Martin Sköld

A general framework for the parametrization of hierarchical models

In this paper, we describe centering and noncentering methodology as complementary techniques for use in parametrization of broad classes of hierarchical models, with a view to the construction of effective MCMC algorithms for exploring posterior distributions from these models. We give a clear qualitative understanding as to when centering and noncentering work well, and introduce theory concerning the convergence time complexity of Gibbs samplers using centered and noncentered parametrizations. We give general recipes for the construction of noncentered parametrizations, including an auxiliary variable technique called the state-space expansion technique. We also describe partially noncentered methods, and demonstrate their use in constructing robust Gibbs sampler algorithms whose convergence properties are not overly sensitive to the data.

Robust Markov chain Monte Carlo Methods for Spatial Generalized Linear Mixed Models

Using Markov chain Monte Carlo methods for statistical inference is often trouble-some in practice, because performance of the algorithm may hugely depend on the observed data, and what works well for one dataset may fail miserably for another. In this article, for spatial generalized linear mixed models (GLMMs), we discuss problems with algorithms previously used, and we construct an algorithm with robust mixing and convergence characteristics, independent of the data. The strategy we have used for this construction is not model specific and could be applied in a much wider context.

Regionally-Varying Combustion Sources of the January 2013 Severe Haze Events over Eastern China

Thick haze plagued northeastern China in January 2013, strongly affecting both regional climate and human respiratory health. Here, we present dual carbon isotope constrained (Δ(14)C and δ(13)C) source apportionment for combustion-derived black carbon aerosol (BC) for three key hotspot regions (megacities): North China Plain (NCP, Beijing), the Yangtze River Delta (YRD, Shanghai), and the Pearl River Delta (PRD, Guangzhou) for January 2013. BC, here quantified as elemental carbon (EC), is one of the most health-detrimental components of PM2.5 and a strong climate warming agent. The results show that these severe haze events were equally affected (∼ 30%) by biomass combustion in all three regions, whereas the sources of the dominant fossil fuel component was dramatically different between north and south. In the NCP region, coal combustion accounted for 66% (46-74%, 95% C.I.) of the EC, whereas, in the YRD and PRD regions, liquid fossil fuel combustion (e.g., traffic) stood for 46% (18-66%) and 58% (38-68%), respectively. Taken together, these findings suggest the need for a regionally-specific description of BC sources in climate models and regionally-tailored mitigation to combat severe air pollution events in East Asia.

Continuous-index hidden Markov modelling of array CGH copy number data

MOTIVATION In recent years, a range of techniques for analysis and segmentation of array comparative genomic hybridization (aCGH) data have been proposed. For array designs in which clones are of unequal lengths, are unevenly spaced or overlap, the discrete-index view typically adopted by such methods may be questionable or improved. RESULTS We describe a continuous-index hidden Markov model for aCGH data as well as a Monte Carlo EM algorithm to estimate its parameters. It is shown that for a dataset from the BT-474 cell line analysed on 32K BAC tiling microarrays, this model yields considerably better model fit in terms of lag-1 residual autocorrelations compared to a discrete-index HMM, and it is also shown how to use the model for e.g. estimation of change points on the base-pair scale and for estimation of conditional state probabilities across the genome. In addition, the model is applied to the Glioblastoma Multiforme data used in the comparative study by Lai et al. (Lai,W.R. et al. (2005) Comparative analysis of algorithms for identifying amplifications and deletions in array CGH data. Bioinformatics, 21, 3763-3370.) giving result similar to theirs but with certain features highlighted in the continuous-index setting.

Stochastic demography and population dynamics in the red kangaroo Macropus rufus

1. Many organisms inhabit strongly fluctuating environments but their demography and population dynamics are often analysed using deterministic models and elasticity analysis, where elasticity is defined as the proportional change in population growth rate caused by a proportional change in a vital rate. Deterministic analyses may not necessarily be informative because large variation in a vital rate with a small deterministic elasticity may affect the population growth rate more than a small change in a less variable vital rate having high deterministic elasticity. 2. We analyse a stochastic environment model of the red kangaroo (Macropus rufus), a species inhabiting an environment characterized by unpredictable and highly variable rainfall, and calculate the elasticity of the stochastic growth rate with respect to the mean and variability in vital rates. 3. Juvenile survival is the most variable vital rate but a proportional change in the mean adult survival rate has a much stronger effect on the stochastic growth rate. 4. Even if changes in average rainfall have a larger impact on population growth rate, increased variability in rainfall may still be important also in long-lived species. The elasticity with respect to the standard deviation of rainfall is comparable to the mean elasticities of all vital rates but the survival in age class 3 because increased variation in rainfall affects both the mean and variability of vital rates. 5. Red kangaroos are harvested and, under the current rainfall pattern, an annual harvest fraction of c. 20% would yield a stochastic growth rate about unity. However, if average rainfall drops by more than c. 10%, any level of harvesting may be unsustainable, emphasizing the need for integrating climate change predictions in population management and increase our understanding of how environmental stochasticity translates into population growth rate.

