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Approximate Bayesian computation (ABC) is a widely used inference method in Bayesian statistics to bypass the point-wise computation of the likelihood. In this paper we develop theoretical bounds for the distance between the statistics used…

The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of un-…

When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior…

Integration over non-negative integrands is a central problem in machine learning (e.g. for model averaging, (hyper-)parameter marginalisation, and computing posterior predictive distributions). Bayesian Quadrature is a probabilistic…

We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the…

We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii)…

Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Monte Carlo techniques such as Markov Chain Monte Carlo (MCMC) and nested sampling. However, these techniques are time…

Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte…

Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…

Bayesian methods are commonly applied to solve image analysis problems such as noise-reduction, feature enhancement and object detection. A primary limitation of these approaches is the computational complexity due to the interdependence of…

We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…

Exponential random graph models are a class of widely used exponential family models for social networks. The topological structure of an observed network is modelled by the relative prevalence of a set of local sub-graph configurations…

I describe an approach to fitting and comparison of radio spectra based on Bayesian analysis and realised using a new implementation of the nested sampling algorithm. Such an approach improves on the commonly used maximum-likelihood fitting…

Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior…

In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…

In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating…

We present a randomized maximum a posteriori (rMAP) method for generating approximate samples of posteriors in high dimensional Bayesian inverse problems governed by large-scale forward problems. We derive the rMAP approach by: 1) casting…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure observed in many such Inverse Problems presents severe…