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In public opinion studies, the relationships between opinions on different topics are likely to shift based on the characteristics of the respondents. Thus, understanding the complexities of public opinion requires methods that can account for the heterogeneity in responses across different groups. Multiple graphs are used to study how external factors-such as time spent online or generational differences-shape the joint dependence relationships between opinions on various topics. Specifically, we propose a class of multiple Ising models where a set of graphs across different groups are able to capture these variations and to model the heterogeneity induced in a set of binary variables by external factors. The proposed Bayesian methodology is based on a Markov Random Field prior for the multiple graph setting. Such prior enables the borrowing of strength across the different groups to encourage common edges when supported by the data. Sparse inducing spike-and-slab priors are employed on the parameters that measure graph similarities to learn which subgroups have a shared graph structure. Two Bayesian approaches are developed for the inference of multiple Ising models with a special focus on model selection: (i) a Fully Bayesian method for low-dimensional graphs based on conjugate priors specified with respect to the exact likelihood, and (ii) an Approximate Bayesian method based on a quasi-likelihood approach for high-dimensional graphs where the normalization constant required in the exact method is computationally intractable. These methods are employed for the analysis of data from two public opinion studies in US. The obtained results display a good trade-off between identifying significant edges (both shared and group-specific) and having sparse networks, all while quantifying the uncertainty of the graph structure and the graphs' similarity.

Precision medicine is an approach for disease treatment that defines treatment strategies based on the individual characteristics of the patients. Motivated by an open problem in cancer genomics, we develop a novel model that flexibly clusters patients with similar predictive characteristics and similar treatment responses; this approach identifies, via predictive inference, which one among a set of treatments is better suited for a new patient. The proposed method is fully model-based, avoiding uncertainty underestimation attained when treatment assignment is performed by adopting heuristic clustering procedures, and belongs to the class of product partition models with covariates, here extended to include the cohesion induced by the Normalized Generalized Gamma process. The method performs particularly well in scenarios characterized by considerable heterogeneity of the predictive covariates in simulation studies. A cancer genomics case study illustrates the potential benefits in terms of treatment response yielded by the proposed approach. Finally, being model-based, the approach allows estimating clusters' specific response probabilities and then identifying patients more likely to benefit from personalized treatment., Comment: 31 pages, 7 figures

In this paper, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to differing disease stage or subtype, is profiled across multiple platforms, such as metabolomics, proteomics, or transcriptomics data. Our proposed Bayesian hierarchical model first links the network structures within each platform using a Markov random field prior to relate edge selection across sample groups, and then links the network similarity parameters across platforms. This enables joint estimation in a flexible manner, as we make no assumptions on the directionality of influence across the data types or the extent of network similarity across the sample groups and platforms. In addition, our model formulation allows the number of variables and number of subjects to differ across the data types, and only requires that we have data for the same set of groups. We illustrate the proposed approach through both simulation studies and an application to gene expression levels and metabolite abundances on subjects with varying severity levels of Chronic Obstructive Pulmonary Disease (COPD).

Alzheimer's disease is the most common neurodegenerative disease. The aim of this study is to infer structural changes in brain connectivity resulting from disease progression using cortical thickness measurements from a cohort of participants who were either healthy control, or with mild cognitive impairment, or Alzheimer's disease patients. For this purpose, we develop a novel approach for inference of multiple networks with related edge values across groups. Specifically, we infer a Gaussian graphical model for each group within a joint framework, where we rely on Bayesian hierarchical priors to link the precision matrix entries across groups. Our proposal differs from existing approaches in that it flexibly learns which groups have the most similar edge values, and accounts for the strength of connection (rather than only edge presence or absence) when sharing information across groups. Our results identify key alterations in structural connectivity which may reflect disruptions to the healthy brain, such as decreased connectivity within the occipital lobe with increasing disease severity. We also illustrate the proposed method through simulations, where we demonstrate its performance in structure learning and precision matrix estimation with respect to alternative approaches., Comment: Accepted to Biometrics January 2020

The vast amount of biological knowledge accumulated over the years has allowed researchers to identify various biochemical interactions and define different families of pathways. There is an increased interest in identifying pathways and pathway elements involved in particular biological processes. Drug discovery efforts, for example, are focused on identifying biomarkers as well as pathways related to a disease. We propose a Bayesian model that addresses this question by incorporating information on pathways and gene networks in the analysis of DNA microarray data. Such information is used to define pathway summaries, specify prior distributions, and structure the MCMC moves to fit the model. We illustrate the method with an application to gene expression data with censored survival outcomes. In addition to identifying markers that would have been missed otherwise and improving prediction accuracy, the integration of existing biological knowledge into the analysis provides a better understanding of underlying molecular processes., Comment: Published in at http://dx.doi.org/10.1214/11-AOAS463 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

It has been estimated that about 30% of the genes in the human genome are regulated by microRNAs (miRNAs). These are short RNA sequences that can down-regulate the levels of mRNAs or proteins in animals and plants. Genes regulated by miRNAs are called targets. Typically, methods for target prediction are based solely on sequence data and on the structure information. In this paper we propose a Bayesian graphical modeling approach that infers the miRNA regulatory network by integrating expression levels of miRNAs with their potential mRNA targets and, via the prior probability model, with their sequence/structure information. We use a directed graphical model with a particular structure adapted to our data based on biological considerations. We then achieve network inference using stochastic search methods for variable selection that allow us to explore the huge model space via MCMC. A time-dependent coefficients model is also implemented. We consider experimental data from a study on a very well-known developmental toxicant causing neural tube defects, hyperthermia. Some of the pairs of target gene and miRNA we identify seem very plausible and warrant future investigation. Our proposed method is general and can be easily applied to other types of network inference by integrating multiple data sources., Comment: Published in at http://dx.doi.org/10.1214/10-AOAS360 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)