Related papers: A Gentle Introduction to Bayesian Hierarchical Lin…

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…

We introduce Bayesian hierarchical models for predicting high-dimensional tabular survey data which can be distributed from one or multiple classes of distributions (e.g., Gaussian, Poisson, Binomial, etc.). We adopt a Bayesian…

Small area estimation has become an important tool in official statistics, used to construct estimates of population quantities for domains with small sample sizes. Typical area-level models function as a type of heteroscedastic regression,…

Using the linear Gaussian latent variable model as a starting point we relax some of the constraints it imposes by deriving a nonparametric latent feature Gaussian variable model. This model introduces additional discrete latent variables…

Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way…

In many applications, the dataset under investigation exhibits heterogeneous regimes that are more appropriately modeled using piece-wise linear models for each of the data segments separated by change-points. Although there have been much…

We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…

We consider the problems of hypothesis testing and model comparison under a flexible Bayesian linear regression model whose formulation is closely connected with the linear mixed effect model and the parametric models for SNP set analysis…

Gibbs random fields play an important role in statistics, for example the autologistic model is commonly used to model the spatial distribution of binary variables defined on a lattice. However they are complicated to work with due to an…

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…

For situations that may benefit from information sharing among datasets, e.g., population-based SHM of similar structures, the hierarchical Bayesian approach provides a useful modelling structure. Hierarchical Bayesian models learn…

Model-based diagnosis reasons backwards from a functional schematic of a system to isolate faults given observations of anomalous behavior. We develop a fully probabilistic approach to model based diagnosis and extend it to support…

An important task for any large-scale organization is to prepare forecasts of key performance metrics. Often these organizations are structured in a hierarchical manner and for operational reasons, projections of these metrics may have been…

Univariate and multivariate general linear regression models, subject to linear inequality constraints, arise in many scientific applications. The linear inequality restrictions on model parameters are often available from phenomenological…

Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…

Multilevel or hierarchical data structures can occur in many areas of research, including economics, psychology, sociology, agriculture, medicine, and public health. Over the last 25 years, there has been increasing interest in developing…

This article focuses on Bayesian estimation of a hierarchical linear model (HLM) from incomplete data assumed missing at random where continuous covariates C and discrete categorical covariates $D$ have interaction effects on a continuous…

We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…

The Bayesian evidence, crucial ingredient for model selection, is arguably the most important quantity in Bayesian data analysis: at the same time, however, it is also one of the most difficult to compute. In this paper we present a…

We provide an introductory review of Bayesian data analytical methods, with a focus on applications for linguistics, psychology, psycholinguistics, and cognitive science. The empirically oriented researcher will benefit from making Bayesian…