Prediction and Estimation Based on Statistical Models –Considerations Using Poisson Models–

DOI
  • Komaki Fumiyasu
    東京大学大学院情報理工学系研究科 理化学研究所脳神経科学研究センター

Bibliographic Information

Other Title
  • 統計モデルに基づく予測と推定–Poissonモデルを例として–

Abstract

<p>We investigate the theory of predictive distributions, which frames statistical inference from the predictive viewpoint. The performance of a predictive distribution is evaluated by the Kullback-Leibler divergence. Bayesian estimation is formulated as a limit of Bayesian prediction for the multidimensional normal models and the multidimensional Poisson models. The choice of a prior distribution is pivotal in Bayesian estimation, and consequently, there is a wealth of studies on noninformative or shrinkage prior distributions. By emphasizing the relationship between prediction and estimation, we demonstrate how insights from Bayesian estimation can be applied to Bayesian prediction, leading to a novel understanding of Bayesian estimation through Bayesian prediction. To elucidate this relationship, we employ examples based on multidimensional Poisson distributions.</p>

Journal

Keywords

Details 詳細情報について

  • CRID
    1390297372147258240
  • DOI
    10.11329/jjssj.53.185
  • ISSN
    21891478
    03895602
  • Text Lang
    ja
  • Data Source
    • JaLC
  • Abstract License Flag
    Disallowed

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