Maximum Likelihood Estimation Using Bayesian Monte Carlo Methods
(2015) MASM01 20151Mathematical Statistics
 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... (More)  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. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/7752717
 author
 Ali Akbari, Danial
 supervisor

 Umberto Picchini ^{LU}
 organization
 course
 MASM01 20151
 year
 2015
 type
 H2  Master's Degree (Two Years)
 subject
 keywords
 bootstrap par ticle lter., Bayesian estimation, maximum likelihood, Data cloning
 language
 English
 id
 7752717
 date added to LUP
 20150803 11:26:47
 date last changed
 20150803 11:26:47
@misc{7752717, 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.}, author = {Ali Akbari, Danial}, keyword = {bootstrap par ticle lter.,Bayesian estimation,maximum likelihood,Data cloning}, language = {eng}, note = {Student Paper}, title = {Maximum Likelihood Estimation Using Bayesian Monte Carlo Methods}, year = {2015}, }