Monte Carlo is fundamentally unsound

By Anthony OʼHagan. 1987

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Control functionals for Monte Carlo integration (2014, methodology): “Oakley and O’Hagan (2002). Specifically, we consider a computer model to be “complex” when either (i) X is expensive to simulate, or (ii) f is expensive to evaluate, where in each case the cost is defined relative to the required estimator precision.”
Importance Sampling Policy Evaluation with an Estimated Behavior Policy (2018, methodology): “The problem of sampling error is related to a Bayesian objection to Monte Carlo integration techniques: OIS ignores information about the closeness of trajectories in D (O’Hagan, 1987; Ghahramani & Rasmussen, 2003).”
Towards Real-Time Information Processing of Sensor Network Data Using Computationally Efficient Multi-output Gaussian Processes (2008, background): “Bayesian Monte Carlo makes the best use of all pertinent information [14].”
Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees (2015, background): “Classical numerical integration schemes do not account for prior information on the integrand and, as a consequence, can require an excessive number of function evaluations to obtain a prescribed level of accuracy [21].”
Information Theory, Inference, and Learning Algorithms (2004, methodology): “One curious defect of these Monte Carlo methods – which are widely used by Bayesian statisticians – is that they are all non-Bayesian (O’Hagan, 1987).”
Bayesian Probabilistic Numerical Methods (2017, unknown): “Bayesian Probabilistic Numerical Methods Jon Cockayne∗ Chris Oates† Tim Sullivan‡ Mark Girolami§ July 10, 2017 The emergent field of probabilistic numerics has thus far lacked clear statistical principals.”
Bayesian Gaussian processes for sequential prediction, optimisation and quadrature (2010, background): “Of course, such an approach ignores relevant information and privileges irrelevant information [O’Hagan, 1987].”
Bayesian Reinforcement Learning (2010, background): “Although MC estimates are unbiased, they tend to suffer from high variance, or alternatively, require excessive sample sizes (see O’Hagan, 1987 for a discussion).”
Black-box Importance Sampling (2016, result): “This appears to be a paradox (using less information yet getting better results), but is consistent with the arguments of O’Hagan (1987) that “Monte Carlo (that uses the proposal information) is fundamentally un-sound” for violating the Likelihood Principle, and the interesting results of Henmi et…”
Bayesian Monte Carlo (2002, background): “As O’Hagan [1987] points out, there are two important objections to these procedures.”
Bayes–Hermite quadrature (1991, background): “However, O’Hagan (1987) criticises the underlying philosophy of Monte Carlo quadrature.”