Bayesian prediction for stochastic processes. Theory and applications

2012/11/10 by Delphine Blanke, Blanke, Delphine, Denis Bosq +1
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1211.2300

18 pages

arxiv created 2013/12/28 · arxiv updated 2013/12/31

Abstract

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, prediction sufficiency, non-unbiasedness, 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.

Related

• Prediction theory in continuous time
• Characterizing predictable classes of processes
• Characterizing predictable classes of processes
• Bayesian Characterizations of Properties of Stochastic Processes with Applications
• Inference, Prediction, and Entropy-Rate Estimation of Continuous-time, Discrete-event Processes