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Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…

We propose a versatile and computationally efficient estimating equation method for a class of hierarchical multiplicative generalized linear mixed models with additive dispersion components, based on explicit modelling of the covariance…

Handling outliers is a fundamental challenge in multivariate data analysis because outliers may distort the structures of correlation or conditional independence. Although robust Bayesian inference has been extensively studied in univariate…

Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be…

Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…

Mixed membership models are an extension of finite mixture models, where each observation can partially belong to more than one mixture component. A probabilistic framework for mixed membership models of high-dimensional continuous data is…

Choosing the number of mixture components remains an elusive challenge. Model selection criteria can be either overly liberal or conservative and return poorly-separated components of limited practical use. We formalize non-local priors…

Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…

We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy…

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…

Dependence modeling of multivariate count data has garnered significant attention in recent years. Multivariate elliptical copulas are typically preferred in statistical literature to analyze dependence between repeated measurements of…

We present a structured additive regression approach to model conditional densities given scalar covariates, where only samples of the conditional distributions are observed. This links our approach to distributional regression models for…

Joint models for a wide class of response variables and longitudinal measurements consist on a mixed-effects model to fit longitudinal trajectories whose random effects enter as covariates in a generalized linear model for the primary…

Robust Bayesian linear regression is a classical but essential statistical tool. Although novel robustness properties of posterior distributions have been proved recently under a certain class of error distributions, their sufficient…

Modern data analysis often involves massive datasets with hundreds of thousands of observations, making traditional inference algorithms computationally prohibitive. Coresets are selection methods designed to choose a smaller subset of…

Regularized regression models are well studied and, under appropriate conditions, offer fast and statistically interpretable results. However, large data in many applications are heterogeneous in the sense of harboring distributional…

A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the…

Compositional data are common in many fields, both as outcomes and predictor variables. The inventory of models for the case when both the outcome and predictor variables are compositional is limited and the existing models are difficult to…

We propose a unified, yet simple to code, non-conjugate variational Bayes algorithm for posterior approximation of generic Bayesian generalized mixed effect models. Specifically, we consider regression models identified by a linear…

Ordinal cumulative probability models (CPMs) -- also known as cumulative link models -- such as the proportional odds regression model are typically used for discrete ordered outcomes, but can accommodate both continuous and mixed…