Open AccessDissertation
Epidemic models and MCMC inference
TLDR
Evidence confirming and demonstrating the importance of understanding the tail behaviour of proposals in importance sampling is presented, and a new algorithm, the Kernel Metropolis Hastings (KMH), is proposed as an approximate algorithm for low dimensional marginal inference in situations where the GIMH algorithm fails because of sticking.Abstract:
Statistical inference and model choice for partially observed epidemics provide a variety of challenges both practical and theoretical. This thesis studies some related aspects of models for epidemics and their inference.
The use of the matrix exponential to facilitate exact calculations in the General Stochastic Epidemic (GSE) is demonstrated, most usefully in providing the exact marginal likelihood when infection times are unobserved.
The bipartite graph epidemic is defined and shown to be a flexible framework which encompasses many existing models. It also provides a way in which a deeper understanding of the relation between existing models could be obtained.
The Indian buffet epidemic is introduced as a non-parametric approach to modelling unknown heterogeneous contact structures in epidemics. Inference for the Indian buffet epidemic is a challenging problem, some progress has been made. However the algorithms which have been studied do not yet scale to the size of problem where significant differences from the GSE are apparent.
Evidence confirming and demonstrating the importance of understanding the tail behaviour of proposals in importance sampling is presented. The adverse impact of heavy tailed proposals on the Grouped Independence Metropolis-Hastings (GIMH) and Monte Carlo within Metropolis (MCWM) algorithms is demonstrated.
A new algorithm, the Kernel Metropolis Hastings (KMH), is proposed as an approximate algorithm for low dimensional marginal inference in situations where the GIMH algorithm fails because of sticking. The KMH is demonstrated on a challenging 2-d problem.read more
Citations
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Analysis Of Infectious Disease Data
TL;DR: The analysis of infectious disease data is universally compatible with any devices to read, allowing you to get the most less latency time to download any of the authors' books like this one.
Book ChapterDOI
Epidemic Modelling: Stochastic Models in Discrete Time
D. J. Daley,Joseph Gani +1 more
Journal ArticleDOI
Bayesian Nonparametrics for Stochastic Epidemic Models
TL;DR: This article focuses on methods for estimating the infection process in simple models under the assumption that this process has an explicit time-dependence.
Posted Content
Bayesian nonparametrics for stochastic epidemic models
TL;DR: In this article, the authors consider the use of Bayesian nonparametric approaches to analyse data from disease outbreaks and focus on methods for estimating the infection process in simple models under the assumption that this process has an explicit time-dependence.
References
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Maximum likelihood from incomplete data via the EM algorithm
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Monte Carlo Sampling Methods Using Markov Chains and Their Applications
TL;DR: A generalization of the sampling method introduced by Metropolis et al. as mentioned in this paper is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates.
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Monte Carlo Statistical Methods
TL;DR: This new edition contains five completely new chapters covering new developments and has sold 4300 copies worldwide of the first edition (1999).
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Sampling-Based Approaches to Calculating Marginal Densities
TL;DR: In this paper, three sampling-based approaches, namely stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm, are compared and contrasted in relation to various joint probability structures frequently encountered in applications.
Journal Article
Sampling-based approaches to calculating marginal densities
TL;DR: Stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm can be viewed as three alternative sampling- (or Monte Carlo-) based approaches to the calculation of numerical estimates of marginal probability distributions.