Bayesian Prediction for Stochastic Processes

Ahadzadeh, Zahra (2019) Bayesian Prediction for Stochastic Processes. Masters thesis, University of Mohaghegh Ardabili.

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Abstract

Research Aim: Primary purpose of dissertation, the study predicts continuous time process from a bayesian perspective. Research method:In this dissertation, needsPoisson process, Ornstein-Uhlenbeck processBayesian predictor, sufficiency and unbiasedness. Findings:Given two equivalent definitions of a Bayesian predictor and considering the predictions of Poisson process and predictions of Ornstein-Uhlenbeck process, study some properties: admissibility, unbiasedness, sufficiencyand also their efficiency. Finally, have been compared using the simulations method Bayesian and non-Bayesian predictors. Conclusion: Inference based on Bayesian method, choicing a priori function for the unknown parameter has a significant effecet on error estimation and prediction. Also, the Bayesian method performs better than in the method classical in estimation and prediction for fewdata samples.

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