On observation distributions for state space models of population survey data

1. State space models are starting to replace more simple time series models in analyses of temporal dynamics of populations that are not perfectly censused. By simultaneously modelling both the dynamics and the observations, consistent estimates of population dynamical parameters may be obtained. For many data sets, the distribution of observation errors is unknown and error models typically chosen in an ad-hoc manner. 2. To investigate the influence of the choice of observation error on inferences, we analyse the dynamics of a replicated time series of red kangaroo surveys using a state space model with linear state dynamics. Surveys were performed through aerial counts and Poisson, overdispersed Poisson, normal and log-normal distributions may all be adequate for modelling observation errors for the data. We fit each of these to the data and compare them using AIC. 3. The state space models were fitted with maximum likelihood methods using a recent importance sampling technique that relies on the Kalman filter. The method relaxes the assumption of Gaussian observation errors required by the basic Kalman filter. Matlab code for fitting linear state space models with Poisson observations is provided. 4. The ability of AIC to identify the correct observation model was investigated in a small simulation study. For the parameter values used in the study, without replicated observations, the correct observation distribution could sometimes be identified but model selection was prone to misclassification. On the other hand, when observations were replicated, the correct distribution could typically be identified. 5. Our results illustrate that inferences may differ markedly depending on the observation distributions used, suggesting that choosing an adequate observation model can be critical. Model selection and simulations show that for the models and parameter values in this study, a suitable observation model can typically be identified if observations are replicated. Model selection and replication of observations, therefore, provide a potential solution when the observation distribution is unknown.

Individual heterogeneity and senescence in silvereyes on Heron Island.

Individual heterogeneity and correlations between life history traits play a fundamental role in life history evolution and population dynamics. Unobserved individual heterogeneity in survival can be a nuisance for estimation of age effects at the individual level by causing bias due to mortality selection. We jointly analyze survival and breeding output from successful breeding attempts in an island population of Silvereyes (Zosterops lateralis chlorocephalus) by fitting models that incorporate age effects and individual heterogeneity via random effects. The number of offspring produced increased with age of parents in their first years of life but then eventually declined with age. A similar pattern was found for the probability of successful breeding. Annual survival declined with age even when individual heterogeneity was not accounted for. The rate of senescence in survival, however, depends on the variance of individual heterogeneity and vice versa; hence, both cannot be simultaneously estimated with precision. Model selection supported individual heterogeneity in breeding performance, but we found no correlation between individual heterogeneity in survival and breeding performance. We argue that individual random effects, unless unambiguously identified, should be treated as statistical nuisance or taken as a starting point in a search for mechanisms rather than given direct biological interpretation.

Kernel regression in the presence of size-bias

Kernel regression estimators of Nadaraya-Watson type for data sampled with size-bias were considered in Ahmad [1]. We consider an alternative definition of the weight-functions which can be applied to a wider variety of practical situations. In these situations the estimators will have a different bias which we remedy by introducing a local linear estimator.

Patchiness and co-existence of indigenous and invasive mussels at small spatial scales: the interaction of facilitation and competition.

Ecological theory predicts that two species with similar requirements will fail to show long-term co-existence in situations where shared resources are limiting, especially at spatial scales that are small relative to the size of the organisms. Two species of intertidal mussels, the indigenous Perna perna and the invasive Mytilus galloprovincialis, form mixed beds on the south coast of South Africa in a situation that has been stable for several generations of these species, even though these populations are often limited by the availability of space. We examined the spatial structure of these species where they co-exist at small spatial scales in the absence of apparent environmental heterogeneity at two sites, testing: whether conspecific aggregation of mussels can occur (using spatial Monte-Carlo tests); the degree of patchiness (using Korcak B patchiness exponent), and whether there was a relationship between percent cover and patchiness. We found that under certain circumstances there is non-random conspecific aggregation, but that in other circumstances there may be random distribution (i.e. the two species are mixed), so that spatial patterns are context-dependent. The relative cover of the species differed between sites, and within each site, the species with higher cover showed low Korcak B values (indicating low patchiness, i.e. the existence of fewer, larger patches), while the less abundant species showed the reverse, i.e. high patchiness. This relationship did not hold for either species within sites. We conclude that co-existence between these mussels is possible, even at small spatial scales because each species is an ecological engineer and, while they have been shown to compete for space, this is preceded by initial facilitation. We suggest that a patchy pattern of co-existence is possible because of a balance between direct (competitive) and indirect (facilitative) interactions.

Multivariate State Space Modelling of Bird Migration Count Data

We analyse 54 year long time series data on the numbers of common redstart (Phoenicurus phoenicurus), common whitethroat (Sylvia communis), garden warbler (Sylvia borin) and lesser whitethroat (Sylvia curruca) trapped in spring and autumn at Ottenby Bird Observatory, Sweden. The Ottenby time series could potentially serve as a reference on how much information on population change is available in count data on migrating birds. To investigate this, we combine spring and autumn data in a Bayesian state-space model trying to separate demographic signals and observation noise. The spring data are assumed to be a measure of the breeding population size, whereas the autumn data measure the population size after reproduction. At the demographic level we include seasonal density dependence and model winter dynamics as a function of precipitation in the Sahel region, south of the Sahara desert, where these species are known to spend the winter. Results show that the large fluctuations in the data restrict what conclusions can be drawn about the dynamics of the species. Annual catches are highly correlated between species and we show that a likely explanation for this is that trapping numbers are strongly dependent on local weather conditions. A comparative analysis of a related data set from the Courish Spit, Russia, gives rather different dynamics which may be caused by low information in the two data sets, but also by distinct populations passing Ottenby and the Courish Spit. This highlights the difficulty of validating results of the analyses when abundance indices derived by other methods or from other populations do not agree.