7395E-04 1.2233E-03 4.3735E-02 38284.4223 130.6014Gamma250 5.8817E-02 3.0505E-04 2.9232E-02 8.8807E-02 48014.8455 104.1345Gamma251 4.8917E-02 9.7887E-04 1.9972E-03 1.0607E-01 36523.3956 136.8986Gamma252 6.4240E-03 5.2194E-05 8.1154E-06 2.3883E-02 33883.8243 147.5630Gamma253 8.1575E-03 2.8191E-05 2.8640E-04 1.7617E-02 15709.6296 318.2761Gamma254 5.3155E-03 2.9752E-05 0.0000E+00 1.2059E-02 28570.1134 175.0081Gamma255 4.4334E-03 1.9147E-05 0.0000E+00 1.4631E-02 34892.3956 143.2977Gamma256 5.4825E-03 2.9670E-05 1.3524E-04 1.4669E-02 19045.1706 262.5337Gamma257 6.8300E-03 4.7635E-05 0.0000E+00 1.8941E-02 29033.1484 172.2169Gamma258 1.3275E-02 9.1295E-05 7.4201E-04 3.0903E-02 28043.2345 178.2961Gamma259 3.8815E-03 1.7372E-05 0.0000E+00 1.2537E-02 24454.0425 204.4652Gamma260 1.0610E-02 5.7112E-05 3.7106E-04 2.4722E-02 31783.3337 157.3152Gamma261 6.3711E-01 2.6489E-03 5.4235E-01 7.2877E-01 65788.9660 76.0006Gamma262 8.8268E-03 9.8065E-05 3.1832E-05 2.7775E-02 24850.7622 201.2011Gamma263 5.9210E-03 1.9170E-05 8.2042E-05 1.4713E-02 20750.6234 240.9566Gamma264 7.3070E-02 3.7953E-04 4.4710E-02 1.1973E-01 40442.9323 123.6310
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Gamma265 4.1779E-03 2.8985E-05 2.9634E-06 1.1795E-02 27245.2398 183.5183Gamma266 3.6660E-03 1.0923E-05 0.0000E+00 1.1055E-02 28282.6364 176.7869Gamma267 8.0333E-02 5.5329E-04 3.7376E-02 1.2613E-01 24671.3012 202.6646Gamma268 3.5894E-02 5.3182E-04 9.1184E-04 7.6760E-02 22406.7080 223.1475Gamma269 5.0000E-03 1.6646E-05 8.0503E-06 1.2885E-02 20377.3673 245.3703Gamma270 6.0987E-03 5.0104E-05 0.0000E+00 1.9194E-02 20392.5245 245.1879Gamma271 5.9221E-03 4.8925E-05 2.2163E-06 1.9486E-02 26498.4931 188.6900Gamma272 5.4337E-03 3.5837E-05 3.2224E-05 1.7387E-02 24207.3908 206.5485Gamma273 5.5041E-03 2.6215E-05 0.0000E+00 1.5638E-02 25953.9721 192.6487Gamma274 5.7329E-03 1.9426E-05 6.6190E-06 1.4090E-02 13558.9442 368.7603Gamma275 3.9834E-03 1.6668E-05 8.5724E-05 1.2867E-02 33148.8933 150.8346Gamma276 2.9681E-03 7.5712E-06 3.9389E-05 7.4899E-03 24184.5647 206.7434Gamma277 3.7934E-03 2.5369E-05 7.5299E-06 1.0718E-02 21527.6928 232.2590Gamma278 4.1185E-03 1.0647E-05 0.0000E+00 1.0465E-02 33540.4810 149.0736Gamma279 4.2983E-03 1.5452E-05 3.3467E-06 1.0948E-02 25237.1937 198.1203Gamma280 1.0858E-02 2.4034E-05 9.7111E-04 2.0302E-02 13321.8237 375.3240Gamma281 5.0261E-03 8.7573E-06 1.0469E-03 1.1525E-02 13832.8982 361.4572Gamma282 6.5803E-03 1.8902E-05 2.3867E-05 1.5060E-02 19289.4499 259.2091Gamma283 5.0972E-03 2.5601E-05 3.0547E-05 1.6494E-02 20443.3423 244.5784Gamma284 4.7241E-02 9.0826E-05 2.9230E-02 6.4696E-02 12236.9987 408.5969Gamma285 5.9855E-03 1.7391E-05 1.7215E-05 1.3667E-02 16319.6658 306.3788Gamma286 6.7989E-03 4.6773E-05 4.4576E-06 1.2852E-02 37887.2385 131.9706Gamma287 7.0529E-01 6.5625E-04 6.5503E-01 7.5514E-01 69707.2689 71.7285Gamma288 4.1422E-03 1.0170E-05 1.0113E-04 1.0852E-02 19079.0956 262.0669Gamma289 4.8746E-02 1.5836E-04 3.0056E-02 7.2797E-02 26323.2367 189.9462Gamma290 2.5543E-03 2.4406E-05 2.8525E-05 9.1834E-03 17013.3777 293.8864Gamma291 1.1412E-03 3.3345E-06 0.0000E+00 2.4611E-03 17679.4058 282.8149
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Gamma292 2.8599E-03 6.6291E-06 1.2848E-04 8.7528E-03 22401.1303 223.2030Gamma293 1.1679E-01 2.8930E-04 8.4514E-02 1.4702E-01 67755.4724 73.7948Gamma294 1.9097E-03 3.0563E-06 0.0000E+00 4.9579E-03 24372.6881 205.1477Gamma295 2.5202E-03 6.4498E-06 0.0000E+00 6.4033E-03 38714.7146 129.1499Gamma296 1.5994E-03 7.4314E-06 0.0000E+00 4.0390E-03 23306.1716 214.5354Gamma297 3.7095E-03 6.1932E-05 7.2249E-05 1.0261E-02 17278.2065 289.3819Gamma298 2.3703E-03 6.8958E-06 0.0000E+00 6.7324E-03 21231.4268 235.5000Gamma299 1.8840E-03 6.6609E-06 1.8302E-06 6.1451E-03 19788.1064 252.6770Gamma300 1.7226E-03 3.0834E-06 7.0403E-06 5.5546E-03 44347.4723 112.7460Gamma301 2.9327E-02 4.2531E-04 3.2592E-03 6.3432E-02 30510.9965 163.8753Gamma302 1.2290E-01 6.3671E-04 7.8302E-02 1.7072E-01 24623.5504 203.0576Gamma303 7.1168E-03 2.6278E-05 2.5334E-04 1.8564E-02 15769.2543 317.0727Gamma304 5.7247E-03 3.1242E-05 5.5859E-05 1.8575E-02 27674.4285 180.6722Gamma305 4.6415E-03 6.6660E-05 1.1610E-04 1.1787E-02 18508.2806 270.1494Gamma306 3.0414E-03 7.5922E-06 1.2860E-05 8.4326E-03 18594.0679 268.9030Gamma307 3.2661E-03 1.1904E-05 2.5661E-06 1.0671E-02 61553.7933 81.2298Gamma308 3.6162E-03 9.8520E-06 5.5995E-06 9.4542E-03 29464.3761 169.6964Gamma309 1.8790E-03 3.4469E-06 0.0000E+00 5.8284E-03 28845.1062 173.3396Gamma310 4.3399E-03 2.5936E-05 3.4381E-06 1.1586E-02 17978.2400 278.1140Gamma311 4.5431E-03 9.5163E-06 2.4009E-04 9.5250E-03 28937.6912 172.7850Gamma312 1.5384E-03 2.1657E-06 1.7842E-06 4.4478E-03 25970.4808 192.5263Gamma313 7.3209E-01 1.1326E-03 6.6362E-01 7.8946E-01 16866.8588 296.4393Gamma314 1.8622E-03 3.4278E-06 6.9320E-07 5.5181E-03 36575.9053 136.7020Gamma315 3.1327E-03 4.8260E-06 1.2577E-06 7.2462E-03 16861.5038 296.5335Gamma316 2.5437E-03 2.2604E-05 3.6101E-05 7.5467E-03 15749.6754 317.4669Gamma317 9.1956E-03 3.5181E-05 4.3308E-05 2.1015E-02 27536.5460 181.5769Gamma318 5.6658E-03 2.1964E-05 5.5923E-05 1.5150E-02 16059.1005 311.3499
