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An important aspect of Bayesian model selection is how to deal with huge model spaces, since exhaustive enumeration of all the models entertained is unfeasible and inferences have to be based on the very small proportion of models visited.…
How to estimate heterogeneity, e.g. the effect of some variable differing across observations, is a key question in political science. Methods for doing so make simplifying assumptions about the underlying nature of the heterogeneity to…
Bayesian hierarchical linear models provide a natural framework to analyze nested and clustered data. Classical estimation with Markov chain Monte Carlo produces well calibrated posterior distributions but becomes computationally expensive…
Multiple imputation has become one of the standard methods in drawing inferences in many incomplete data applications. Applications of multiple imputation in relatively more complex settings, such as high-dimensional clustered data, require…
We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…
In several linear regression data sets, $Y (\in R)$ on ${\bf X} (\in R^p),$ visual comparisons of $L_1$ and $L_2$-residuals' plots indicate bad leverage cases. The phenomenon is confirmed theoretically by introducing Location Breakdown…
Bayesian inference involves the specification of a statistical model by a statistician or practitioner, with careful thought about what each parameter represents. This results in particularly interpretable models which can be used to…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
This paper focuses on the Bregman divergence defined by the reciprocal function, called the inverse divergence. For the loss function defined by the monotonically increasing function $f$ and inverse divergence, the conditions for the…
Bayesian sociality models provide a scalable and flexible alternative for network analysis, capturing degree heterogeneity through actor-specific parameters while mitigating the identifiability challenges of latent space models. This paper…
In large-scale genomic applications vast numbers of molecular features are scanned in order to find a small number of candidates which are linked to a particular disease or phenotype. This is a variable selection problem in the "large p,…
Network data are increasingly collected along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring brain connectivity networks for a sample of individuals along with their membership to a low or…
This paper develops a Bayesian framework for robust causal inference from longitudinal observational data. Many contemporary methods rely on structural assumptions, such as factor models, to adjust for unobserved confounding, but they can…
The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes…
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…
We develop a fully Bayesian framework for function-on-scalars regression with many predictors. The functional data response is modeled nonparametrically using unknown basis functions, which produces a flexible and data-adaptive functional…
Bregman divergences generalize measures such as the squared Euclidean distance and the KL divergence, and arise throughout many areas of machine learning. In this paper, we focus on the problem of approximating an arbitrary Bregman…
To determine the universality class of critical phenomena, we propose a method of statistical inference in the scaling analysis of critical phenomena. The method is based on Bayesian statistics, most specifically, the Gaussian process…
Importance sampling is a popular technique in Bayesian inference: by reweighting samples drawn from a proposal distribution we are able to obtain samples and moment estimates from a Bayesian posterior over latent variables. Recent work,…
Motivated by genome-wide association studies, we consider a standard linear model with one additional random effect in situations where many predictors have been collected on the same subjects and each predictor is analyzed separately.…