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The development of statistical methods and numerical algorithms for model choice is vital to many real-world applications. In practice, the ABC approach can be instrumental for sequential model design; however, the theoretical basis of its…

Approximate Bayesian Computation (ABC) has become increasingly prominent as a method for conducting parameter inference in a range of challenging statistical problems, most notably those characterized by an intractable likelihood function.…

We develop a computationally efficient framework for quasi-Bayesian inference based on linear moment conditions. The approach employs a delayed acceptance Markov chain Monte Carlo (DA-MCMC) algorithm that uses a surrogate target kernel and…

Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…

A popular method for likelihood-free inference is approximate Bayesian computation sequential Monte Carlo (ABC-SMC) algorithms. These approximate the posterior using a population of particles, which are updated using Markov kernels. Several…

There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the…

The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…

We present a data augmentation scheme to perform Markov chain Monte Carlo inference for models where data generation involves a rejection sampling algorithm. Our idea, which seems to be missing in the literature, is a simple scheme to…

Gibbs sampling is one of the most commonly used Markov Chain Monte Carlo (MCMC) algorithms due to its simplicity and efficiency. It cycles through the latent variables, sampling each one from its distribution conditional on the current…

Model selection in the presence of intractable likelihoods remains a central challenge in Bayesian inference. Approximate Bayesian computation (ABC) provides a flexible likelihood-free framework, but its use for model choice is known to be…

The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…

Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…

In the following article we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which…

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…

We introduce Preconditioned Monte Carlo (PMC), a novel Monte Carlo method for Bayesian inference that facilitates efficient sampling of probability distributions with non-trivial geometry. PMC utilises a Normalising Flow (NF) in order to…

The computational efficiency of approximate Bayesian computation (ABC) has been improved by using surrogate models such as Gaussian processes (GP). In one such promising framework the discrepancy between the simulated and observed data is…

We use approximate Bayesian computation (ABC) combined with an "improved" Markov chain Monte Carlo (IMCMC) method to estimate posterior distributions of model parameters in subgrid-scale (SGS) closures for large eddy simulations (LES) of…

Gibbs sampling is a Markov Chain Monte Carlo (MCMC) method often used in Bayesian learning. MCMC methods can be difficult to deploy on parallel and distributed systems due to their inherently sequential nature. We study asynchronous Gibbs…

This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del…

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an…