Bayesian Prediction for Stochastic Processes: Theory and Applications

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• 作者：Delphine Blanke (1)
  Denis Bosq (2)
  
  1. Avignon University ; LMA EA2151 ; F-84000 ; Avignon ; France
  2. Sorbonne Universit茅s ; UPMC Univ Paris 06 ; EA 3124 ; L.S.T.A. F-75005 ; Paris ; France
  
• 关键词：Bayesian prediction ; MAP ; Comparing predictors ; Poisson process ; Ornstein ; Uhlenbeck process. ; 62M20 ; 62F15.
• 刊名：Sankhya A
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：77
• 期：1
• 页码：79-105
• 全文大小：458 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistical Theory and Methods
  Statistics Computing and Software
  Statistics
  
• 出版者：Springer India
• ISSN：0976-8378

文摘

In this paper, we adopt a Bayesian point of view for predicting real continuous-time processes. We give two equivalent definitions of a Bayesian predictor and study some properties: admissibility, non-unbiasedness, prediction sufficiency, comparison with efficient predictors. Prediction of Poisson process and prediction of Ornstein-Uhlenbeck process in the continuous and sampled situations are considered. Various simulations illustrate comparison with non-Bayesian predictors.