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We consider Bayesian estimation of a hierarchical linear model (HLM) from partially observed data, assumed to be missing at random, and small sample sizes. A vector of continuous covariates $C$ includes cluster-level partially observed…

We propose a random-effects approach to missing values for generalized linear mixed model (GLMM) analysis. The method converts a GLMM with missing covariates to another GLMM without missing covariates. The standard GLMM analysis tools for…

Linear mixed models (LMMs) are a popular class of methods for analyzing longitudinal and clustered data. However, such models can be sensitive to outliers, and this can lead to biased inference on model parameters and inaccurate prediction…

Gibbs samplers are popular algorithms to approximate posterior distributions arising from Bayesian hierarchical models. Despite their popularity and good empirical performances, however, there are still relatively few quantitative results…

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…

We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…

We introduce a Bayesian approach for multivariate spatio-temporal prediction for high-dimensional count-valued data. Our primary interest is when there are possibly millions of data points referenced over different variables, geographic…

In many applications, survey data are collected from different survey centers in different regions. It happens that in some circumstances, response variables are completely observed while the covariates have missing values. In this paper,…

Detecting associations between microbial compositions and sample characteristics is one of the most important tasks in microbiome studies. Most of the existing methods apply univariate models to single microbial species separately, with…

We study general coordinate-wise MCMC schemes (such as Metropolis-within-Gibbs samplers), which are commonly used to fit Bayesian non-conjugate hierarchical models. We relate their convergence properties to the ones of the corresponding…

The missing data issue often complicates the task of estimating generalized linear models (GLMs). We describe why the pseudo-marginal Metropolis-Hastings algorithm, used in this setting, is an effective strategy for parameter estimation.…

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…

Missing data theory deals with the statistical methods in the occurrence of missing data. Missing data occurs when some values are not stored or observed for variables of interest. However, most of the statistical theory assumes that data…

Dynamic Bayesian networks (DBNs) are increasingly used in healthcare due to their ability to model complex temporal relationships in patient data while maintaining interpretability, an essential feature for clinical decision-making.…

We pursue tractable Bayesian analysis of generalized linear models (GLMs) for categorical data. Thus far, GLMs are difficult to scale to more than a few dozen categories due to non-conjugacy or strong posterior dependencies when using…

We propose a general Bayesian nonparametric (BNP) approach to causal inference in the point treatment setting. The joint distribution of the observed data (outcome, treatment, and confounders) is modeled using an enriched Dirichlet process.…

Missing data arises when certain values are not recorded or observed for variables of interest. However, most of the statistical theory assume complete data availability. To address incomplete databases, one approach is to fill the gaps…

Penalized likelihood and quasi-likelihood methods dominate inference in high-dimensional linear mixed-effects models. Sampling-based Bayesian inference is less explored due to the computational bottlenecks introduced by the random effects…

The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to conduct such sampling, but such a method can converge…

This paper describes the hierarchical infinite relational model (HIRM), a new probabilistic generative model for noisy, sparse, and heterogeneous relational data. Given a set of relations defined over a collection of domains, the model…