BAYESIAN MODEL SEARCH AND MULTILEVEL INFERENCE FOR SNP ASSOCIATION STUDIES.

Technological advances in genotyping have given rise to hypothesis-based association studies of increasing scope. As a result, the scientific hypotheses addressed by these studies have become more complex and more difficult to address using existing analytic methodologies. Obstacles to analysis include inference in the face of multiple comparisons, complications arising from correlations among the SNPs (single nucleotide polymorphisms), choice of their genetic parametrization and missing data. In this paper we present an efficient Bayesian model search strategy that searches over the space of genetic markers and their genetic parametrization. The resulting method for Multilevel Inference of SNP Associations, MISA, allows computation of multilevel posterior probabilities and Bayes factors at the global, gene and SNP level, with the prior distribution on SNP inclusion in the model providing an intrinsic multiplicity correction. We use simulated data sets to characterize MISA's statistical power, and show that MISA has higher power to detect association than standard procedures. Using data from the North Carolina Ovarian Cancer Study (NCOCS), MISA identifies variants that were not identified by standard methods and have been externally "validated" in independent studies. We examine sensitivity of the NCOCS results to prior choice and method for imputing missing data. MISA is available in an R package on CRAN.

Bayesian Gaussian Copula Factor Models for Mixed Data.

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies.

BACKGROUND: Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. RESULTS: Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. CONCLUSIONS: Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.

VizMaps: A Bayesian Topic Modeling Based PubMed Search Interface

A common challenge that users of academic databases face is making sense of their query outputs for knowledge discovery. This is exacerbated by the size and growth of modern databases. PubMed, a central index of biomedical literature, contains over 25 million citations, and can output search results containing hundreds of thousands of citations. Under these conditions, efficient knowledge discovery requires a different data structure than a chronological list of articles. It requires a method of conveying what the important ideas are, where they are located, and how they are connected; a method of allowing users to see the underlying topical structure of their search. This paper presents VizMaps, a PubMed search interface that addresses some of these problems. Given search terms, our main backend pipeline extracts relevant words from the title and abstract, and clusters them into discovered topics using Bayesian topic models, in particular the Latent Dirichlet Allocation (LDA). It then outputs a visual, navigable map of the query results.

Bagging and the Bayesian Bootstrap

Bagging is a method of obtaining more ro- bust predictions when the model class under consideration is unstable with respect to the data, i.e., small changes in the data can cause the predicted values to change significantly. In this paper, we introduce a Bayesian ver- sion of bagging based on the Bayesian boot- strap. The Bayesian bootstrap resolves a the- oretical problem with ordinary bagging and often results in more efficient estimators. We show how model averaging can be combined within the Bayesian bootstrap and illustrate the procedure with several examples.

Bayesian Model Averaging in the M-Open Framework

This chapter presents a model averaging approach in the M-open setting using sample re-use methods to approximate the predictive distribution of future observations. It first reviews the standard M-closed Bayesian Model Averaging approach and decision-theoretic methods for producing inferences and decisions. It then reviews model selection from the M-complete and M-open perspectives, before formulating a Bayesian solution to model averaging in the M-open perspective. It constructs optimal weights for MOMA:M-open Model Averaging using a decision-theoretic framework, where models are treated as part of the ‘action space’ rather than unknown states of nature. Using ‘incompatible’ retrospective and prospective models for data from a case-control study, the chapter demonstrates that MOMA gives better predictive accuracy than the proxy models. It concludes with open questions and future directions.

SMERED: A Bayesian Approach to Graphical Record Linkage and De-duplication

We propose a novel unsupervised approach for linking records across arbitrarily many files, while simultaneously detecting duplicate records within files. Our key innovation is to represent the pattern of links between records as a {\em bipartite} graph, in which records are directly linked to latent true individuals, and only indirectly linked to other records. This flexible new representation of the linkage structure naturally allows us to estimate the attributes of the unique observable people in the population, calculate $k$-way posterior probabilities of matches across records, and propagate the uncertainty of record linkage into later analyses. Our linkage structure lends itself to an efficient, linear-time, hybrid Markov chain Monte Carlo algorithm, which overcomes many obstacles encountered by previously proposed methods of record linkage, despite the high dimensional parameter space. We assess our results on real and simulated data.

Spatio-temporal Bayesian network models with latent variables for revealing trophic dynamics and functional networks in fisheries ecology

Ecosystems consist of complex dynamic interactions among species and the environment, the understanding of which has implications for predicting the environmental response to changes in climate and biodiversity. However, with the recent adoption of more explorative tools, like Bayesian networks, in predictive ecology, few assumptions can be made about the data and complex, spatially varying interactions can be recovered from collected field data. In this study, we compare Bayesian network modelling approaches accounting for latent effects to reveal species dynamics for 7 geographically and temporally varied areas within the North Sea. We also apply structure learning techniques to identify functional relationships such as prey–predator between trophic groups of species that vary across space and time. We examine if the use of a general hidden variable can reflect overall changes in the trophic dynamics of each spatial system and whether the inclusion of a specific hidden variable can model unmeasured group of species. The general hidden variable appears to capture changes in the variance of different groups of species biomass. Models that include both general and specific hidden variables resulted in identifying similarity with the underlying food web dynamics and modelling spatial unmeasured effect. We predict the biomass of the trophic groups and find that predictive accuracy varies with the models' features and across the different spatial areas thus proposing a model that allows for spatial autocorrelation and two hidden variables. Our proposed model was able to produce novel insights on this ecosystem's dynamics and ecological interactions mainly because we account for the heterogeneous nature of the driving factors within each area and their changes over time. Our findings demonstrate that accounting for additional sources of variation, by combining structure learning from data and experts' knowledge in the model architecture, has the potential for gaining deeper insights into the structure and stability of ecosystems. Finally, we were able to discover meaningful functional networks that were spatially and temporally differentiated with the particular mechanisms varying from trophic associations through interactions with climate and commercial fisheries.