Bayesian Numerical Analysis

By Persi Diaconis. 1988

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Control functionals for Monte Carlo integration (2014, background): “ntication (BUQ) for Monte Carlo integration. In brief, BUQ attempts to model the numerical error that arises from implementing various mathematical and statistical procedures on a computer (see e.g. Diaconis, 1988; O’Hagan, 1992). We brie y review BUQ in the context of Monte Carlo integration and de”
Bayes–Hermite quadrature (1991, background): “Diaconis (1988) traces the origins of this Bayesian approach to quadrature as far back as Poincare (1896), and presents a useful review.”
Predicting the output from a complex computer code when fast approximations are available (2000, methodology): “Diaconis (1988) and O'Hagan (1992) provide useful reviews. In common with many of these techniques, we use a Gaussian process to model the code output. Sacks et al. (1989) present a statistical approach for the speci c problems of design and analysis of computer experiments which uses essentially th”
Bayesian Solution Uncertainty Quantification for Differential Equations (2013, unknown): “iﬁc and engineering problems. Theoretical analyses of Bayesian statistical approaches to classical numerical analysis problems appear to date back all the way to Poincare, as eloquently summarised by Diaconis (1988). O’Hagan (1992); Skilling (1991) 3 also provided practical motivations for developin”
Bayesian Probabilistic Numerical Methods (2017, methodology): “The belief update operator proposed therein, and later considered in Diaconis (1988); O’Hagan (1991) and others, was B(µ, a) = Q#µ a.”
Probabilistic machine learning and artificial intelligence (2015, background): “More generally, Bayesian optimisation is a special case of Bayesian numerical computation [75, 76] which is re-emerging as a very active area of research4, and also includes topics such as solving ordinary differential equations and numerical integration.”
An Analysis of Bayesian Inference for Nonparametric Regression (1993, unknown): “Related models and applications are discussed by Diaconis (1988). More abstract models are discussed in Section 2.”