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Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees
TLDR
This paper presents the first probabilistic integrator that admits such theoretical treatment, called Frank-Wolfe Bayesian Quadrature (FWBQ), which is applied to successfully quantify numerical error in the solution to a challenging Bayesian model choice problem in cellular biology.
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Probabilistic Integration: A Role for Statisticians in Numerical Analysis?
TLDR
This paper examines thoroughly the case for probabilistic numerical methods in statistical computation and a specific case study is presented for Markov chain and Quasi Monte Carlo methods.
Minimum Stein Discrepancy Estimators
TLDR
This work establishes the consistency, asymptotic normality, and robustness of DKSD and DSM estimators, then derive stochastic Riemannian gradient descent algorithms for their efficient optimisation.
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Statistical Inference for Generative Models with Maximum Mean Discrepancy
TLDR
Theoretical properties of a class of minimum distance estimators for intractable generative models, that is, statistical models for which the likelihood is intracted, but simulation is cheap, are studied, showing that they are consistent, asymptotically normal and robust to model misspecification.
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Stein Points
TLDR
The empirical results demonstrate that Stein Points enable accurate approximation of the posterior at modest computational cost, and theoretical results are provided to establish convergence of the method.
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Bayesian Quadrature for Multiple Related Integrals
TLDR
This paper proposes the first Bayesian probabilistic numerical method by extending the well-known Bayesian quadrature algorithm to the case where it is interested in computing the integral of several related functions, and demonstrates its efficiency in the context of multi-fidelity models for complex engineering systems, as well as a problem of global illumination in computer graphics.
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Robust generalised Bayesian inference for intractable likelihoods
Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis‐specification of the…
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On the Sampling Problem for Kernel Quadrature
TLDR
It is argued that the practical choice of sampling distribution is an important open problem and a novel automatic approach based on adaptive tempering and sequential Monte Carlo is considered, demonstrating a dramatic reduction in integration error.
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Stein’s Method Meets Statistics: A Review of Some Recent Developments
Stein’s method is a collection of tools for analysing distributional comparisons through the study of a class of linear operators called Stein operators. Originally studied in probability, Stein’s…
Geometry and Dynamics for Markov Chain Monte Carlo
TLDR
The aim of this review is to provide a comprehensive introduction to the geometric tools used in Hamiltonian Monte Carlo at a level accessible to statisticians, machine learners, and other users of the methodology with only a basic understanding of Monte Carlo methods.
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