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Recent advances on overfitting Bayesian mixture models provide a solid and straightforward approach for inferring the underlying number of clusters and model parameters in heterogeneous datasets. The applicability of such a framework in…
Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…
Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…
Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC)…
We consider the problem of optimizing a real-valued continuous function $f$ using a Bayesian approach, where the evaluations of $f$ are chosen sequentially by combining prior information about $f$, which is described by a random process…
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…
We develop clustering procedures for longitudinal trajectories based on a continuous-time hidden Markov model (CTHMM) and a generalized linear observation model. Specifically in this paper, we carry out finite and infinite mixture…
Bayesian data analysis is widely used across many disciplines, and representative examples in materials science include spectral analysis and sparse modeling. In such applications, the underlying models often become complex and yield…
This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…
This paper presents a Markov chain Monte Carlo method to generate approximate posterior samples in retrospective multiple changepoint problems where the number of changes is not known in advance. The method uses conjugate models whereby the…
Finite mixture models are used in statistics and other disciplines, but inference for mixture models is challenging due, in part, to the multimodality of the likelihood function and the so-called label switching problem. We propose…
In many applications of Bayesian clustering, posterior sampling on the discrete state space of cluster allocations is achieved via Markov chain Monte Carlo (MCMC) techniques. As it is typically challenging to design transition kernels to…
Bayesian Decision Trees (DTs) are generally considered a more advanced and accurate model than a regular Decision Tree (DT) because they can handle complex and uncertain data. Existing work on Bayesian DTs uses Markov Chain Monte Carlo…
Decision tree learning is a popular approach for classification and regression in machine learning and statistics, and Bayesian formulations---which introduce a prior distribution over decision trees, and formulate learning as posterior…
Recent developments in big data and analytics research have produced an abundance of large data sets that are too big to be analyzed in their entirety, due to limits on computer memory or storage capacity. To address these issues,…
Conditional heteroscedastic (CH) models are routinely used to analyze financial datasets. The classical models such as ARCH-GARCH with time-invariant coefficients are often inadequate to describe frequent changes over time due to market…