GIBBS SAMPLING FOR MARGINAL POSTERIOR EXPECTATIONS

被引：43
作者：
GELFAND, AE
SMITH, AFM
机构：
[1] UNIV CONNECTICUT,DEPT STAT,STORRS,CT 06269
[2] IMPERIAL COLL SCI TECHNOL & MED,DEPT MATH,LONDON SW7 2BZ,ENGLAND
来源：
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 1991年 / 20卷 / 5-6期
关键词：
BAYESIAN INFERENCE; MARGINAL POSTERIOR EXPECTATIONS; GIBBS SAMPLER; LAPLACE METHOD; AGGREGATED MULTINOMIAL MODEL; VARIANCE COMPONENTS MODEL; NORMAL-LINEAR HIERARCHICAL MODEL;
D O I：
10.1080/03610929108830595
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In earlier work (Gelfand and Smith, 1990 and Gelfand et al, 1990) a sampling based approach using the Gibbs sampler was offered as a means for developing marginal posterior densities for a wide range of Bayesian problems several of which were previously inaccessible. Our purpose here is two-fold. First we flesh out the implementation of this approach for calculation of arbitrary expectations of interest. Secondly we offer comparison with perhaps the most prominent approach for calculating posterior expectations, analytic approximation involving application of the LaPlace method. Several illustrative examples are discussed as well. Clear advantages for the sampling based approach emerge.
引用
收藏
页码：1747 / 1766
页数：20
相关论文
共 39 条
  • [1] ACHCAR JA, 1990, ESSAYS HONOR GA BARN
  • [2] BARTLEY HO, 1958, BIOMETRICS, V14, P174
  • [3] BESAG J, 1974, J ROY STAT SOC B MET, V36, P192
  • [4] Box G.E.P., 1992, BAYESIAN INFERENCE S
  • [5] DEBRUIJN NG, 1961, ASYMPTOTIC METHODS A
  • [6] MAXIMUM LIKELIHOOD FROM INCOMPLETE DATA VIA EM ALGORITHM
    DEMPSTER, AP
    LAIRD, NM
    RUBIN, DB
    [J]. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL, 1977, 39 (01): : 1 - 38
  • [7] Devroye L., 1986, NONUNIFORM RANDOM VA
  • [8] SAMPLING-BASED APPROACHES TO CALCULATING MARGINAL DENSITIES
    GELFAND, AE
    SMITH, AFM
    [J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1990, 85 (410) : 398 - 409
  • [9] ILLUSTRATION OF BAYESIAN-INFERENCE IN NORMAL DATA MODELS USING GIBBS SAMPLING
    GELFAND, AE
    HILLS, SE
    RACINEPOON, A
    SMITH, AFM
    [J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1990, 85 (412) : 972 - 985
  • [10] STOCHASTIC RELAXATION, GIBBS DISTRIBUTIONS, AND THE BAYESIAN RESTORATION OF IMAGES
    GEMAN, S
    GEMAN, D
    [J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 1984, 6 (06) : 721 - 741
1234