Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Monte Carlo Estimation of Multivariate Normal Probabilities

  • Published : 1999.12.01
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Abstract

A simulation-based approach to estimating the probability of an arbitrary region under a multivariate normal distribution is developed. In specific, the probability is expressed as the ratio of the unrestricted and the restricted multivariate normal density functions, where the restriction is given by the region whose probability is of interest. The density function of the restricted distribution is then estimated by using a sample generated from the Gibbs sampling algorithm.

Keywords

References

  1. Journal of the American Statistical Association v.90 Marginal Likelihood from the Gibbs Output Chib, S.
  2. Non-Uniform Random Generation Devroye, M.
  3. Journal of Statistical Computation and Simulation v.30 Monte Carlo Computation of Some Multivariate Normal Probabilities Evans, M.;Swartz, T.
  4. Journal of the American Statistical Association v.85 Sampling-Based Approaches to Calculating Marginal Densities Gelfand, A.E.;Smith, A.F.M.
  5. Journal of Computational and Graphical Statistics v.1 Numerical Computation of Multivariate Normal Probabilities Genz, A.
  6. Journal of Applied Econometrics v.1 Exact Inference in the Inequality Constrainded Normal Linear Regression Model Geweke, M.
  7. Computing Science and Statistics (Proceeding of the 23rd Symposium on the Interface) Efficient Simulation from the Multivariate Normal and Student-t Distributions Subject to Linear Constraints Geweke, M.
  8. Continuous Multivariate Distributions Johnson, N.L.;Kotz, S.
  9. Communications in Statistics-Theory and Methods(to appear) A Bayes Test for Simple versus One-sided Hypotheses on Multivariate Normal Mean Oh, M-S
  10. Computational Statistics and Data Analysis(in revision) Estimation of Posterior Density Functions from a Posterior Sample Oh, M-S
  11. Simulation and the Monte Carlo Method Rubinstein, R. Y.
  12. The Annals of Statistics v.22 Markov Chains for Exploring Posterior Distributions Tierney, L.