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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…

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…

Bayesian model selection enables comparison and ranking of conceptual subsurface models described by spatial prior models, according to the support provided by available geophysical data. Deep generative neural networks can efficiently…

Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…

We introduce a framework for efficient Markov Chain Monte Carlo (MCMC) algorithms targeting discrete-valued high-dimensional distributions, such as posterior distributions in Bayesian variable selection (BVS) problems. We show that many…

Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single…

Riemannian manifold Hamiltonian Monte Carlo (RMHMC) is a sampling algorithm that seeks to adapt proposals to the local geometry of the posterior distribution. The specific form of the Hamiltonian used in RMHMC necessitates {\it…

Leaving posterior sensitivity concerns aside, non-identifiability of the parameters does not raise a difficulty for Bayesian inference as far as the posterior is proper, but multi-modality or flat regions of the posterior induced by the…

As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…

Importance sampling (IS) is commonly used for cross validation (CV) in Bayesian models, because it only involves reweighting existing posterior draws without needing to re-estimate the model by re-running Markov chain Monte Carlo (MCMC).…

Many scientific and engineering problems require to perform Bayesian inferences in function spaces, in which the unknowns are of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary…

This paper studies distributed Bayesian learning in a setting encompassing a central server and multiple workers by focusing on the problem of mitigating the impact of stragglers. The standard one-shot, or embarrassingly parallel, Bayesian…

Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…

In this paper we consider fully Bayesian inference in general state space models. Existing particle Markov chain Monte Carlo (MCMC) algorithms use an augmented model that takes into account all the variable sampled in a sequential Monte…

Reversible Markov chains play a central role in stochastic modelling and in algorithms such as Markov chain Monte Carlo (MCMC). Motivated by the fundamental importance of reversibility in classical settings, this paper develops a…

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…

An important feature of Bayesian statistics is the opportunity to do sequential inference: the posterior distribution obtained after seeing a dataset can be used as prior for a second inference. However, when Monte Carlo sampling methods…

Markov Chain Monte Carlo (MCMC) algorithms are routinely used to draw samples from distributions with intractable normalization constants. However, standard MCMC algorithms do not apply to doubly-intractable distributions in which there are…

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…

Developing an efficient computational scheme for high-dimensional Bayesian variable selection in generalised linear models and survival models has always been a challenging problem due to the absence of closed-form solutions for the…