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RISS 인기검색어
- 검색키워드
- 저자 : MacEachern Steven N. (검색결과 2 건)
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Nonparametric Bayesian methods: a gentle introduction and overview
MacEachern, Steven N. The Korean Statistical Society 2016 Communications for statistical applications and me Vol.23 No.6
Nonparametric Bayesian methods have seen rapid and sustained growth over the past 25 years. We present a gentle introduction to the methods, motivating the methods through the twin perspectives of consistency and false consistency. We then step through the various constructions of the Dirichlet process, outline a number of the basic properties of this process and move on to the mixture of Dirichlet processes model, including a quick discussion of the computational methods used to fit the model. We touch on the main philosophies for nonparametric Bayesian data analysis and then reanalyze a famous data set. The reanalysis illustrates the concept of admissibility through a novel perturbation of the problem and data, showing the benefit of shrinkage estimation and the much greater benefit of nonparametric Bayesian modelling. We conclude with a too-brief survey of fancier nonparametric Bayesian methods.
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A new proof of the stick-breaking representation of Dirichlet processes
이재용,MacEachern Steven N. 한국통계학회 2020 Journal of the Korean Statistical Society Vol.49 No.2
The stick-breaking representation is one of the fundamental properties of the Dirichlet process. It represents the random probability measure as a discrete random sum whose weights and atoms are formed by independent and identically distributed sequences of beta variates and draws from the normalized base measure of the Dirichlet process parameter. It is used extensively in posterior simulation for statistical models with Dirichlet processes. The original proof of Sethuraman (Stat Sin 4:639–650, 1994) relies on an indirect distributional equation and does not encourage an intuitive understanding of the property. In this paper, we give a new proof of the stick-breaking representation of the Dirichlet process that provides an intuitive understanding of the theorem. The proof is based on the posterior distribution and self-similarity properties of the Dirichlet process.
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