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The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

This paper proposes approaches for the analysis of multiple changepoint models when dependency in the data is modelled through a hierarchical Gaussian Markov random field. Integrated nested Laplace approximations are used to approximate…

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…

Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and…

In this work we propose a new matrix-free implementation of the Wiener sampler which is traditionally applied to high dimensional analysis when signal covariances are unknown. Specifically, the proposed method addresses the problem of…

Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with…

Gaussian Process Regression (GPR) is widely used for inferring functions from noisy data. GPR crucially relies on the choice of a kernel, which might be specified in terms of a collection of hyperparameters that must be chosen or learned.…

This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…

We use Bayesian model selection paradigms, such as group least absolute shrinkage and selection operator priors, to facilitate generalized additive model selection. Our approach allows for the effects of continuous predictors to be…

Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…

In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing…

Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for…

Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We…

We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…

We develop a new method to sample from posterior distributions in hierarchical models without using Markov chain Monte Carlo. This method, which is a variant of importance sampling ideas, is generally applicable to high-dimensional models…

We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any…

Although variable selection is one of the most popular areas of modern statistical research, much of its development has taken place in the classical paradigm compared to the Bayesian counterpart. Somewhat surprisingly, both the paradigms…

Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…

A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…

This paper is devoted to the problem of sampling Gaussian fields in high dimension. Solutions exist for two specific structures of inverse covariance : sparse and circulant. The proposed approach is valid in a more general case and…