Chad M. Schafer

Computational Design and Performance of the Fast Ocean Atmosphere Model, Version One

The Fast Ocean Atmosphere Model (FOAM) is a climate system model intended for application to climate science questions that require long simulations. FOAM is a distributed-memory parallel climate model consisting of parallel general circulation models of the atmosphere and ocean with complete physics paramaterizations as well as sea-ice, land surface, and river transport models. FOAMs coupling strategy was chosen for high throughput (simulated years per day). A new coupler was written for FOAM and some modifications were required of the component models. Performance data for FOAM on the IBM SP3 and SGI Origin2000 demonstrates that it can simulate over thirty years per day on modest numbers of processors.

LIKELIHOOD-FREE COSMOLOGICAL INFERENCE WITH TYPE Ia SUPERNOVAE: APPROXIMATE BAYESIAN COMPUTATION FOR A COMPLETE TREATMENT OF UNCERTAINTY

Cosmological inference becomes increasingly difficult when complex data-generating processes cannot be modeled by simple probability distributions. With the ever-increasing size of data sets in cosmology, there is an increasing burden placed on adequate modeling; systematic errors in the model will dominate where previously these were swamped by statistical errors. For example, Gaussian distributions are an insufficient representation for errors in quantities like photometric redshifts. Likewise, it can be difficult to quantify analytically the distribution of errors that are introduced in complex fitting codes. Without a simple form for these distributions, it becomes difficult to accurately construct a likelihood function for the data as a function of parameters of interest. Approximate Bayesian computation (ABC) provides a means of probing the posterior distribution when direct calculation of a sufficiently accurate likelihood is intractable. ABC allows one to bypass direct calculation of the likelihood but instead relies upon the ability to simulate the forward process that generated the data. These simulations can naturally incorporate priors placed on nuisance parameters, and hence these can be marginalized in a natural way. We present and discuss ABC methods in the context of supernova cosmology using data from the SDSS-II Supernova Survey. Assuming a flat cosmology and constant dark energy equation of state, we demonstrate that ABC can recover an accurate posterior distribution. Finally, we show that ABC can still produce an accurate posterior distribution when we contaminate the sample with Type IIP supernovae.

Photometric redshift estimation using spectral connectivity analysis

The development of fast and accurate methods of photometric redshift estimation is a vital step towards being able to fully utilize the data of next-generation surveys within precision cosmology. In this paper we apply a specific approach to spectral connectivity analysis (SCA; Lee & Wasserman 2009) called diffusion map. SCA is a class of non-linear techniques for transforming observed data (e.g., photometric colours for each galaxy, where the data lie on a complex subset of p-dimensional space) to a simpler, more natural coordinate system wherein we apply regression to make redshift predictions. As SCA relies upon eigen-decomposition, our training set size is limited to ~ 10,000 galaxies; we use the Nystrom extension to quickly estimate diffusion coordinates for objects not in the training set. We apply our method to 350,738 SDSS main sample galaxies, 29,816 SDSS luminous red galaxies, and 5,223 galaxies from DEEP2 with CFHTLS ugriz photometry. For all three datasets, we achieve prediction accuracies on par with previous analyses, and find that use of the Nystrom extension leads to a negligible loss of prediction accuracy relative to that achieved with the training sets. As in some previous analyses (e.g., Collister & Lahav 2004, Ball et al. 2008), we observe that our predictions are generally too high (low) in the low (high) redshift regimes. We demonstrate that this is a manifestation of attenuation bias, wherein measurement error (i.e., uncertainty in diffusion coordinates due to uncertainty in the measured fluxes/magnitudes) reduces the slope of the best-fit regression line. Mitigation of this bias is necessary if we are to use photometric redshift estimates produced by computationally efficient empirical methods in precision cosmology.

Exploring Coupled Atmosphere-Ocean Models Using Vis5D

A distributed client/server system can be used to visualize very large simulation data sets. An example of a very large simulation data set is a 100-year simulation of the Earths coupled atmosphere-ocean system. This model run was produced by an Argonne National Laboratory/University of Wisconsin collaborative project that is studying atmosphere-ocean coupling dynamics to understand the intrinsic low-frequency variability of the climate system. This understanding is crucial for the prediction and detec tion of human impacts on the Earths climate. To visually explore this simulation, an IBM SP-2 is used as a data server and a pair of SGI Onyxes driving a CAVE are used as a graphics client. The SP-2 server divides the data set into sections that will fit in the memory of the graphics client. The data set is divided along the time axis. One data set section covers the entire 100-year span of the simula tion at reduced-time resolution, while the other data set sections cover short subintervals at full-time resolution. The visualization user interface allows users to switch between low and high time resolution.

EXPLOITING LOW-DIMENSIONAL STRUCTURE IN ASTRONOMICAL SPECTRA

Dimension-reduction techniques can greatly improve statistical inference in astronomy. A standard approach is to use Principal Components Analysis (PCA). In this work, we apply a recently developed technique, diffusion maps, to astronomical spectra for data parameterization and dimensionality reduction, and develop a robust, eigenmode-based framework for regression. We show how our framework provides a computationally efficient means by which to predict redshifts of galaxies, and thus could inform more expensive redshift estimators such as template cross-correlation. It also provides a natural means by which to identify outliers (e.g., misclassified spectra, spectra with anomalous features). We analyze 3835 Sloan Digital Sky Survey spectra and show how our framework yields a more than 95% reduction in dimensionality. Finally, we show that the prediction error of the diffusion-map-based regression approach is markedly smaller than that of a similar approach based on PCA, clearly demonstrating the superiority of diffusion maps over PCA for this regression task.