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Gamma319 4.1368E-03 2.9159E-05 5.8963E-05 1.1556E-02 21005.5369 238.0325Gamma320 5.5329E-03 1.8947E-05 1.9608E-04 1.5499E-02 16956.3464 294.8748Gamma321 2.4158E-02 6.8231E-05 1.0261E-02 3.7861E-02 6766.1119 738.9768Gamma322 3.6947E-03 1.1449E-05 6.7122E-138 9.9310E-03 20442.0729 244.5936Gamma323 9.9583E-03 5.0129E-05 5.4610E-04 2.2615E-02 24769.9109 201.8578Gamma324 2.0962E-03 5.0383E-06 0.0000E+00 6.3166E-03 18788.8331 266.1155Gamma325 4.0082E-03 1.7494E-05 1.9199E-05 1.4044E-02 35960.8150 139.0402Gamma326 2.4669E-03 6.8498E-06 2.6688E-06 7.8518E-03 30845.1923 162.0998Gamma327 2.7149E-03 1.0769E-05 2.8700E-246 7.3696E-03 20326.7589 245.9812Gamma328 4.2796E-03 1.2370E-05 9.5174E-05 1.0872E-02 32612.1957 153.3169Gamma329 2.5964E-03 7.0825E-06 5.3002E-06 7.6621E-03 20614.7673 242.5446Gamma330 1.7047E-03 1.7693E-05 9.7357E-06 5.5125E-03 23923.4003 209.0004Gamma331 1.0921E-03 2.7578E-06 5.4262E-06 3.8869E-03 23087.1659 216.5705Gamma332 1.5254E-03 4.0615E-06 2.2535E-05 3.9127E-03 8463.8927 590.7447Gamma333 4.5659E-03 9.2828E-06 1.0744E-04 1.0630E-02 43707.7232 114.3963Gamma334 8.1321E-03 2.3897E-05 1.5494E-03 1.8872E-02 22710.8803 220.1588Gamma335 1.6005E-02 4.9995E-05 5.6207E-03 2.8615E-02 64528.7687 77.4848Gamma336 2.3665E-02 6.6610E-05 1.0211E-02 4.3433E-02 21460.8618 232.9823Gamma337 4.5288E-02 9.5400E-05 2.6571E-02 6.3111E-02 35760.0416 139.8209Gamma338 1.9542E-03 2.6936E-06 1.1975E-105 5.3739E-03 16936.6509 295.2178Gamma339 7.3149E-01 6.6108E-04 6.8932E-01 7.8483E-01 41576.3816 120.2606Gamma340 1.4309E-03 1.5812E-05 8.7102E-06 3.1581E-03 17139.3611 291.7262Gamma341 1.5732E-03 4.4854E-06 0.0000E+00 4.3259E-03 24026.0963 208.1070Gamma342 5.0500E-03 1.5580E-05 2.3646E-04 1.1701E-02 33677.8372 148.4656Gamma343 1.2851E-01 3.7326E-04 9.3754E-02 1.6243E-01 50482.0442 99.0451Gamma344 1.1096E-03 1.0636E-05 1.0640E-103 3.2372E-03 20442.1127 244.5931Gamma345 1.1524E-03 1.5336E-06 2.3512E-05 3.4638E-03 15780.5214 316.8463
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Gamma346 2.6502E-03 7.4835E-06 1.1649E-209 6.1499E-03 23170.2820 215.7937Gamma347 2.4587E-03 1.0587E-05 2.4929E-66 7.9508E-03 26962.0248 185.4460Gamma348 2.5180E-03 4.8702E-06 0.0000E+00 7.5496E-03 18700.3745 267.3743Gamma349 2.8176E-03 9.8475E-06 5.2767E-05 8.0141E-03 20869.7338 239.5814Gamma350 3.2411E-03 2.9135E-05 2.8385E-06 1.0693E-02 25938.5472 192.7633Gamma351 2.4793E-02 3.3018E-04 9.0062E-04 5.9350E-02 33327.8158 150.0248Gamma352 5.1001E-02 6.1874E-04 2.6070E-03 9.2298E-02 37286.2379 134.0977Gamma353 6.1075E-03 6.7308E-05 0.0000E+00 2.5894E-02 38588.0048 129.5739Gamma354 3.7852E-03 1.4613E-05 0.0000E+00 1.2001E-02 8916.7918 560.7398Gamma355 7.7790E-03 6.9994E-05 2.7015E-05 2.5643E-02 31182.7687 160.3450Gamma356 4.9178E-03 3.2680E-05 0.0000E+00 1.7044E-02 34944.3649 143.0846Gamma357 6.1894E-03 5.0146E-05 0.0000E+00 1.8185E-02 29584.5974 169.0069Gamma358 7.1705E-03 6.8995E-05 0.0000E+00 2.7270E-02 24876.9587 200.9892Gamma359 4.6590E-03 2.1364E-05 6.4461E-06 1.3523E-02 28535.3499 175.2213Gamma360 9.1733E-03 5.5219E-05 3.8856E-05 2.3279E-02 37390.2793 133.7246Gamma361 6.2608E-03 7.4079E-05 0.0000E+00 2.5291E-02 40482.6649 123.5097Gamma362 3.8615E-03 1.0624E-05 7.8225E-06 9.8337E-03 14735.0059 339.3280Gamma363 7.0250E-03 5.3764E-05 0.0000E+00 2.0566E-02 24005.2184 208.2880Gamma364 4.3183E-03 2.7370E-05 1.8785E-06 1.2305E-02 29506.0729 169.4566Gamma365 6.0414E-01 3.5649E-03 4.6988E-01 7.0603E-01 45696.0153 109.4187Gamma366 1.6645E-02 1.3086E-04 4.1311E-04 3.2876E-02 12823.9967 389.8940Gamma367 3.3010E-02 3.7879E-04 6.9911E-03 6.6756E-02 28993.9751 172.4496Gamma368 1.8315E-02 1.6982E-04 3.3724E-04 4.5120E-02 12876.7647 388.2963Gamma369 6.8801E-03 4.4235E-05 1.1847E-04 2.0388E-02 28752.5357 173.8977Gamma370 1.0269E-01 1.5614E-03 2.4741E-02 1.7153E-01 36482.7202 137.0512Gamma371 1.8484E-02 1.1383E-04 1.8662E-04 3.6468E-02 22382.4058 223.3897Gamma372 1.0651E-02 1.2899E-04 0.0000E+00 3.1775E-02 20097.0589 248.7926
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Gamma373 1.7435E-02 1.5667E-04 3.3653E-04 3.8187E-02 20262.4381 246.7620Gamma374 8.3769E-03 9.3021E-05 0.0000E+00 3.0907E-02 36945.3840 135.3349Gamma375 1.6333E-02 1.4734E-04 8.4483E-04 4.1077E-02 27353.5296 182.7918Gamma376 2.5206E-03 5.0930E-06 2.9205E-05 7.2401E-03 20979.2645 238.3306Gamma377 3.1381E-03 9.6389E-06 0.0000E+00 9.6390E-03 23175.4021 215.7460Gamma378 3.2783E-03 4.6262E-06 1.4914E-04 7.0207E-03 18371.5781 272.1595Gamma379 1.9466E-03 4.3353E-06 1.9932E-05 6.0063E-03 37457.2433 133.4855Gamma380 1.5848E-03 3.9237E-06 0.0000E+00 4.5166E-03 20140.3158 248.2583Gamma381 3.8456E-03 2.2601E-05 2.3276E-05 1.4362E-02 28454.7058 175.7179Gamma382 2.3889E-03 1.7898E-05 5.8433E-06 7.2489E-03 20698.5296 241.5631Gamma383 1.9750E-03 4.4970E-06 5.0407E-06 5.5307E-03 20741.2644 241.0653Gamma384 3.1523E-03 6.6443E-06 1.1953E-04 7.5092E-03 20241.7043 247.0148Gamma385 3.1986E-02 6.3682E-05 1.9275E-02 4.8261E-02 20170.9672 247.8810Gamma386 