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Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
Models of biological systems often have many unknown parameters that must be determined in order for model behavior to match experimental observations. Commonly-used methods for parameter estimation that return point estimates of the…
We develop a new Bayesian modelling framework for the class of higher-order, variable-memory Markov chains, and introduce an associated collection of methodological tools for exact inference with discrete time series. We show that a version…
The study of Markov processes and broadcasting on trees has deep connections to a variety of areas including statistical physics, graphical models, phylogenetic reconstruction, Markov Chain Monte Carlo, and community detection in random…
In this paper we investigate the use of staged tree models for discrete longitudinal data. Staged trees are a type of probabilistic graphical model for finite sample space processes. They are a natural fit for longitudinal data because a…
We consider statistical inference in the density estimation model using a tree-based Bayesian approach, with Optional P\'olya trees as prior distribution. We derive near-optimal convergence rates for corresponding posterior distributions…
In Bayesian phylogenetics, our goal is to estimate the posterior distribution over phylogenetic trees. Markov chain Monte Carlo methods are widely used to approximate the phylogenetic posterior distributions. For large-scale sequence data,…
Bayesian Additive Regression Trees (BART) is a Bayesian approach to flexible non-linear regression which has been shown to be competitive with the best modern predictive methods such as those based on bagging and boosting. BART offers some…
We develop two models for Bayesian estimation and selection in high-order, discrete-state Markov chains. Both are based on the mixture transition distribution, which constructs a transition probability tensor with additive mixing of…
Several natural phenomena exhibit long-range conditional dependencies. High-order mixture transition distribution (MTD) are parsimonious non-parametric models to study these phenomena. An MTD is a Markov chain in which the transition…
We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the transition density is not analytically tractable. Markov processes with intractable transition…
Bayesian Decision Trees are known for their probabilistic interpretability. However, their construction can sometimes be costly. In this article we present a general Bayesian Decision Tree algorithm applicable to both regression and…
Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of…
Analyzing data collected from multiple sources to estimate common and heterogeneous structures through a hierarchical model is a central task in Bayesian inference, and to this end, Bayesian factor models are one of the most widely used…
Forecasting tasks using large datasets gathering thousands of heterogeneous time series is a crucial statistical problem in numerous sectors. The main challenge is to model a rich variety of time series, leverage any available external…
Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…
There has been considerable recent interest in Bayesian modeling of high-dimensional networks via latent space approaches. When the number of nodes increases, estimation based on Markov Chain Monte Carlo can be extremely slow and show poor…
Spatial generalized linear mixed-effects models are popularly used to analyze spatially indexed univariate responses. However, with modern technology, it is common to observe vector-valued mixed-type responses, e.g., a combination of…
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
Bayesian regression trees are flexible non-parametric models that are well suited to many modern statistical regression problems. Many such tree models have been proposed, from the simple single- tree model to more complex tree ensembles.…