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Ensemble of regression trees have become popular statistical tools for the estimation of conditional mean given a set of predictors. However, quantile regression trees and their ensembles have not yet garnered much attention despite the…

Quantile regression (QR) is a statistical tool for distribution-free estimation of conditional quantiles of a target variable given explanatory features. QR is limited by the assumption that the target distribution is univariate and defined…

Markov chain Monte Carlo (MCMC) is the predominant tool used in Bayesian parameter estimation for hierarchical models. When the model expands due to an increasing number of hierarchical levels, number of groups at a particular level, or…

We introduce the Multiple Quantile Graphical Model (MQGM), which extends the neighborhood selection approach of Meinshausen and Buhlmann for learning sparse graphical models. The latter is defined by the basic subproblem of modeling the…

This paper studies quantile regression with an endogenous regressor and measurement error in the dependent variable. Standard quantile regression estimators ignoring these two elements can induce substantial bias. We adopt a…

Brute force cross-validation (CV) is a method for predictive assessment and model selection that is general and applicable to a wide range of Bayesian models. Naive or `brute force' CV approaches are often too computationally costly for…

Data integration has become increasingly popular owing to the availability of multiple data sources. This study considered quantile regression estimation when a key covariate had multiple proxies across several datasets. In a unified…

Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…

When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior…

Reversible jump Markov chain Monte Carlo (RJMCMC) is a Bayesian model estimation method which has been used for trans-dimensional sampling. In this study, we propose utilization of RJMCMC beyond trans-dimensional sampling. This new…

Bounded continuous data on the unit interval frequently arise in applied fields and often exhibit a non-negligible proportion of observations at the boundaries. Inflated regression models address this feature by combining a continuous…

Quantile regression has received increased attention in the statistics community in recent years. This article adapts an auxiliary variable method, commonly used in Bayesian variable selection for mean regression models, to the fitting of…

Estimating the structures at high or low quantiles has become an important subject and attracted increasing attention across numerous fields. However, due to data sparsity at tails, it usually is a challenging task to obtain reliable…

Varying coefficient models are popular for estimating nonlinear regression functions in functional data models. Their Bayesian variants have received limited attention in large data applications, primarily due to prohibitively slow…

Quantile estimation and regression within the Bayesian framework is challenging as the choice of likelihood and prior is not obvious. In this paper, we introduce a novel Bayesian nonparametric method for quantile estimation and regression…

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…

We consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain.…

We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $\mathbb{P}(\mathbf{y}|\mathbf{X}=x)$ in regression…

A new class of models, named dynamic quantile linear models, is presented. It combines dynamic linear models with distribution free quantile regression producing a robust statistical method. Bayesian inference for dynamic quantile linear…

This paper proposes a Vector Autoregression augmented with nonlinear factors that are modeled nonparametrically using regression trees. There are four main advantages of our model. First, modeling potential nonlinearities nonparametrically…