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Approximate Bayesian computation (ABC) is one of the most popular "likelihood-free" methods. These methods have been applied in a wide range of fields by providing solutions to intractable likelihood problems in which exact Bayesian…
Bayesian nonparametric mixture models offer a rich framework for model based clustering. We consider the situation where the kernel of the mixture is available only up to an intractable normalizing constant. In this case, most of the…
Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalising constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and…
By the nature of their construction, many statistical models for extremes result in likelihood functions that are computationally prohibitive to evaluate. This is consequently problematic for the purposes of likelihood-based inference. With…
This Chapter, "ABC Samplers", is to appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). It details the main ideas and algorithms used to sample from the ABC approximation to the posterior distribution, including…
Modern imaging methods rely strongly on Bayesian inference techniques to solve challenging imaging problems. Currently, the predominant Bayesian computation approach is convex optimisation, which scales very efficiently to high dimensional…
Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…
Likelihood-free methods, such as approximate Bayesian computation, are powerful tools for practical inference problems with intractable likelihood functions. Markov chain Monte Carlo and sequential Monte Carlo variants of approximate…
Cosmological inference becomes increasingly difficult when complex data-generating processes cannot be modeled by simple probability distributions. With the ever-increasing size of data sets in cosmology, there is increasing burden placed…
Almost all fields of science rely upon statistical inference to estimate unknown parameters in theoretical and computational models. While the performance of modern computer hardware continues to grow, the computational requirements for the…
Approximate Bayesian Computation (ABC) methods have become essential tools for performing inference when likelihood functions are intractable or computationally prohibitive. However, their scalability remains a major challenge in…
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…
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…
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…
Approximate Bayesian computation (ABC) is a class of algorithmic methods in Bayesian inference using statistical summaries and computer simulations. ABC has become popular in evolutionary genetics and in other branches of biology. However…
We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for…
We derive the optimal proposal density for Approximate Bayesian Computation (ABC) using Sequential Monte Carlo (SMC) (or Population Monte Carlo, PMC). The criterion for optimality is that the SMC/PMC-ABC sampler maximise the effective…
Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also…
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…
This position paper summarizes a recently developed research program focused on inference in the context of data centric science and engineering applications, and forecasts its trajectory forward over the next decade. Often one endeavours…