Related papers: A Gentle Introduction to Bayesian Hierarchical Lin…

Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can…

We investigate two empirical Bayes methods and a hierarchical Bayes method for adapting the scale of a Gaussian process prior in a nonparametric regression model. We show that all methods lead to a posterior contraction rate that adapts to…

Hierarchical Bayesian methods enable information sharing across multiple related regression problems. While standard practice is to model regression parameters (effects) as (1) exchangeable across datasets and (2) correlated to differing…

Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the…

We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…

It has become increasingly common to collect high-dimensional binary response data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for…

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 incorporate heteroskedasticity into Bayesian Additive Regression Trees (BART) by modeling the log of the error variance parameter as a linear function of prespecified covariates. Under this scheme, the Gibbs sampling procedure for the…

We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…

Items in modern recommender systems are often organized in hierarchical structures. These hierarchical structures and the data within them provide valuable information for building personalized recommendation systems. In this paper, we…

One of the challenges in model-based control of stochastic dynamical systems is that the state transition dynamics are involved, and it is not easy or efficient to make good-quality predictions of the states. Moreover, there are not many…

We present a Bayesian approach to machine learning with probabilistic programs. In our approach, training on available data is implemented as inference on a hierarchical model. The posterior distribution of model parameters is then used to…

This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian…

It is often of interest to combine available estimates of a similar quantity from multiple data sources. When the corresponding variances of each estimate are also available, a model should take into account the uncertainty of the estimates…

The standard procedures for analysing hierarquical or grouped data are by (non)linear mixed models or generalized mixed models. However, the generalized additive models for location, scale and shape (GAMLSSs) also allow different types of…

Bayesian graphical models have been shown to be a powerful tool for discovering uncertainty and causal structure from real-world data in many application fields. Current inference methods primarily follow different kinds of trade-offs…

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

Models for distributions of shapes contained within images can be widely used in biomedical applications ranging from tumor tracking for targeted radiation therapy to classifying cells in a blood sample. Our focus is on hierarchical…

Variational Inference is a powerful tool in the Bayesian modeling toolkit, however, its effectiveness is determined by the expressivity of the utilized variational distributions in terms of their ability to match the true posterior…

In this note we derive a simple Bayesian sampler for linear regression with the horseshoe hierarchy. A new interpretation of the horseshoe model is presented, and extensions to logistic regression and alternative hierarchies, such as…