Bayesian prediction for stochastic processes

Delphine Blanke (1) , Denis Bosq (2)

1 LANLG - Laboratoire d'Analyse non linéaire et Géométrie
2 LSTA - Laboratoire de Statistique Théorique et Appliquée

In this paper, we adopt a Bayesian point of view for predicting real stochastic processes. We give two equivalent definition of a Bayesian predictor and study some properties: admissibility, prediction sufficiency, 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: Bayesian prediction; MAP; Comparing predictors; Poisson process; Ornstein-Uhlenbeck process

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

Delphine Blanke, Denis Bosq. Bayesian prediction for stochastic processes. 2012. ⟨hal-00750263v1⟩