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The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…

Advances in digital sensors, digital data storage and communications have resulted in systems being capable of accumulating large collections of data. In the light of dealing with the challenges that massive data present, this work proposes…

Bayesian computation crucially relies on Markov chain Monte Carlo (MCMC) algorithms. In the case of massive data sets, running the Metropolis-Hastings sampler to draw from the posterior distribution becomes prohibitive due to the large…

In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target…

Modern macroeconometrics often relies on time series models for which it is time-consuming to evaluate the likelihood function. We demonstrate how Bayesian computations for such models can be drastically accelerated by reweighting and…

Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…

In the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo sampling strategies are the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density…

We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the…

We deal with Bayesian inference for Beta autoregressive processes. We restrict our attention to the class of conditionally linear processes. These processes are particularly suitable for forecasting purposes, but are difficult to estimate…

Discrete mixture models are routinely used for density estimation and clustering. While conducting inferences on the cluster-specific parameters, current frequentist and Bayesian methods often encounter problems when clusters are placed too…

Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…

We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency…

Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…

In this paper we consider the modeling of measurement error for fund returns data. In particular, given access to a time-series of discretely observed log-returns and the associated maximum over the observation period, we develop a…

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…

In cohort studies binary outcomes are very often analyzed by logistic regression. However, it is well-known that when the goal is to estimate a risk ratio, the logistic regression is inappropriate if the outcome is common. In these cases, a…

Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…

Rich data generating mechanisms are ubiquitous in this age of information and require complex statistical models to draw meaningful inference. While Bayesian analysis has seen enormous development in the last 30 years, benefitting from the…

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…

We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…