Accurate parameter estimation for star formation history in galaxies using SDSS spectra

To further our knowledge of the complex physical process of galaxy formation, it is essential that we characterize the formation and evolution of large data bases of galaxies. The spectral synthesis starlight code of Cid Fernandes et al. was designed for this purpose. Results of starlight are highly dependent on the choice of input basis of simple stellar population (SSP) spectra. Speed of the code, which uses random walks through the parameter space, scales as the square of the number of the basis spectra, making it computationally necessary to choose a small number of SSPs that are coarsely sampled in age and metallicity. In this paper, we develop methods based on a diffusion map that, for the first time, choose appropriate bases of prototype SSP spectra from a large set of SSP spectra designed to approximate the continuous grid of age and metallicity of SSPs of which galaxies are truly composed. We show that our techniques achieve better accuracy of physical parameter estimation for simulated galaxies. Specifically, we show that our methods significantly decrease the age–metallicity degeneracy that is common in galaxy population synthesis methods. We analyse a sample of 3046 galaxies in Sloan Digital Sky Survey Data Release 6 and compare the parameter estimates obtained from different basis choices.

A Statistical Method for Estimating Luminosity Functions Using Truncated Data

The observational limitations of astronomical surveys lead to significant statistical inference challenges. One such challenge is the estimation of luminosity functions given redshift (z) and absolute magnitude (M) measurements from an irregularly truncated sample of objects. This is a bivariate density estimation problem; we develop here a statistically rigorous method which (1) does not assume a strict parametric form for the bivariate density; (2) does not assume independence between redshift and absolute magnitude (and hence allows evolution of the luminosity function with redshift); (3) does not require dividing the data into arbitrary bins; and (4) naturally incorporates a varying selection function. We accomplish this by decomposing the bivariate density (z,M) via log (z,M) = f(z) + g(M) + h(z,M,θ), where f and g are estimated nonparametrically and h takes an assumed parametric form. There is a simple way of estimating the integrated mean squared error of the estimator; smoothing parameters are selected to minimize this quantity. Results are presented from the analysis of a sample of quasars.

FOAM: Expanding the Horizons of Climate Modeling

We report here on a project that expands the applicability of dynamic climate modeling to very long time scales. The Fast Ocean Atmosphere Model (FOAM) is a coupled ocean- atmosphere model that incorporates physics of interest in understanding decade to century time scale variability. It addresses the high computational cost of this endeavor with a combination of improved ocean model formulation, low atmosphere resolution, and efficient coupling. It also uses message-passing parallel processing techniques, allowing for the use of cost-effective distributed memory platforms. The resulting model runs over 6000 times faster than real time with good fidelity and has yielded significant results.

Prototype selection for parameter estimation in complex models

Parameter estimation in astrophysics often requires the use of complex physical models. In this paper we study the problem of estimating the parameters that describe star formation history (SFH) in galaxies. Here, high-dimensional spectral data from galaxies are appropriately modeled as linear combinations of physical components, called simple stellar populations (SSPs), plus some nonlinear distortions. Theoretical data for each SSP is produced for a fixed parameter vector via computer modeling. Though the parameters that define each SSP are continuous, optimizing the signal model over a large set of SSPs on a fine parameter grid is computationally infeasible and inefficient. The goal of this study is to estimate the set of parameters that describes the SFH of each galaxy. These target parameters, such as the average ages and chemical compositions of the galaxys stellar populations, are derived from the SSP parameters and the component weights in the signal model. Here, we introduce a principled approach of choosing a small basis of SSP prototypes for SFH parameter estimation. The basic idea is to quantize the vector space and effective support of the model components. In addition to greater computational efficiency, we achieve better estimates of the SFH target parameters. In simulations, our proposed quantization method obtains a substantial improvement in estimating the target parameters over the common method of employing a parameter grid. Sparse coding techniques are not appropriate for this problem without proper constraints, while constrained sparse coding methods perform poorly for parameter estimation because their objective is signal reconstruction, not estimation of the target parameters.

Likelihood-Free Inference in Cosmology: Potential for the Estimation of Luminosity Functions

Statistical inference of cosmological quantities of interest is complicated by significant observational limitations, including heteroscedastic measurement error and irregular selection effects. These observational difficulties exacerbate challenges posed by the often-complex relationship between estimands and the distribution of observables; indeed, in some situations it is only possible to simulate realizations of observations under various assumed cosmological theories. When faced with these challenges, one is naturally led to consider utilizing repeated simulations of the full data generation process, and then comparing observed and simulated data sets to constrain the parameters. In such a scenario, one would not have a likelihood function relating the parameters to the observable data. This paper will present an overview of methods that allow a likelihood-free approach to inference, with emphasis on approximate Bayesian computation, a class of procedures originally motivated by similar inference problems in population genetics.