### Retrospective simulation and the Bernoulli factory

Roberts, G; Papaspiliopoulos, O *(Warwick; Pompeu Fabra)*

Wednesday 23 June 2010, 13:40-14.30

Seminar Room 1, Newton Institute

#### Abstract

Retrospective simulation techniques offer flexible and powerful methods for enhancing well-established simulation tools such as Rejection Sampling, Importance Sampling, MCMC and Sequential Monte Carlo. Special cases have been known for a while (for instance coupling from the past for simulating
from Markov chain stationary distributions). This presentation will touch on a number of applications of the methodology, including the exact simulation of diffusion sample paths, and other (apparently) infinite-dimensional simulation problems. The second half of the talk will present joint work with Krzysztof Latuszynski and Ioannis Kosmidis on a solution to the well-known Bernoulli factory problem: given a black box for generating from events of probability p, how can we construct a black box to generate events of probability f(p).
Beskos, A., Papaspiliopoulos, O. and Roberts, G.O. Retrospective Exact Simulation of Diffusion
Sample Paths with Applications, Bernoulli, 12, 6, 1077-1098, 2006. Papaspilioulos, O. and Roberts, G.O. Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models Biometrika, 95, 169–186, 2008.
Latuszyinski, K., Kosmidis, I., Papaspiliopoulos, O. and Roberts, G.O. Simulating events of unknown
probabilities via reverse time martingales, to appear in Random Structures and Algorithms,
2010.

#### Presentation

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