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We develop Bayesian nonparametric models for spatially indexed data of mixed type. Our work is motivated by challenges that occur in environmental epidemiology, where the usual presence of several confounding variables that exhibit complex…

We consider the prediction of weak effects in a multiple-output regression setup, when covariates are expected to explain a small amount, less than $\approx 1%$, of the variance of the target variables. To facilitate the prediction of the…

This study investigates an inverse problem associated with a time-fractional HIV infection model incorporating nonlinear diffusion. The model describes the dynamics of uninfected target cells, infected cells, and free virus particles, where…

Image data are increasingly encountered and are of growing importance in many areas of science. Much of these data are quantitative image data, which are characterized by intensities that represent some measurement of interest in the…

It is argued that the Calibrated Bayesian (CB) approach to statistical inference capitalizes on the strength of Bayesian and frequentist approaches to statistical inference. In the CB approach, inferences under a particular model are…

This paper introduces new techniques for estimating, identifying and simulating mixed causal-noncausal invertible-noninvertible models. We propose a framework that integrates high-order cumulants, merging both the spectrum and bispectrum…

Medical prediction applications often need to deal with small sample sizes compared to the number of covariates. Such data pose problems for prediction and variable selection, especially when the covariate-response relationship is…

The explosion in known microbial diversity in the last two decades has made it abundantly clear that microbes in the environment do not exist in isolation; they are members of communities. Accordingly, omics approaches such as metagenomics…

The assessment of diversity and similarity is relevant in monitoring the status of ecosystems. The respective indicators are based on the taxonomic composition of biological communities of interest, currently estimated through the…

Distributed Lag Models (DLMs) and similar regression approaches such as MIDAS have been used for many decades in econometrics and more recently to investigate how poor air quality adversely affects human health. In this paper we describe…

We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of…

Dynamic prediction of causal effects under different treatment regimes conditional on an individual's characteristics and longitudinal history is an essential problem in precision medicine. This is challenging in practice because outcomes…

Motivated by the need to study the molecular mechanism underlying Type 1 Diabetes (T1D) with the gene expression data collected from both the patients and healthy controls at multiple time points, we propose an innovative method for jointly…

We develop a new longitudinal count data regression model that accounts for zero-inflation and spatio-temporal correlation across responses. This project is motivated by an analysis of Iowa Fluoride Study (IFS) data, a longitudinal cohort…

Clustering is commonly performed as an initial analysis step for uncovering structure in 'omics datasets, e.g. to discover molecular subtypes of disease. The high-throughput, high-dimensional nature of these datasets means that they provide…

We propose a Bayesian nonparametric model for mixed-type bounded data, where some variables are compositional and others are interval-bounded. Compositional variables are non-negative and sum to a given constant, such as the proportion of…

Network estimation and variable selection have been extensively studied in the statistical literature, but only recently have those two challenges been addressed simultaneously. In this paper, we seek to develop a novel method to…

The case-cohort study design bypasses resource constraints by collecting certain expensive covariates for only a small subset of the full cohort. Weighted Cox regression is the most widely used approach for analysing case-cohort data within…

We develop and apply a learning framework for parameter estimation in initial value problems that are assessed only indirectly via aggregate data such as sample means and/or standard deviations. Our comprehensive framework follows Bayesian…

Microbial ecology serves as a foundation for a wide range of scientific and biomedical studies. Rapidly-evolving high-throughput sequencing technology enables the comprehensive search for microbial biomarkers using longitudinal experiments.…