1.9295E-03 5.7482E-06 9.4874E-06 6.3732E-03 21484.8529 232.7221Gamma387 1.3705E-03 2.1416E-06 9.1667E-06 4.3620E-03 30328.2155 164.8630Gamma388 1.6270E-03 2.5758E-06 1.9328E-07 4.6204E-03 27632.8669 180.9439Gamma389 1.7055E-03 2.6181E-06 0.0000E+00 5.0687E-03 27168.1551 184.0390Gamma390 1.0854E-02 2.1510E-05 3.3281E-03 2.0403E-02 29059.2892 172.0620Gamma391 7.1509E-01 5.9987E-04 6.6839E-01 7.6232E-01 16853.6152 296.6723Gamma392 2.8702E-03 1.3946E-05 0.0000E+00 1.1007E-02 33926.4352 147.3777Gamma393 3.2691E-03 1.4818E-05 5.2630E-06 1.2622E-02 12896.3590 387.7063Gamma394 3.4814E-02 9.0375E-05 1.6997E-02 5.2017E-02 22320.0818 224.0135Gamma395 1.3375E-01 2.6785E-04 9.8756E-02 1.6443E-01 31435.8188 159.0542Gamma396 3.6185E-03 1.2274E-05 2.1532E-04 1.0387E-02 17364.7334 287.9399Gamma397 3.5225E-03 1.0651E-05 0.0000E+00 9.8298E-03 23028.6780 217.1206Gamma398 1.2023E-02 4.8850E-05 5.7406E-04 2.4273E-02 43936.2306 113.8013Gamma399 7.1335E-03 2.2365E-05 2.8489E-04 1.5523E-02 19134.3241 261.3105
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Gamma400 1.0605E-02 3.5265E-05 2.2637E-03 1.9447E-02 18513.1736 270.0780Gamma401 1.4145E-01 5.6709E-04 9.5771E-02 1.8805E-01 46561.6260 107.3846Gamma402 1.1253E-02 6.0266E-05 8.2796E-06 2.6947E-02 31745.4089 157.5031Gamma403 1.0800E-02 2.5388E-05 1.8994E-03 2.0844E-02 14008.5219 356.9256Gamma404 1.4723E-03 2.4668E-06 8.5575E-07 4.0427E-03 27293.1690 183.1960Gamma405 5.1690E-03 6.1864E-06 8.0014E-04 1.0367E-02 17573.1706 284.5246Gamma406 2.4912E-03 4.0882E-06 1.5439E-04 6.6381E-03 17474.4905 286.1314Gamma407 2.6837E-03 5.2157E-06 3.7603E-05 7.0031E-03 25231.3303 198.1663Gamma408 2.7472E-03 7.4211E-06 4.1349E-05 8.4109E-03 83638.5474 59.7810Gamma409 2.4838E-03 8.3758E-06 3.0316E-05 8.3449E-03 14372.5505 347.8854Gamma410 9.7625E-03 3.1184E-05 8.8820E-04 2.0287E-02 23276.3846 214.8100Gamma411 2.5801E-02 7.9244E-05 6.7707E-03 4.3522E-02 31942.0713 156.5334Gamma412 3.0284E-03 6.9727E-06 1.9368E-05 7.8618E-03 24849.1321 201.2143Gamma413 4.9011E-03 1.0844E-05 9.8124E-05 1.0737E-02 12502.6231 399.9161Gamma414 6.3975E-03 1.7203E-05 1.3161E-03 1.6126E-02 13817.0982 361.8705Gamma415 5.2195E-03 1.0166E-05 1.4682E-04 1.1186E-02 17327.3056 288.5619Gamma416 2.4188E-03 3.8366E-06 0.0000E+00 5.6751E-03 13496.7349 370.4600Gamma417 7.0950E-01 6.3763E-04 6.5662E-01 7.5761E-01 46169.2866 108.2971Gamma418 1.0090E-02 4.1201E-05 2.1459E-04 1.9922E-02 49123.0598 101.7852Gamma419 2.8005E-03 7.3404E-06 4.7947E-05 9.7403E-03 25931.2775 192.8173Gamma420 4.8523E-03 2.1230E-05 1.3610E-05 1.5738E-02 16063.6154 311.2624Gamma421 2.1635E-02 6.2529E-05 6.5801E-03 3.7325E-02 16900.7761 295.8444Gamma422 2.8975E-03 6.7063E-06 0.0000E+00 8.1080E-03 27776.0669 180.0111Gamma423 5.6688E-03 2.0444E-05 6.2900E-05 1.4027E-02 15309.3126 326.5986Gamma424 2.8593E-03 8.1163E-06 8.5713E-06 8.6236E-03 64005.0544 78.1188Gamma425 1.6124E-03 2.2344E-06 3.4202E-06 4.5395E-03 25226.5574 198.2038Gamma426 2.0740E-03 4.0899E-06 2.0857E-05 6.1500E-03 31370.0390 159.3878
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Gamma427 9.9544E-03 2.0338E-05 6.3560E-04 1.6414E-02 43002.3537 116.2727Gamma428 2.9525E-03 7.1782E-06 2.1226E-04 7.0641E-03 25471.4357 196.2983Gamma429 1.6369E-03 2.7502E-06 9.2684E-06 4.9787E-03 24336.0265 205.4567Gamma430 1.3922E-03 3.1853E-06 0.0000E+00 5.0678E-03 32406.8350 154.2884Gamma431 1.4245E-03 6.8981E-06 5.7031E-06 4.4679E-03 26461.6035 188.9530Gamma432 1.4795E-03 2.3451E-06 6.7581E-06 3.8377E-03 28039.3865 178.3206Gamma433 1.5035E-02 6.3199E-05 3.4628E-03 2.6602E-02 43256.3488 115.5900Gamma434 5.0448E-03 7.4097E-06 3.6836E-04 1.0538E-02 33605.9976 148.7830Gamma435 1.7197E-03 9.7988E-06 6.9005E-06 4.5959E-03 14081.1043 355.0858Gamma436 3.7395E-03 1.7747E-05 9.4233E-05 1.1876E-02 17872.4177 279.7607Gamma437 4.4831E-02 8.2069E-05 2.4317E-02 5.9053E-02 55420.5429 90.2193Gamma438 2.0099E-03 2.9398E-06 4.0242E-06 5.3215E-03 23310.4666 214.4959Gamma439 5.7917E-02 5.4776E-05 4.4385E-02 7.1556E-02 18974.4135 263.5128Gamma440 1.2071E-03 8.7368E-07 2.0884E-05 3.0730E-03 21556.4801 231.9488Gamma441 7.7877E-04 1.2320E-06 3.9643E-06 2.7132E-03 34442.7165 145.1686Gamma442 2.8372E-03 6.8045E-06 3.3803E-06 5.9055E-03 14566.5388 343.2524Gamma443 8.3304E-01 1.6314E-04 8.0840E-01 8.5844E-01 32451.6730 154.0753Gamma444 7.0302E-04 5.6680E-07 2.1415E-235 1.9467E-03 22644.6403 220.8028Gamma445 1.2805E-03 1.7479E-06 0.0000E+00 3.6397E-03 22109.1297 226.1509Gamma446 7.8547E-04 8.4742E-07 1.3043E-05 2.7585E-03 31651.8098 157.9689Gamma447 2.0870E-03 4.3782E-06 1.0134E-05 6.9000E-03 20642.3162 242.2209Gamma448 2.9245E-03 1.2113E-05 2.6652E-06 6.9217E-03 13529.3141 369.5679Gamma449 1.1445E-03 1.0144E-06 1.9544E-05 3.1386E-03 20352.2298 245.6733Gamma450 2.0047E-03 3.2108E-06 3.2630E-06 5.7242E-03 17725.7266 282.0759Gamma451 7.1105E-03 4.8820E-05 5.8517E-06 2.3692E-02 26338.7144 189.8346Gamma452 1.2013E-02 1.0252E-04 1.1897E-05 3.1603E-02 23952.7096 208.7447Gamma453 4.1419E-03 3.2262E-05 8.8946E-05 1.6086E-02 48457.2786 103.1837
