Maximum Likelihood Estimation Using Bayesian Monte Carlo Methods

University essay from Lunds universitet/Matematisk statistik

Abstract: The objective of this thesis is to give a general account of the MCMC estimation approach dubbed data cloning, specically performing maximum likelihood estimation via Bayesian Monte Carlo methods. An account of the procedure will be given, and it will applied to four dierent maximum likelihood estimation problems: simple linear regression, multiple linear regression, a stochastic dynamical model (Gompertz), and a state space model. In each case, dierent aspects of the method will be performed, and a comparison with the true or a approximative measure of the MLE will be done. In the nal example, a comparison with the bootstrap particle lter is conducted. The data cloning approach was found to have several advantages over the SMC methods, some of these are simple implementation, fewer numerical issues and less complicated choice of proposal function. Most importantly, it avoids numerical optimization of a function. Other benets of the data cloning procedure is that the convergence of the estimates to the true MLE as the number of clones increases, is invariant to the choice of the prior distribution. Furthermore, the approximative normality of the estimates, provides a convenient way of producing condence intervals. The data cloning method is also accompanied by several diagnostic tools which are mentioned in the study.

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