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We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely…
In this article, we consider the problem of testing the independence between two random variables. Our primary objective is to develop tests that are highly effective at detecting associations arising from explicit or implicit functional…
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…
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…
A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying…
In this article, we propose a new method for the fundamental task of testing for dependence between two groups of variables. The response densities under the null hypothesis of independence and the alternative hypothesis of dependence are…
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…
In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…
Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…
Decision trees are commonly used predictive models due to their flexibility and interpretability. This paper is directed at quantifying the uncertainty of decision tree predictions by employing a Bayesian inference approach. This is…
Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper,…
Markov Chain Monte Carlo (MCMC) is a popular class of statistical methods for simulating autocorrelated draws from target distributions, including posterior distributions in Bayesian analysis. An important consideration in using simulated…
This paper concerns differentially private Bayesian estimation of the parameters of a population distribution, when a statistic of a sample from that population is shared in noise to provide differential privacy. This work mainly addresses…
We consider the problem of Bayesian inference for changepoints where the number and position of the changepoints are both unknown. In particular, we consider product partition models where it is possible to integrate out model parameters…
McKean-Vlasov stochastic differential equations (MVSDEs) describe systems whose dynamics depend on both individual states and the population distribution, and they arise widely in neuroscience, finance, and epidemiology. In many…
Many analyses of multivariate data focus on evaluating the dependence between two sets of variables, rather than the dependence among individual variables within each set. Canonical correlation analysis (CCA) is a classical data analysis…
Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large…
Prominent features of simulated moving bed (SMB) chromatography processes in the downstream processing is based on the determination of operating conditions. However, effects of different types of uncertainties have to be studied and…