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Gamma454 6.0563E-03 1.1015E-04 0.0000E+00 1.7585E-02 22774.3455 219.5453Gamma455 5.1958E-03 1.9394E-05 1.4232E-04 1.3593E-02 29107.8441 171.7750Gamma456 9.3003E-03 3.1841E-05 3.9921E-04 2.1125E-02 24715.7050 202.3005Gamma457 5.6489E-03 2.3863E-05 0.0000E+00 1.6950E-02 25998.2037 192.3210Gamma458 2.2142E-03 5.1309E-06 0.0000E+00 7.4352E-03 33010.7600 151.4658Gamma459 3.2802E-03 1.5509E-05 0.0000E+00 8.8765E-03 11562.4319 432.4350Gamma460 2.5709E-02 1.0707E-04 7.3453E-03 4.4883E-02 19696.9727 253.8461Gamma461 3.2744E-03 8.1703E-06 2.0800E-05 8.9429E-03 50279.2180 99.4447Gamma462 3.7221E-03 1.0454E-05 2.1471E-06 1.1410E-02 21433.3031 233.2818Gamma463 3.6508E-03 1.4389E-05 1.4977E-05 1.0892E-02 28069.2042 178.1312Gamma464 4.3139E-03 1.7651E-05 5.4271E-05 1.2524E-02 21386.6295 233.7909Gamma465 6.8082E-03 2.5981E-05 3.0086E-04 1.5746E-02 15262.2073 327.6066Gamma466 6.6788E-02 2.5808E-04 3.8270E-02 9.6085E-02 33162.6412 150.7721Gamma467 4.7363E-03 2.5146E-05 2.1756E-05 1.3580E-02 24894.7832 200.8453Gamma468 2.5679E-03 1.2170E-05 0.0000E+00 9.7807E-03 45902.5130 108.9265Gamma469 5.5808E-01 1.4357E-03 4.7133E-01 6.2205E-01 28278.1542 176.8149Gamma470 1.6805E-01 8.0602E-04 1.2388E-01 2.3427E-01 35056.1824 142.6282Gamma471 4.1599E-03 2.0401E-05 1.7421E-06 1.2528E-02 17364.7550 287.9396Gamma472 7.6984E-03 5.7707E-05 1.7294E-66 2.1739E-02 33902.9657 147.4797Gamma473 5.9583E-02 5.5918E-04 1.4012E-02 9.9320E-02 102335.1947 48.8590Gamma474 5.1308E-03 3.7137E-05 2.9308E-05 1.9383E-02 18410.6335 271.5822Gamma475 2.0768E-02 6.8060E-05 6.6840E-03 3.7132E-02 18835.5876 265.4550Gamma476 4.5246E-03 2.9527E-05 1.2246E-05 1.5367E-02 28418.4006 175.9423Gamma477 7.9723E-03 3.4245E-05 3.6387E-04 1.6831E-02 28131.9693 177.7337Gamma478 1.8001E-03 3.8621E-06 3.6605E-06 5.4703E-03 34500.3679 144.9260Gamma479 2.1294E-03 2.6664E-06 2.6298E-06 5.2907E-03 10274.7777 486.6285Gamma480 1.8446E-03 3.9387E-06 2.2398E-05 5.2873E-03 45227.5387 110.5521
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Gamma481 1.7509E-03 3.8855E-06 3.6611E-97 4.4719E-03 21426.9780 233.3507Gamma482 2.7513E-03 1.2285E-05 1.4434E-05 6.9678E-03 25084.5453 199.3259Gamma483 3.2090E-03 9.4208E-06 6.0894E-05 8.6159E-03 35241.6479 141.8776Gamma484 1.2637E-03 1.5646E-06 0.0000E+00 3.2678E-03 26065.9621 191.8210Gamma485 6.6660E-03 1.2467E-05 1.1263E-03 1.3715E-02 21821.2805 229.1341Gamma486 9.9720E-04 1.2262E-06 0.0000E+00 3.8547E-03 40447.7451 123.6163Gamma487 1.6581E-03 5.8962E-06 8.4528E-06 5.3982E-03 11862.0810 421.5112Gamma488 3.1126E-03 6.7946E-06 6.7868E-05 7.3754E-03 23350.4316 214.1288Gamma489 1.2443E-03 2.4282E-06 6.0437E-06 3.9047E-03 26562.3243 188.2365Gamma490 1.1049E-02 2.9569E-05 8.7339E-04 1.9780E-02 23895.0789 209.2481Gamma491 4.8344E-02 1.0015E-04 2.9564E-02 6.9302E-02 25991.7975 192.3684Gamma492 2.3050E-03 3.3382E-06 9.9957E-05 5.4752E-03 17442.8134 286.6510Gamma493 1.8940E-03 1.0811E-05 0.0000E+00 4.7140E-03 30163.3613 165.7640Gamma494 3.2402E-02 5.7514E-05 2.1006E-02 4.7081E-02 24356.8705 205.2809Gamma495 8.2957E-01 3.3422E-04 7.9682E-01 8.6667E-01 20813.6358 240.2271Gamma496 1.7734E-03 2.7448E-06 1.5778E-06 5.3464E-03 27772.7873 180.0323Gamma497 2.8291E-03 7.4174E-06 2.0672E-238 7.7762E-03 66433.4908 75.2632Gamma498 1.9807E-02 1.1193E-04 4.7007E-03 3.9870E-02 55844.1523 89.5349Gamma499 3.7384E-03 1.0750E-05 6.1443E-06 9.4147E-03 27539.7138 181.5560Gamma500 5.3652E-03 9.2246E-06 8.6062E-04 1.1890E-02 72948.9489 68.5411Gamma501 1.3157E-01 2.7214E-04 1.0350E-01 1.6442E-01 16829.9330 297.0897Gamma502 3.6686E-03 1.1225E-05 1.7460E-06 1.0535E-02 37864.7786 132.0488Gamma503 8.1465E-03 1.5319E-05 2.2713E-03 1.5033E-02 16359.8070 305.6271Gamma504 3.0005E-03 7.1040E-06 2.8331E-07 8.7553E-03 22353.0670 223.6830Gamma505 2.3504E-03 4.2734E-06 6.3767E-06 6.3886E-03 19613.4301 254.9274Gamma506 3.4265E-03 6.4921E-06 1.4338E-04 7.8648E-03 28198.0034 177.3175Gamma507 2.2086E-03 4.2489E-06 6.6654E-06 6.9498E-03 28960.2604 172.6504
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Gamma508 1.8329E-03 3.4288E-06 2.5296E-05 4.4587E-03 20578.9871 242.9663Gamma509 1.7202E-03 3.1004E-06 0.0000E+00 5.2366E-03 22627.6876 220.9682Gamma510 2.4846E-02 5.0564E-05 8.7965E-03 3.6573E-02 19652.0538 254.4263Gamma511 3.0427E-03 7.0590E-06 4.7212E-07 7.9829E-03 24954.0345 200.3684Gamma512 1.6581E-03 2.4683E-06 5.2152E-07 4.7452E-03 42106.3515 118.7469Gamma513 2.7028E-03 7.0896E-06 3.5590E-205 8.0023E-03 33245.8452 150.3947Gamma514 2.5833E-03 8.3656E-06 1.1496E-06 6.5102E-03 21024.7301 237.8152Gamma515 1.4949E-02 2.1112E-05 7.6734E-03 2.3874E-02 14787.2077 338.1301Gamma516 4.5785E-03 9.8908E-06 1.4013E-04 9.7391E-03 28731.1410 174.0272Gamma517 2.1947E-02 1.2392E-04 7.0573E-03 4.2178E-02 11922.9571 419.3591Gamma518 2.0214E-03 3.1687E-06 1.8265E-05 5.6039E-03 16504.4170 302.9492Gamma519 1.9063E-03 1.5384E-05 0.0000E+00 5.5721E-03 17525.8421 285.2930Gamma520 2.5680E-03 1.0041E-05 1.2352E-253 7.7990E-03 17917.6273 279.0548Gamma521 7.4956E-01 6.0872E-04 7.0241E-01 7.8861E-01 30806.1306 162.3054Gamma522 2.2303E-03 4.3630E-06 1.5289E-05 5.6639E-03 9786.4206 510.9120Gamma523 