The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Further development in the integration of multimodal functions by Monte Caro importance sampling

다봉 함수의 다차원 적분을 위한 몬테카를로 기법의 개선

  • Man Suk Oh (Department of Statistics, Ewha Womens University, Seo-Dae-Moon-Gu, Seoul 120-750, Korea)
  • Published : 1994.09.01
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Abstract

The algorithm of Oh and Berger (1993) is extended to handle more general cases where the integrand $f(\theta)$ is not only multimodal but also skewed or has some undetected modes, each having curvature not much different from that of the nearest component. It runs Oh and Berger's algorithm in an iterative way, adding a component in each stage to the mixture importance function from previous stage for better approximation between $f(\theta)$ and the importance function.

본 논문에서는 Oh and Berger (1993)의 알고리즘을 확장하여, Oh and Berger의 알고리즘으로 효율적 처리가 어려웠던 복잡한 모양을 가진 다차원 함수의 적분에 보다 더 일반적으로 적용될 수 있는 알고리즘을 제시한다. 예를 들면 다봉함수이면서 동시에 기울어진 모양을 갖는 함수나 모든 극대점들이 다 파악되지 못한 경우 등이다. 제시된 알고리즘은 Oh and Berger의 알고리즘을 단계적으로 수행해 가면서 각 단계마다 새로운 부확률밀도 함수 (component density functin)를 함성 밀도 함수(mixture importance function) 형태인 중요함 수 (importance function에 더해 감으로써 중요함수를 적분 함수에 접근시킨다.

Keywords

References

  1. Biometrika v.76 Latent Class Anaysis of Two-way Contingency Tables by Bayesian Methods Evans,M.;Gilula,Z.;Guttman,I.
  2. Annals of Statistics v.19 Chaining via Annealing Evans,M.
  3. American Mathematical Society Contemporary Mathematics Adaptive Importance Sampling and Chaining Evans,M.;N.Flournoy(eds.);R.Tsutakawa(eds.)
  4. Finite Mixture Distributions Everitt,B.S.;Hand,D.J.
  5. Journal of the American Statistical Association v.85 Sampling Based Approaches to Calculating Marginal Densities Gelfand,A.;Smith,A.F.M.
  6. Journal of the American Statistical Association v.87 Bayesian Anaysis of Constrained Parameter and Truncated Data Problems Using Gibbs Sampling Gelfand,A.;Smith,A.F.M.;Lee,T.M.
  7. Journal of the American Statistical Association v.85 Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling Gelfand,A.;Hills,S.;Racine-Poon,A.;Smith,A.F.M.
  8. IEEE Transactionson Pattern Analysis and Machine Inteligence v.6 Stochastic Relaxation, Gibbs Distributions and Bayesian Restoration of Images Geman,S.;Geman,D.
  9. Journal of Econometrics v.38 Antithetic Acceleration of Monte Carlo Integration in Bayesian Inference Geweke,J.
  10. Econometrica v.46 Bayesian Inference in Econometric Models Using Monte Carlo Integration Geweke,J.
  11. Applied Statistics v.31 Application of a Method for the Efficient Computation of Posterior Distributions Naylor,J.C.;Smith,A.F.M.
  12. Journal of Econometrics v.38 Econometric Illustrations of Novel Numerical Integration Strategies for Bayesian Inference Naylor,J.C.;Smith,A.F.M.
  13. Journal of Statistical Computing and Simulation v.41 Adaptive Importance Smapling in Monte Carlo Integration Oh,M.S.;Berger,J.O.
  14. Journal of the American Statistical Association v.88 Integration of Multimodal Functions by Monte Carlo Importance Function Oh,M.S.;Berger,J.O.
  15. Communications in Statistics - Theory and Method v.14 The Implementation of the Bayesian Paradigm Smith,A.F.M.;Sken,A.M.;Shaw,J.E.H.;Naylor,J.C.;Dransfield,M.
  16. Journal of the American Statistical Association v.82 The Calculation of Posterior Distributions by Data Augmentation Tanner,M.;Wong,W.
  17. Statistical Analysis of Finite Mixture Distributions Titterlington,D.M.;Smith,A.F.M.;Makov,U.E.
  18. Tech Report 90-A10 Bayesian Computation: Monte Carlo Density Estimation West,M.
  19. Journal of Econometrics v.29 Posterior Moments Computed by Mixed Integration van Dijk,H.K.;Klock,T.;Boender,C.G.E.