9 papers
Discussion of "Unbiased Markov chain Monte Carlo with couplings" by Pierre E. Jacob, John O'Leary and Yves F. Atchadé
Leah F. South, Chris Nemeth, Chris J. Oates
This is a contribution for the discussion on "Unbiased Markov chain Monte Carlo with couplings" by Pierre E. Jacob, John O'Leary and Yves F. Atchadé to appear in the Journal of the…
Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions
Toni Karvonen, George Wynne, Filip Tronarp +2
Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically ne…
A Locally Adaptive Bayesian Cubature Method
Matthew A Fisher, Chris J Oates, Catherine Powell +1
Bayesian cubature (BC) is a popular inferential perspective on the cubature of expensive integrands, wherein the integrand is emulated using a stochastic process model. Several app…
A Role for Symmetry in the Bayesian Solution of Differential Equations
Junyang Wang, Jon Cockayne, Chris J. Oates
The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators suggests that formal uncertainty quantification can also…
Stein Point Markov Chain Monte Carlo
Wilson Ye Chen, Alessandro Barp, François-Xavier Briol +4
An important task in machine learning and statistics is the approximation of a probability measure by an empirical measure supported on a discrete point set. Stein Points are a cla…
Optimality Criteria for Probabilistic Numerical Methods
Chris. J. Oates, Jon Cockayne, Dennis Prangle +2
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for…