3.3383E-03 2.8680E-05 1.7586E-06 1.4263E-02 31699.7803 157.7298Gamma524 1.2529E-03 1.4225E-06 0.0000E+00 3.6943E-03 12450.4991 401.5903Gamma525 2.8892E-03 3.2576E-05 2.7673E-06 1.0769E-02 24567.9091 203.5175Gamma526 1.0670E-03 1.3093E-06 3.7588E-305 3.7336E-03 25525.8323 195.8800Gamma527 6.8261E-03 2.3397E-05 2.8033E-04 1.6208E-02 51743.5942 96.6303Gamma528 3.3637E-02 2.6144E-04 2.8814E-03 5.1314E-02 56874.1537 87.9134Gamma529 1.2611E-02 3.3020E-05 1.6657E-03 2.2728E-02 169947.5985 29.4208Gamma530 1.6999E-03 5.2823E-06 1.3537E-05 4.3540E-03 25726.4129 194.3528Gamma531 3.5967E-03 3.5060E-06 8.3529E-06 7.0724E-03 17345.1166 288.2656Gamma532 3.1536E-03 5.6114E-06 7.2577E-113 7.7095E-03 33188.7328 150.6535Gamma533 8.3641E-03 1.9661E-05 1.6485E-03 1.7416E-02 26295.3614 190.1476Gamma534 8.4514E-03 2.7209E-05 2.8089E-04 1.7232E-02 124216.1730 40.2524
Continued on next page able 1 – Continued from previous page hmmer mean variance HPD HPD ACT ESS
Gamma535 2.6716E-03 1.3608E-05 4.0078E-06 7.4991E-03 81553.5622 61.3094Gamma536 9.3193E-04 2.9252E-06 7.9932E-06 3.8403E-03 18179.8773 275.0294Gamma537 1.1114E-03 1.3498E-06 6.6574E-06 3.2932E-03 19534.9622 255.9514Gamma538 1.5258E-03 3.8594E-06 2.1416E-06 4.9796E-03 15821.6917 316.0218Gamma539 1.3697E-03 6.3098E-06 2.7123E-06 5.3163E-03 18226.7989 274.3213Gamma540 1.8537E-03 8.1875E-06 9.3136E-07 8.5293E-03 103611.6168 48.2571Gamma541 1.5786E-03 8.1487E-06 8.1707E-06 4.0892E-03 21485.0467 232.7200Gamma542 1.4865E-03 6.0516E-06 0.0000E+00 5.9249E-03 27535.5807 181.5832Gamma543 1.1454E-03 2.7441E-06 9.3162E-06 4.0491E-03 28161.6175 177.5466Gamma544 1.0501E-03 3.8784E-06 9.7212E-238 4.1070E-03 17075.4013 292.8189Gamma545 1.1498E-03 1.1439E-06 2.2421E-06 3.1272E-03 12510.7885 399.6551Gamma546 8.7337E-04 2.8368E-06 1.0350E-05 2.3897E-03 12978.9781 385.2383Gamma547 8.8294E-01 2.7952E-04 8.5074E-01 9.1435E-01 18172.1093 275.1469Gamma548 5.6532E-03 2.3565E-05 6.5690E-05 1.6203E-02 123254.6503 40.5664Gamma549 1.4508E-03 1.4327E-05 6.4857E-07 4.0106E-03 10878.6212 459.6171Gamma550 1.3803E-02 1.8331E-04 2.2917E-03 4.4794E-02 34666.3023 144.2323Gamma551 6.7310E-03 2.7680E-05 1.1266E-04 1.7192E-02 35142.0623 142.2796Gamma552 2.4209E-01 8.7090E-03 3.8008E-02 3.7133E-01 162869.1094 30.6995Gamma553 3.1470E-03 6.9356E-06 2.8290E-05 8.0054E-03 33272.2618 150.2753Gamma554 3.9453E-03 1.3509E-05 1.0103E-04 1.2127E-02 24520.4763 203.9112Gamma555 3.6845E-03 9.3521E-06 5.2495E-05 9.5950E-03 24818.6934 201.4610Gamma556 7.3746E-03 2.0730E-05 1.2310E-03 1.6435E-02 29287.3525 170.7222Gamma557 4.5495E-03 1.0316E-05 3.0097E-04 1.0594E-02 21781.4116 229.5535Gamma558 9.9648E-03 5.5931E-05 9.4161E-04 2.7924E-02 32907.5859 151.9407Gamma559 1.9224E-03 3.7264E-06 1.4318E-05 5.3916E-03 25555.6939 195.6511Gamma560 8.1419E-03 2.9276E-05 1.1023E-03 1.9852E-02 81626.1404 61.2549Gamma561 1.9963E-03 7.0339E-06 1.4485E-286 5.6362E-03 39974.1572 125.0808
Continued on next page able 1 – Continued from previous page hmmer mean variance HPD HPD ACT ESS
Gamma562 1.4446E-03 2.2048E-06 1.4879E-05 4.5418E-03 44515.1380 112.3213Gamma563 6.0201E-03 5.3759E-05 9.1406E-05 1.8311E-02 43368.0244 115.2923Gamma564 2.6932E-03 6.5481E-06 8.6165E-05 7.5424E-03 19725.0931 253.4842Gamma565 4.9005E-03 8.1615E-06 3.5200E-04 1.0600E-02 45810.4813 109.1453Gamma566 6.7075E-03 6.6712E-05 3.4673E-06 1.4944E-02 50579.6758 98.8539Gamma567 3.6168E-03 1.1999E-05 1.0541E-04 1.0273E-02 22432.4382 222.8915Gamma568 5.4354E-03 2.0577E-05 4.0865E-07 1.4374E-02 34782.8385 143.7491Gamma569 1.3744E-02 4.3454E-05 4.8660E-03 2.7866E-02 89800.7279 55.6788Gamma570 2.0294E-02 2.9998E-04 2.1426E-03 6.0205E-02 108491.3389 46.0866Gamma571 1.2219E-03 2.3025E-06 0.0000E+00 3.5279E-03 26854.9602 186.1853Gamma572 1.0003E-02 3.9214E-05 6.9248E-04 2.2608E-02 70626.9782 70.7945Gamma573 6.1290E-01 1.9880E-02 3.9848E-01 9.0596E-01 63459.6414 78.7902Gamma574 7.6587E-03 2.6901E-05 1.7922E-04 1.6135E-02 37523.9088 133.2484Gamma575 9.8089E-03 4.2591E-05 1.0069E-03 2.3786E-02 63298.2454 78.9911Gamma576 8.3441E-03 5.9303E-05 1.0641E-04 2.4359E-02 48248.9802 103.6291Gamma577 1.1359E-01 5.5179E-04 7.9416E-02 1.6391E-01 29470.7144 169.6600Gamma578 2.0572E-03 4.9978E-06 1.9914E-06 5.1430E-03 19695.0448 253.8710Gamma579 5.0992E-03 1.8647E-05 1.0823E-05 1.2779E-02 45835.5124 109.0857Gamma580 3.0145E-03 1.6992E-05 9.0696E-06 9.2287E-03 18390.8363 271.8745Gamma581 6.3175E-03 2.1863E-05 2.0929E-04 1.5309E-02 37372.7549 133.7873Gamma582 5.5664E-03 1.5330E-05 2.5135E-04 1.2761E-02 27636.1311 180.9226Gamma583 7.1495E-03 2.5749E-05 2.6355E-05 1.7411E-02 16700.0796 299.3998Gamma584 2.3959E-03 9.8418E-06 0.0000E+00 8.6192E-03 31609.9241 158.1782Gamma585 1.3901E-02 5.7898E-05 1.1593E-04 2.6953E-02 28774.4422 173.7653Gamma586 4.5053E-03 1.5922E-05 1.3999E-05 1.1896E-02 24670.6474 202.6700Gamma587 2.3749E-03 4.3713E-06 4.6294E-06 6.3873E-03 18980.6039 263.4268Gamma588 6.2443E-03 1.9280E-05 6.4128E-04 1.6022E-02 19087.7909 261.9475
