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When using Markov chain Monte Carlo (MCMC) algorithms to perform inference for Bayesian clustering models, such as mixture models, the output is typically a sample of clusterings (partitions) drawn from the posterior distribution. In…

For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare…

Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of partial differential equations. In…

Gene-gene and gene-environment interactions are widely believed to play significant roles in explaining the variability of complex traits. While substantial research exists in this area, a comprehensive statistical framework that addresses…

Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference…

Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density.…

Understanding how features interact with each other is of paramount importance in many scientific discoveries and contemporary applications. Yet interaction identification becomes challenging even for a moderate number of covariates. In…

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…

Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the…

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…

We address the common yet often-overlooked selection bias in interventional studies, where subjects are selectively enrolled into experiments. For instance, participants in a drug trial are usually patients of the relevant disease; A/B…

Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…

Telling apart the cause and effect between two random variables with purely observational data is a challenging problem that finds applications in various scientific disciplines. A key principle utilized in this task is the algorithmic…

Autoencoders gained popularity in the deep learning revolution given their ability to compress data and provide dimensionality reduction. Although prominent deep learning methods have been used to enhance autoencoders, the need to provide…

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…

Probabilistic modeling of multidimensional spatiotemporal data is critical to many real-world applications. As real-world spatiotemporal data often exhibits complex dependencies that are nonstationary and nonseparable, developing effective…

Predicated on the increasing abundance of electronic health records, we investi- gate the problem of inferring individualized treatment effects using observational data. Stemming from the potential outcomes model, we propose a novel multi-…

We study the problem of high-dimensional regression when there may be interacting variables. Approaches using sparsity-inducing penalty functions such as the Lasso can be useful for producing interpretable models. However, when the number…

Due to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for…