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Markov chain Monte Carlo (MCMC) allows one to generate dependent replicates from a posterior distribution for effectively any Bayesian hierarchical model. However, MCMC can produce a significant computational burden. This motivates us to…

Markov chain Monte Carlo (MCMC) is a popular and successful general-purpose tool for Bayesian inference. However, MCMC cannot be practically applied to large data sets because of the prohibitive cost of evaluating every likelihood term at…

We consider continuous-time diffusion models driven by fractional Brownian motion. Observations are assumed to possess a non-trivial likelihood given the latent path. Due to the non-Markovianity and high-dimensionality of the latent paths,…

Statistical machine learning methods, especially nonparametric Bayesian methods, have become increasingly popular to infer clonal population structure of tumors. Here we describe the treeCRP, an extension of the Chinese restaurant process…

Yang et al. (2016) proved that the symmetric random walk Metropolis--Hastings algorithm for Bayesian variable selection is rapidly mixing under mild high-dimensional assumptions. We propose a novel MCMC sampler using an informed proposal…

We present a Bayesian nonparametric framework for multilevel clustering which utilizes group-level context information to simultaneously discover low-dimensional structures of the group contents and partitions groups into clusters. Using…

Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…

Latent class analysis is used to perform model based clustering for multivariate categorical responses. Selection of the variables most relevant for clustering is an important task which can affect the quality of clustering considerably.…

High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…

In tracking multiple objects, it is often assumed that each observation (measurement) is originated from one and only one object. However, we may encounter a situation that each measurement may or may not be associated with multiple objects…

Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…

Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence…

In this paper, we present a method for computing the marginal likelihood, also known as the model likelihood or Bayesian evidence, from Markov Chain Monte Carlo (MCMC), or other sampled posterior distributions. In order to do this, one…

Radial velocity (RV) planet searches are increasingly finding planets with small velocity amplitudes, with long orbital periods, or in multiple planet systems. Bayesian inference has the potential to improve the interpretation of existing…

Switching state-space models (SSSM) are a very popular class of time series models that have found many applications in statistics, econometrics and advanced signal processing. Bayesian inference for these models typically relies on Markov…

Bayesian inference in the physical sciences faces a fundamental challenge: the imperative for high-fidelity physical modeling often clashes with the intrinsic limitations of stochastic sampling algorithms. Complex, high-dimensional…

We present a case-study demonstrating the usefulness of Bayesian hierarchical mixture modelling for investigating cognitive processes. In sentence comprehension, it is widely assumed that the distance between linguistic co-dependents…

In this work, we propose a new Bayesian spatial homogeneity pursuit method for survival data under the proportional hazards model to detect spatially clustered patterns in baseline hazard and regression coefficients. Specially, regression…

Bayesian inference in biological modeling commonly relies on Markov chain Monte Carlo (MCMC) sampling of a multidimensional and non-Gaussian posterior distribution that is not analytically tractable. Here, we present the implementation of a…

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…