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Gamma589 2.6017E-03 7.3585E-06 0.0000E+00 7.6996E-03 29942.2713 166.9880Gamma590 3.9186E-03 3.8209E-05 8.5562E-07 8.2811E-03 38640.8552 129.3967Gamma591 3.3120E-02 1.3032E-04 1.4226E-02 5.1841E-02 14839.2761 336.9437Gamma592 1.1356E-02 6.4249E-05 3.9847E-04 2.5152E-02 36637.9856 136.4704Gamma593 2.5612E-03 7.2270E-06 1.8899E-05 8.2262E-03 43793.8830 114.1712Gamma594 4.0829E-03 9.9005E-06 1.9282E-139 9.1253E-03 26159.3926 191.1359Gamma595 1.6455E-02 1.4091E-04 9.8861E-04 4.0410E-02 25487.0538 196.1780Gamma596 4.6105E-03 7.1124E-05 1.6447E-05 2.3031E-02 12820.6463 389.9959Gamma597 1.2425E-02 1.0413E-04 2.9849E-04 3.5192E-02 29425.0675 169.9231Gamma598 5.9868E-03 2.9668E-05 9.7568E-307 1.4641E-02 19891.5709 251.3628Gamma599 7.1850E-01 1.4458E-03 6.4775E-01 7.9540E-01 43147.8720 115.8806Gamma600 3.8137E-03 1.5407E-05 3.7176E-107 1.2743E-02 36807.9025 135.8404Gamma601 4.5700E-03 2.5936E-05 1.2255E-05 1.4629E-02 61878.8181 80.8031Gamma602 5.9703E-02 5.4771E-04 8.3209E-03 9.8580E-02 97691.4403 51.1816Gamma603 3.7547E-03 1.2219E-05 1.3979E-06 1.0969E-02 18740.0983 266.8076Gamma604 3.3626E-03 3.0958E-05 7.2764E-06 9.5617E-03 23786.6937 210.2016Gamma605 2.8119E-03 1.2861E-05 1.2029E-05 1.0376E-02 39130.1276 127.7788Gamma606 8.8095E-03 3.7352E-05 7.7500E-04 2.0562E-02 16802.9664 297.5665Gamma607 5.9677E-03 2.1292E-05 1.5958E-05 1.4337E-02 26793.4490 186.6128Gamma608 6.4906E-03 3.8496E-05 8.2154E-05 1.8456E-02 25738.6885 194.2601Gamma609 3.4075E-03 1.1365E-05 1.9948E-06 9.8028E-03 19701.1370 253.7925Gamma610 3.7020E-02 1.5706E-04 1.8155E-02 6.0903E-02 30342.1325 164.7874Gamma611 2.7671E-03 7.2091E-06 1.7110E-06 8.7172E-03 13700.4153 364.9524Gamma612 2.5592E-03 7.2477E-06 0.0000E+00 7.1332E-03 42692.5417 117.1165Gamma613 5.1943E-03 1.5530E-05 1.3503E-06 1.2906E-02 51838.7161 96.4530Gamma614 3.7065E-03 1.0699E-05 2.1408E-06 1.0606E-02 24862.7780 201.1038Gamma615 4.0503E-03 9.8144E-06 4.5949E-05 1.0229E-02 42991.9561 116.3008
Continued on next page able 1 – Continued from previous page hmmer mean variance HPD HPD ACT ESS
Gamma616 1.5509E-02 6.6455E-05 5.7150E-03 3.5507E-02 34656.8095 144.2718Gamma617 5.9456E-03 2.8665E-05 1.7264E-04 1.7430E-02 31807.6331 157.1950Gamma618 1.0786E-02 5.9151E-05 5.5395E-05 2.5488E-02 16244.7560 307.7916Gamma619 8.3767E-03 2.0980E-05 3.4127E-04 1.7033E-02 16412.7446 304.6413Gamma620 1.8622E-02 2.2345E-04 2.2046E-04 5.1229E-02 134100.5341 37.2855Gamma621 3.7281E-03 1.7661E-05 0.0000E+00 1.0159E-02 30196.9492 165.5796Gamma622 9.0645E-02 2.0393E-03 2.7301E-02 1.7825E-01 13895.2991 359.8339Gamma623 1.4109E-02 1.2263E-04 8.9471E-05 3.6890E-02 39533.6827 126.4744Gamma624 5.2883E-03 2.2810E-05 0.0000E+00 1.3935E-02 33696.7899 148.3821Gamma625 6.7281E-01 1.8216E-03 5.8844E-01 7.4477E-01 102972.9902 48.5564mean00 3.3153E+01 6.2187E-06 3.3148E+01 3.3157E+01 92575.8051 54.0098mean01 1.3207E+02 2.1123E-05 1.3206E+02 1.3207E+02 40296.2464 124.0810mean02 3.3530E+01 1.1900E-05 3.3524E+01 3.3535E+01 23306.5483 214.5320mean03 1.3223E+02 1.5145E-05 1.3223E+02 1.3224E+02 18904.7864 264.4833mean04 3.3143E+01 3.1642E-05 3.3134E+01 3.3154E+01 312025.9022 16.0243mean05 1.3222E+02 9.8978E-05 1.3221E+02 1.3224E+02 185982.0670 26.8843mean06 3.3227E+01 4.6647E-05 3.3215E+01 3.3240E+01 142592.6571 35.0649mean07 1.3218E+02 3.5168E-05 1.3217E+02 1.3219E+02 45558.0184 109.7502mean08 3.3646E+01 4.3518E-05 3.3640E+01 3.3660E+01 36341.5325 137.5836mean09 1.3244E+02 1.0831E-05 1.3244E+02 1.3245E+02 14098.1236 354.6571mean10 3.3349E+01 2.8868E-05 3.3337E+01 3.3358E+01 42864.7199 116.6460mean11 1.3212E+02 3.0243E-05 1.3211E+02 1.3213E+02 19599.8797 255.1036mean12 3.3524E+01 5.5641E-05 3.3512E+01 3.3540E+01 55988.4161 89.3042mean13 1.3238E+02 4.4698E-05 1.3237E+02 1.3239E+02 40444.0229 123.6277mean14 3.3468E+01 4.4562E-05 3.3455E+01 3.3476E+01 136234.5080 36.7014mean15 1.3274E+02 4.3066E-05 1.3274E+02 1.3276E+02 142630.1781 35.0557mean16 3.3375E+01 9.4142E-05 3.3356E+01 3.3389E+01 113550.4454 44.0333
Continued on next page able 1 – Continued from previous page hmmer mean variance HPD HPD ACT ESS mean17 1.3251E+02 7.9729E-05 1.3249E+02 1.3252E+02 42178.8880 118.5427mean18 3.3736E+01 6.2646E-04 3.3699E+01 3.3785E+01 214245.2839 23.3377mean19 1.3315E+02 1.3344E-03 1.3309E+02 1.3322E+02 104416.6575 47.8851mean20 3.3720E+01 7.8763E-05 3.3704E+01 3.3737E+01 69508.4940 71.9337mean21 1.3294E+02 9.5506E-05 1.3292E+02 1.3296E+02 108031.1650 46.2829mean22 3.3536E+01 5.8907E-06 3.3531E+01 3.3541E+01 18076.7866 276.5978mean23 1.3269E+02 4.6310E-05 1.3268E+02 1.3271E+02 66099.5260 75.6435mean24 3.3957E+01 2.6005E-05 3.3950E+01 3.3965E+01 4633.3471 1079.1335mean25 1.3324E+02 1.9592E-05 1.3323E+02 1.3324E+02 13775.2710 362.9693mean26 3.3621E+01 1.9563E-05 3.3615E+01 3.3627E+01 75168.1397 66.5175mean27 1.3286E+02 2.7768E-05 1.3285E+02 1.3287E+02 72290.7471 69.1651mean28 3.3967E+01 1.9263E-06 3.3964E+01 3.3969E+01 7635.2819 654.8547mean29 1.3344E+02 9.1469E-06 1.3344E+02 1.3345E+02 21692.2676 230.4969mean30 3.3965E+01 1.7468E-06 3.3962E+01 3.3968E+01 30107.9168 166.0693mean31 1.3372E+02 2.5383E-05 1.3371E+02 1.3373E+02 29180.7359 171.3459mean32 3.3807E+01 9.2728E-06 3.3800E+01 