Bayesian prediction for stochastic processes. Theory and applications

TL;DR

This paper develops a Bayesian framework for predicting continuous-time stochastic processes, analyzing properties and comparing with non-Bayesian methods through simulations on Poisson and Ornstein-Uhlenbeck processes.

Contribution

It introduces two equivalent Bayesian predictor definitions and studies their properties, applying them to Poisson and Ornstein-Uhlenbeck processes with simulation comparisons.

Findings

Bayesian predictors are shown to be admissible and prediction sufficient.

Simulations demonstrate advantages over non-Bayesian predictors.

The approach applies to both continuous and sampled data scenarios.

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.