Author: Thi Pham
Pham, Thi, 2017 Parameter estimation for stage-duration models, Flinders University, School of Computer Science, Engineering and Mathematics
Terms of Use: This electronic version is (or will be) made publicly available by Flinders University in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. You may use this material for uses permitted under the Copyright Act 1968. If you are the owner of any included third party copyright material and/or you believe that any material has been made available without permission of the copyright owner please contact copyright@flinders.edu.au with the details.
Multi-stage time evolving models, so called stage-duration models, have been studied in
various biological contexts. We consider stage-duration models that describe single cohort
stage-frequency data with destructive samples. These models can give an understanding
of the maturation of biological systems, industrial processes or the progression of disease.
The main goal of this thesis is to estimate the stage-dependent maturation parameters
and hazard rate parameters of the models. The contributions of the thesis are as follows:
First, we obtain novel methods for estimating maturation parameters in models with
stage-wise constant hazard rates and with linear time-dependent hazard rates. We use
Laplace transform methods with the assumption of constant scale parameters or constant
shape parameters. The key result is the exploration of the relationships between the
stage-dependent maturation parameters in each stage.
Second, we obtain methods for estimating maturation parameters and hazard rate parameters
without imposing unrealistic conditions as in previous studies. In particular,
by using a Bayesian approach, we derive estimators of the maturation parameters and
the hazard rate parameters in each stage simultaneously, without initial knowledge about
maturation parameters. The Metropolis-Hastings (MH) algorithm based on deterministic
transformations is applied in order to accelerate the convergence of the Markov process.
We embed the relationships of the stage-dependent maturation parameters within the
deterministic MH algorithms. The number of sampling times for the deterministic MH
methods is reduced compared to the Laplace transform methods.
Third, the application of the methodology in the models is evaluated using both simulated
data and case studies including cattle parasitic data and breast development data of New
Zealander schoolgirls. From the simulated data, results show that the proposed methods
are able to estimate parameters in situations where non-trivial hazard rates apply. The
methods also work well when the assumptions of maturation parameters are relaxed.
From the case studies, the results show that parameter estimation is better using these
methods in comparison to Laplace transform methods in previous studies.
Keywords: Multi-stage models, Stage duration, Stage frequency data, Bayesian analysis, Destructive samples.
Subject: Statistical Science thesis, Computer Science thesis, Mathematics thesis
Thesis type: Doctor of Philosophy
Completed: 2017
School: School of Computer Science, Engineering and Mathematics
Supervisor: Professor Jerzy Filar