3.3811E+01 51407.7307 97.2616mean33 1.3317E+02 5.2719E-05 1.3316E+02 1.3318E+02 64555.7808 77.4524mean34 3.3589E+01 1.6618E-05 3.3583E+01 3.3596E+01 24340.1354 205.4220mean35 1.3289E+02 1.0972E-05 1.3288E+02 1.3289E+02 25239.1536 198.1049mean36 3.3957E+01 5.4964E-06 3.3953E+01 3.3961E+01 33494.4226 149.2786mean37 1.3388E+02 1.4084E-05 1.3387E+02 1.3389E+02 19086.3787 261.9669mean38 3.3869E+01 1.1937E-04 3.3852E+01 3.3888E+01 146107.2442 34.2214mean39 1.3381E+02 2.1818E-04 1.3379E+02 1.3383E+02 126098.6469 39.6515mean40 3.3899E+01 6.3637E-06 3.3896E+01 3.3903E+01 29684.1219 168.4402mean41 1.3334E+02 1.2572E-05 1.3334E+02 1.3335E+02 28284.2642 176.7767mean42 3.4005E+01 8.7598E-05 3.3990E+01 3.4022E+01 34455.4313 145.1150mean43 1.3439E+02 7.7585E-05 1.3437E+02 1.3441E+02 44015.9496 113.5952
Continued on next page able 1 – Continued from previous page hmmer mean variance HPD HPD ACT ESS mean44 3.4089E+01 1.0985E-05 3.4087E+01 3.4092E+01 10783.1209 463.6876mean45 1.3389E+02 2.1354E-06 1.3389E+02 1.3390E+02 16814.1550 297.3685mean46 3.4030E+01 1.4371E-05 3.4023E+01 3.4037E+01 24344.4476 205.3856mean47 1.3368E+02 6.3650E-06 1.3368E+02 1.3369E+02 26869.3262 186.0858mean48 3.3974E+01 1.8305E-05 3.3969E+01 3.3982E+01 16220.0577 308.2603mean49 1.3418E+02 4.3357E-05 1.3417E+02 1.3419E+02 33984.2140 147.1271sig0 1.0397E-02 5.1172E-06 7.3910E-03 1.4208E-02 101753.1033 49.1386sig1 1.1494E-02 2.2762E-05 6.9227E-03 1.6940E-02 89742.0891 55.7152sig2 2.2147E-02 7.5291E-06 1.7002E-02 2.6493E-02 18702.3423 267.3462sig3 2.5312E-02 1.3278E-05 2.0509E-02 3.3648E-02 16758.0436 298.3642sig4 6.7377E-02 3.4771E-05 5.8035E-02 7.7321E-02 90886.8280 55.0135sig5 1.2037E-01 8.2671E-05 1.0577E-01 1.3751E-01 79241.5240 63.0982sig6 7.6083E-02 1.2216E-05 6.9972E-02 8.3122E-02 55230.0747 90.5304sig7 8.9054E-02 1.8748E-05 8.0247E-02 9.5237E-02 33024.4230 151.4031sig8 2.3056E-02 3.7189E-06 1.8870E-02 2.6342E-02 23756.2145 210.4712sig9 2.7127E-02 3.8963E-06 2.4081E-02 3.1347E-02 28984.7066 172.5048sig10 4.4864E-02 1.5913E-05 3.8071E-02 5.1483E-02 21330.6113 234.4049sig11 2.8569E-02 1.6763E-05 2.2633E-02 3.5289E-02 79364.6376 63.0004sig12 7.3945E-02 1.4626E-05 6.6090E-02 8.0964E-02 16359.3461 305.6357sig13 6.0247E-02 4.9425E-05 5.0572E-02 7.5667E-02 45307.7279 110.3564sig14 4.7560E-02 6.7658E-05 3.7400E-02 5.9961E-02 71546.1485 69.8850sig15 4.5253E-02 5.1485E-05 3.2712E-02 5.8367E-02 122438.7684 40.8367sig16 8.1149E-02 6.4461E-05 7.3386E-02 9.7219E-02 35379.4699 141.3249sig17 9.8157E-02 1.0560E-04 8.1357E-02 1.1856E-01 65447.2037 76.3975sig18 1.7481E-01 4.9086E-04 1.4254E-01 2.1546E-01 118957.1502 42.0319sig19 3.7826E-01 2.1703E-03 2.9221E-01 4.5453E-01 98079.9965 50.9788sig20 6.3216E-02 3.0365E-05 5.2831E-02 7.1833E-02 63138.9261 79.1905
Continued on next page able 1 – Continued from previous page hmmer mean variance HPD HPD ACT ESS sig21 8.3011E-02 3.0218E-05 7.2707E-02 9.3286E-02 67121.1605 74.4922sig22 4.2591E-02 5.3225E-06 3.8782E-02 4.7331E-02 11863.5828 421.4578sig23 7.9679E-02 1.6019E-05 7.4067E-02 8.7572E-02 30533.1187 163.7566sig24 4.0758E-02 1.3113E-05 3.5724E-02 4.5320E-02 18413.7036 271.5369sig25 3.6311E-02 5.4108E-05 2.5687E-02 4.5761E-02 319437.7767 15.6525sig26 3.3717E-02 1.8502E-05 2.7022E-02 4.1190E-02 38797.8225 128.8732sig27 3.2957E-02 1.9160E-05 2.7969E-02 4.3278E-02 85318.1770 58.6042sig28 1.3705E-02 1.3658E-06 1.1576E-02 1.5649E-02 11658.0919 428.8867sig29 1.7861E-02 5.2670E-05 1.3820E-02 2.7240E-02 8839.8629 565.6196sig30 2.3851E-02 4.9658E-06 2.1458E-02 2.6093E-02 20196.0798 247.5728sig31 6.3047E-02 1.3221E-05 5.5082E-02 6.8559E-02 20046.4462 249.4208sig32 3.3400E-02 3.7970E-06 2.9305E-02 3.6581E-02 50200.1253 99.6013sig33 8.9384E-02 1.3365E-05 8.3359E-02 9.6302E-02 40222.3843 124.3089sig34 1.6552E-02 7.3247E-05 1.2323E-02 2.3667E-02 20320.9017 246.0521sig35 1.9078E-02 9.0345E-06 1.5246E-02 2.6690E-02 18222.0431 274.3929sig36 2.9753E-02 3.2640E-06 2.6535E-02 3.3308E-02 12711.3278 393.3499sig37 3.9156E-02 9.5006E-06 3.3603E-02 4.3555E-02 15530.8432 321.9400sig38 4.3736E-02 8.1981E-05 3.3489E-02 5.9352E-02 87473.4563 57.1602sig39 5.6483E-02 7.0326E-05 4.4777E-02 7.5767E-02 44498.5518 112.3632sig40 3.2181E-02 1.0031E-05 2.9040E-02 3.4087E-02 18767.5229 266.4177sig41 5.8665E-02 7.4578E-06 5.3512E-02 6.2982E-02 8008.1789 624.3617sig42 4.3597E-02 2.8268E-05 3.5905E-02 5.3344E-02 35259.9516 141.8039sig43 4.2660E-02 1.8198E-05 3.4373E-02 5.0306E-02 31057.7121 160.9906sig44 2.0933E-02 2.7451E-05 1.7862E-02 2.2511E-02 15465.7156 323.2957sig45 2.1647E-02 1.2810E-06 1.9749E-02 2.4108E-02 18882.7570 264.7918sig46 3.4843E-02 1.1288E-05 3.0400E-02 4.1280E-02 12880.6637 388.1788sig47 2.9820E-02 4.6206E-06 2.5811E-02 3.3832E-02 14872.4660 336.1917
