Bayesian prediction for stochastic processes. Theory and applications

Delphine Blanke (1) , Denis Bosq (2)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 LSTA - Laboratoire de Statistique Théorique et Appliquée

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.

Mots clés: Comparing predictors; Poisson process; Ornstein-Uhlenbeck process; Bayesian prediction; MAP

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Delphine Blanke, Denis Bosq. Bayesian prediction for stochastic processes. Theory and applications. 2013. ⟨hal-00750263v2⟩