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Conditional Monte Carlo revisited

Author

Listed:
  • Bo H. Lindqvist
  • Rasmus Erlemann
  • Gunnar Taraldsen

Abstract

Conditional Monte Carlo refers to sampling from the conditional distribution of a random vector X given the value T(X)=t for a function T(X). Classical conditional Monte Carlo methods were designed for estimating conditional expectations of functions ϕ(X) by sampling from unconditional distributions obtained by certain weighting schemes. The basic ingredients were the use of importance sampling and change of variables. In the present paper we reformulate the problem by introducing an artificial parametric model in which X is a pivotal quantity, and next representing the conditional distribution of X given T(X)=t within this new model. The approach is illustrated by several examples, including a short simulation study and an application to goodness‐of‐fit testing of real data. The connection to a related approach based on sufficient statistics is briefly discussed.

Suggested Citation

  • Bo H. Lindqvist & Rasmus Erlemann & Gunnar Taraldsen, 2022. "Conditional Monte Carlo revisited," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 943-968, September.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:3:p:943-968
    DOI: 10.1111/sjos.12549
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    References listed on IDEAS

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    1. Mikael Sunnåker & Alberto Giovanni Busetto & Elina Numminen & Jukka Corander & Matthieu Foll & Christophe Dessimoz, 2013. "Approximate Bayesian Computation," PLOS Computational Biology, Public Library of Science, vol. 9(1), pages 1-10, January.
    2. Richard A. Lockhart & Federico J. O'Reilly & Michael A. Stephens, 2007. "Use of the Gibbs Sampler to Obtain Conditional Tests, with Applications," Biometrika, Biometrika Trust, vol. 94(4), pages 992-998.
    3. Evans, Michael & Swartz, Timothy, 2000. "Approximating Integrals via Monte Carlo and Deterministic Methods," OUP Catalogue, Oxford University Press, number 9780198502784.
    4. Bo Henry Lindqvist & Gunnar Taraldsen, 2005. "Monte Carlo conditioning on a sufficient statistic," Biometrika, Biometrika Trust, vol. 92(2), pages 451-464, June.
    5. Bo Henry Lindqvist, 2003. "A counterexample to a claim about stochastic simulations," Biometrika, Biometrika Trust, vol. 90(2), pages 489-490, June.
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