Bayesian Non-Parametric Inference for Infectious Disease Data

We propose a framework for Bayesian non-parametric estimation of the rate at which new infections occur assuming that the epidemic is partially observed. The developed methodology relies on modelling the rate at which new infections occur as a function which only depends on time. Two different types of prior distributions are proposed namely using step-functions and B-splines. The methodology is illustrated using both simulated and real datasets and we show that certain aspects of the epidemic such as seasonality and super-spreading events are picked up without having to explicitly incorporate them into a parametric model

Exact Bayesian inference via data augmentation

Data augmentation is a common tool in Bayesian statistics, especially in the application of MCMC. Data augmentation is used where direct computation of the posterior density, π(θ|x), of the parameters θ, given the observed data x, is not possible. We show that for a range of problems, it is possible to augment the data by y, such that, π(θ|x,y) is known, and π(y|x) can easily be computed. In particular, π(y|x) is obtained by collapsing π(y,θ|x) through integrating out θ. This allows the exact computation of π(θ|x) as a mixture distribution without recourse to approximating methods such as MCMC. Useful byproducts of the exact posterior distribution are the marginal likelihood of the model and the exact predictive distribution

Bayesian nonparametrics for stochastic epidemic models

The vast majority of models for the spread of communicable diseases are parametric in nature and involve underlying assumptions about how the disease spreads through a population. In this article we consider the use of Bayesian nonparametric approaches to analysing data from disease outbreaks. Specifically we focus on methods for estimating the infection process in simple models under the assumption that this process has an explicit time-dependence

A two-level Markov model for packet loss in UDP/IP-based real-time video applications targeting residential users

The packet loss characteristics of Internet paths that include residential broadband links are not well understood, and there are no good models for their behaviour. This compli- cates the design of real-time video applications targeting home users, since it is difficult to choose appropriate error correction and concealment algorithms without a good model for the types of loss observed. Using measurements of residential broadband networks in the UK and Finland, we show that existing models for packet loss, such as the Gilbert model and simple hidden Markov models, do not effectively model the loss patterns seen in this environment. We present a new two-level Markov model for packet loss that can more accurately describe the characteristics of these links, and quantify the effectiveness of this model. We demonstrate that our new packet loss model allows for improved application design, by using it to model the performance of forward error correction on such links

Bayesian model choice via mixture distributions with application to epidemics and population process models

We consider Bayesian model choice for the setting where the observed data are partially observed realisations of a stochastic population process. A new method for computing Bayes factors is described which avoids the need to use reversible jump approaches. The key idea is to perform inference for a hypermodel in which the competing models are components of a mixture distribution. The method itself has fairly general applicability. The methods are illustrated using simple population process models and stochastic epidemics