Continued on next page able 1 – Continued from previous page hmmer mean variance HPD HPD ACT ESS sig48 3.8268E-02 1.7943E-05 3.2641E-02 4.4989E-02 37424.5456 133.6022sig49 7.3317E-02 4.4131E-05 6.2792E-02 8.3872E-02 37615.4550 132.9241rho0 -1.6297E-02 5.2185E-02 -4.6878E-01 3.7495E-01 26512.5997 188.5896rho1 -6.2773E-01 9.5917E-03 -7.8494E-01 -4.5777E-01 26590.6405 188.0361rho2 9.3617E-01 1.7745E-04 9.1451E-01 9.5750E-01 230515.6332 21.6905rho3 3.8187E-01 2.3841E-03 2.6518E-01 4.5914E-01 44177.0986 113.1808rho4 -4.7966E-01 4.1922E-03 -5.9941E-01 -3.5422E-01 19050.5638 262.4594rho5 1.1060E-01 1.5303E-02 -1.2180E-01 2.9967E-01 57679.1470 86.6864rho6 -4.9259E-01 2.0951E-02 -6.5592E-01 -8.0627E-02 116877.5009 42.7798rho7 -9.3090E-01 3.7978E-04 -9.5990E-01 -8.9145E-01 105535.7505 47.3773rho8 7.6369E-01 8.3119E-04 6.9430E-01 8.1311E-01 46400.7472 107.7569rho9 7.9118E-01 1.3539E-02 5.9939E-01 9.1923E-01 145895.9604 34.2710rho10 2.3060E-02 3.1655E-02 -2.6114E-01 3.6095E-01 144155.6079 34.6847rho11 -6.2912E-02 7.3775E-03 -1.9036E-01 1.2205E-01 27496.0159 181.8445rho12 -2.5315E-01 7.2828E-03 -3.9030E-01 -6.6908E-02 38868.7962 128.6379rho13 5.4412E-01 5.7701E-03 4.2760E-01 7.1766E-01 86363.9160 57.8945rho14 3.1846E-02 6.8279E-03 -1.2925E-01 1.6057E-01 39234.2156 127.4398rho15 -4.9963E-03 3.9516E-03 -1.1434E-01 1.0178E-01 42726.6201 117.0231rho16 3.6540E-01 3.1031E-03 2.8682E-01 4.8095E-01 126902.3632 39.4004rho17 -7.3498E-01 5.5361E-03 -8.5863E-01 -6.2345E-01 23100.7809 216.4429rho18 -5.7640E-01 3.0451E-03 -6.7629E-01 -4.8114E-01 29505.4889 169.4600rho19 -9.6126E-01 1.9381E-04 -9.8534E-01 -9.3612E-01 42478.2570 117.7073rho20 -4.5866E-01 1.6254E-03 -5.2164E-01 -3.5626E-01 36729.7248 136.1295rho21 6.6679E-01 6.4360E-03 5.3659E-01 8.0395E-01 25260.9133 197.9343rho22 -5.5560E-01 1.3427E-03 -6.1193E-01 -4.7605E-01 25955.2914 192.6389rho23 2.9981E-01 4.8525E-03 1.7641E-01 4.3718E-01 14442.0845 346.2104rho24 -8.1558E-01 1.4636E-03 -8.8326E-01 -7.4729E-01 51720.3490 96.6737
Continued on next page able 1 – Continued from previous page hmmer mean variance HPD HPD ACT ESS p0 9.4841E-03 8.8157E-06 3.7773E-03 1.4609E-02 19695.7896 253.8614p1 1.3091E-03 5.0283E-07 6.7313E-04 1.9354E-03 19060.7841 262.3187p2 5.2091E-01 3.1162E-02 2.0918E-01 7.0672E-01 39399.0310 126.9067p3 6.8907E-01 1.1123E-03 6.3295E-01 7.5842E-01 122348.5804 40.8668p4 4.8204E-01 1.1005E-03 4.0973E-01 5.4387E-01 25151.2564 198.7972p5 6.1286E-01 3.2653E-03 5.2855E-01 7.4532E-01 45865.3068 109.0149p6 4.5864E-01 1.9018E-03 3.7606E-01 5.4930E-01 33871.6865 147.6159p7 6.4258E-01 3.2882E-02 3.4405E-01 1.0000E+00 257471.7527 19.4196p8 4.9533E-01 2.1998E-03 4.2800E-01 5.9699E-01 82995.0090 60.2446p9 9.6980E-01 1.4932E-03 8.9655E-01 9.9985E-01 38433.8119 130.0938p10 7.1425E-01 3.0174E-03 6.2227E-01 7.9271E-01 15718.6406 318.0937p11 7.7223E-01 9.7882E-04 7.0868E-01 8.3627E-01 45482.2677 109.9330p12 4.1091E-01 2.1401E-03 3.2501E-01 4.9506E-01 29664.4736 168.5518p13 7.0933E-01 8.8617E-04 6.5631E-01 7.6445E-01 47446.1868 105.3825p14 5.4156E-01 5.2855E-03 4.2643E-01 6.7479E-01 24435.7993 204.6178p15 8.4811E-01 6.0109E-04 8.0251E-01 8.9474E-01 20822.5178 240.1247p16 6.0290E-01 8.1748E-04 5.4996E-01 6.6087E-01 22349.5548 223.7181p17 5.6851E-02 7.7910E-05 3.9254E-02 7.0971E-02 14496.7123 344.9058p18 8.3788E-01 2.4751E-03 7.5064E-01 9.5049E-01 31895.1454 156.7637p19 3.6076E-02 7.1633E-05 1.8826E-02 5.1437E-02 48798.1506 102.4629p20 7.9248E-01 1.0195E-03 7.4217E-01 8.4501E-01 19238.1132 259.9007p21 2.4458E-02 3.2593E-04 1.0902E-02 6.8324E-02 37652.1742 132.7945p22 2.1440E-01 7.4085E-03 7.4024E-02 3.8601E-01 108925.6785 45.9029p23 4.4622E-01 2.4041E-03 3.5150E-01 5.2919E-01 20916.1565 239.0497p24 4.5593E-01 1.6771E-03 3.7982E-01 5.3879E-01 129941.7537 38.4788p0 9.4841E-03 8.8157E-06 3.7773E-03 1.4609E-02 19695.7896 253.8614p1 1.3091E-03 5.0283E-07 6.7313E-04 1.9354E-03 19060.7841 262.3187p2 5.2091E-01 3.1162E-02 2.0918E-01 7.0672E-01 39399.0310 126.9067p3 6.8907E-01 1.1123E-03 6.3295E-01 7.5842E-01 122348.5804 40.8668p4 4.8204E-01 1.1005E-03 4.0973E-01 5.4387E-01 25151.2564 198.7972p5 6.1286E-01 3.2653E-03 5.2855E-01 7.4532E-01 45865.3068 109.0149p6 4.5864E-01 1.9018E-03 3.7606E-01 5.4930E-01 33871.6865 147.6159p7 6.4258E-01 3.2882E-02 3.4405E-01 1.0000E+00 257471.7527 19.4196p8 4.9533E-01 2.1998E-03 4.2800E-01 5.9699E-01 82995.0090 60.2446p9 9.6980E-01 1.4932E-03 8.9655E-01 9.9985E-01 38433.8119 130.0938p10 7.1425E-01 3.0174E-03 6.2227E-01 7.9271E-01 15718.6406 318.0937p11 7.7223E-01 9.7882E-04 7.0868E-01 8.3627E-01 45482.2677 109.9330p12 4.1091E-01 2.1401E-03 3.2501E-01 4.9506E-01 29664.4736 168.5518p13 7.0933E-01 8.8617E-04 6.5631E-01 7.6445E-01 47446.1868 105.3825p14 5.4156E-01 5.2855E-03 4.2643E-01 6.7479E-01 24435.7993 204.6178p15 8.4811E-01 6.0109E-04 8.0251E-01 8.9474E-01 20822.5178 240.1247p16 6.0290E-01 8.1748E-04 5.4996E-01 6.6087E-01 22349.5548 223.7181p17 5.6851E-02 7.7910E-05 3.9254E-02 7.0971E-02 14496.7123 344.9058p18 8.3788E-01 2.4751E-03 7.5064E-01 9.5049E-01 31895.1454 156.7637p19 3.6076E-02 7.1633E-05 1.8826E-02 5.1437E-02 48798.1506 102.4629p20 7.9248E-01 1.0195E-03 7.4217E-01 8.4501E-01 19238.1132 259.9007p21 2.4458E-02 3.2593E-04 1.0902E-02 6.8324E-02 37652.1742 132.7945p22 2.1440E-01 7.4085E-03 7.4024E-02 3.8601E-01 108925.6785 45.9029p23 4.4622E-01 2.4041E-03 3.5150E-01 5.2919E-01 20916.1565 239.0497p24 4.5593E-01 1.6771E-03 3.7982E-01 5.3879E-01 129941.7537 38.4788