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Maximum Likelihood Estimation Using Bayesian Monte Carlo Methods

Ali Akbari, Danial (2015) MASM01 20151
Mathematical 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)
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author
Ali Akbari, Danial
supervisor
organization
course
MASM01 20151
year
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
2015-08-03 11:26:47
date last changed
2015-08-03 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},
}