This session will focus on Bayesian model-based methods that use Bayesian principles to estimate and make inferences about parameters in wide variety of models with applications such as Nuclear Physics and Climate, Epidemiology, Microbial Diversity Assessment, Environment and Ecology, and Health Sciences. The broad range of models such as Bayesian Model Mixing for uncertainty quantification, Bayesian quantile regression models, Bayesian capture recapture models, Bayesian Multinomial models with Smoothed Dirichlet Distribution and hierarchical Pitman-Yor process models will be explored.

Some novel results and methods focusing on the Bayesian Additive Regression Trees (BART) models and their non-linearities, interactions, and heteroscedasticity will be discussed. As computing power grows, computer experiments have become an increasingly popular approach to study the relationship between the inputs and resulting outputs of a computational model. The most popular statistical model in computer experiments is the Gaussian Process model. However, the Bayesian Additive Regression Trees (BART) model can better handle the explosive increase in the quantity of available data. We introduce a BART model with multidimensional outputs and provide an algorithm to find the exact Pareto Front and Set of the function that results from a trained multiple-output BART model. We also introduce two approaches of quantifying the uncertainty of these estimates. We then empirically compare these two uncertainty quantification approaches to each other on several test functions. For this comparison, we propose two metrics that capture certain desirable properties of a Pareto Front or Set estimate.

Bayesian phylogenetic trees to infer the evolutionary relationships among microbial taxa, Hierarchical Bayesian Modeling for Community Dynamics, Uncertainty Quantification in Metagenomic Data; Bayesian capture-recapture models to estimate population sizes or other parameters based on multiple samples and probabilistic framework for capturing uncertainty in parameter estimation; Bayesian quantile regression with asymmetric Laplace distributions with results coming from above applications will be presented. For Multinomial models, we introduce a novel approcah for borrowing information among neighboring cells in order to provide reliable estimates for cell probabilities. The proposed smoothed Dirichlet distribution based approach forces the probabilities of neighboring cells to be closer to each other than under the standard Dirichlet distribution. Basic properties of the proposed distribution, including normalizing constant, moments, and marginal distributions, are developed. Sample generation of smoothed Dirichlet distribution is also discussed using an acceptance-rejection algorithm.

The session includes a set of speakers with diverse career paths, research interests and profiles, stages of career, and backgrounds appealing to a broad audience as given below.

Dr. Matt Pratola - Associate Professor, Department of Statistics, Ohio State University, USA
Dr. Lawrence McCnadless – Professor and Director Faculty of Health Sciences and Associate member of the Department of Statistics and Actuarial Sciences, Simon Fraser University, Burnaby, Canada
Dr. Kevin McGregor - Assistant Professor, Department of Mathematics and Statistics, York University, Canada
Dr. Audrey Béliveau - Assistant Professor in the Department of Statistics and Actuarial Science, University of waterloo, Ontario, Canada
Dr. Saman Muthukumarana – Professor and Director of Data Science Nexus, Department of Statistics, University of Manitoba, Winnipeg, Canada
Dr. Veronica Berrocal (Chair) – Professor of Statistics, University of California, Irvine, USA