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Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision…
We develop a modeling framework for dynamic function-on-scalars regression, in which a time series of functional data is regressed on a time series of scalar predictors. The regression coefficient function for each predictor is allowed to…
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or…
Gibbs sampling is the de facto Markov chain Monte Carlo method used for inference and learning on large scale graphical models. For complicated factor graphs with lots of factors, the performance of Gibbs sampling can be limited by the…
We present a new sampling-based approach for enabling efficient computation of low-rank Bayesian matrix completion and quantifying the associated uncertainty. Firstly, we design a new prior model based on the singular-value-decomposition…
The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
We propose Bayesian Univariate-Guided Sparse Regression (BUGS), a novel global-local shrinkage framework that incorporates marginal association information directly into the prior through a continuous modulation of shrinkage. Unlike…
We consider a class of colored graphical Gaussian models obtained by placing symmetry constraints on the precision matrix in a Bayesian framework. The prior distribution on the precision matrix is the colored $G$-Wishart prior which is the…
The particle Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm to sample from the full posterior distribution of a state-space model. It does so by executing Gibbs sampling steps on an extended target distribution defined on the…
Gibbs sampling is a widely used Markov chain Monte Carlo (MCMC) method for numerically approximating integrals of interest in Bayesian statistics and other mathematical sciences. Many implementations of MCMC methods do not extend easily to…
The MC$^3$ (Madigan and York, 1995) and Gibbs (George and McCulloch, 1997) samplers are the most widely implemented algorithms for Bayesian Model Averaging (BMA) in linear regression models. These samplers draw a variable at random in each…
Gaussian concentration graph models and covariance graph models are two classes of graphical models that are useful for uncovering latent dependence structures among multivariate variables. In the Bayesian literature, graphs are often…
We study parameter inference in large-scale latent variable models. We first propose an unified treatment of online inference for latent variable models from a non-canonical exponential family, and draw explicit links between several…
We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…
Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension…
Precision matrices are crucial in many fields such as social networks, neuroscience, and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off-diagonal position of the precision matrix…
Latent factor GARCH models are difficult to estimate using Bayesian methods because standard Markov chain Monte Carlo samplers produce slowly mixing and inefficient draws from the posterior distributions of the model parameters. This paper…
In the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a…
Modeling binary and categorical data is one of the most commonly encountered tasks of applied statisticians and econometricians. While Bayesian methods in this context have been available for decades now, they often require a high level of…