Inference with implicit likelihoods for infectious disease models
Open Access
- Author:
- Jandarov, Roman A
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 18, 2012
- Committee Members:
- Murali Haran, Dissertation Advisor/Co-Advisor
Murali Haran, Committee Chair/Co-Chair
Francesca Chiaromonte, Committee Member
David Russell Hunter, Committee Member
Ottar N Bjornstad, Committee Member - Keywords:
- Expensive likelihood
SIR model
Gaussian processes
emulation
infectious diseases
meningitis
measles. - Abstract:
- Probabilistic models for infectious diseases are important for understanding mechanisms underlying the spread of infection. I develop new models and computational approaches motivated by several research projects including a study of the dynamics of meningitis in Nigeria, measles infection in England and Wales, and gypsy moth infestations in Pennsylvania. Likelihood functions for infectious disease models are often expensive to evaluate, making traditional likelihood-based inference computationally infeasible. Furthermore, traditional inference may lead to poor parameter estimates and the fitted model may not capture important biological characteristics of the observed data. I explore efficient inferential methods based on so-called approximate Bayesian computation (ABC). I develop a new model for meningitis dynamics in Nigeria and show how a version of ABC is effective when it is relatively inexpensive to simulate from the model. When the likelihood function is expensive to evaluate and simulations are time consuming ABC-based inference is infeasible. For such models I propose a novel approach that is inspired by recent work in emulation and calibration for complex computer models. My motivating example is the gravity time series susceptible-infectious-recovered (TSIR) model. My approach is based on obtaining a Gaussian process approximation to the model using key summary statistics calculated from model simulations. Unlike traditional likelihood-based inference, the new approach is computationally expedient, provides accurate parameter inference, and results in a good model fit. I apply my approach to the analysis of measles outbreaks in England and Wales. In general, my approach is applicable to many problems where traditional likelihood-based inference is computationally intractable or leads to poor inference. I demonstrate how this methodology can be used to learn about the parameters of a complex mixture random graph model. The gypsy moth is the most important forest defoliating insect in the northeastern United States. Inferring gypsy moth population periodicities is challenging because population sizes of the insect are not directly observable. I develop a new space-time Gaussian process model for inferring gypsy moth populations based on indirect information from defoliation data. I demonstrate via simulated examples that this approach provides accurate population periodicity estimates; I apply this methodology to a Pennsylvania defoliation data set.