Bayesian parameter estimation applied to (non-)Gaussian random fields

Bachelor thesis (2021)

Authors

L. Klomp Electrical Engineering, Mathematics and Computer Science

Contributors

G.N.J.C. Bierkens Statistics - EEMCS (mentor)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2021 Levi Klomp
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Published Date

30-06-2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

The purpose of this study is to define and estimate multivariate statistic models, inspired by the data of the Cosmic Microwave Background Radiation, and apply those models to self-simulated data. Two distinct models are constructed using random fields, which include a set of parameters, structural covariance among random variables and a multivariate (non-)Gaussian distribution. To obtain the optimal parameter estimates for a model, methods like Maximum likelihood estimation and Bayesian parameter estimation, are utilised for these predefined models. Only the Bayesian parameter estimation is used, since it is illustrated to be superior, compared to Maximum likelihood estimation, for parameter estimation of statistical models consisting of random fields. The structure of the models makes it impossible to compute estimates analytically, hence the Metropolis-Hastings algorithm is employed to calculate the estimates. Finally a comparison about the performance of parameter estimation among several models with dissimilar mask sizes is established.