Survey of algorithms for exact distributions of test statistics in RxC contingency tables with fixed margins

Datatheorie voor analyse van individuele verschille

A Sequential Importance Sampling Algorithm for Generating Random Graphs with Prescribed Degrees

Random graphs with a given degree sequence are a useful model capturing several features absent in the classical Erd˝os-R´enyi model, such as dependent edges and non-binomial degrees. In this paper, we use a characterization due to Erd˝os and Gallai to develop a sequential algorithm for generating a random labeled graph with a given degree sequence. The algorithm is easy to implement and allows surprisingly efficient sequential importance sampling. Applications are given, including simulating a biological network and estimating the number of graphs with a given degree sequence.Statistic

Enhancing Bayesian risk prediction for epidemics using contact tracing

Contact tracing data collected from disease outbreaks has received relatively little attention in the epidemic modelling literature because it is thought to be unreliable: infection sources might be wrongly attributed, or data might be missing due to resource contraints in the questionnaire exercise. Nevertheless, these data might provide a rich source of information on disease transmission rate. This paper presents novel methodology for combining contact tracing data with rate-based contact network data to improve posterior precision, and therefore predictive accuracy. We present an advancement in Bayesian inference for epidemics that assimilates these data, and is robust to partial contact tracing. Using a simulation study based on the British poultry industry, we show how the presence of contact tracing data improves posterior predictive accuracy, and can directly inform a more effective control strategy.Comment: 40 pages, 9 figures. Submitted to Biostatistic

Hyper and structural Markov laws for graphical models

My thesis focuses on the parameterisation and estimation of graphical models, based on the concept of hyper and meta Markov properties. These state that the parameters should exhibit conditional independencies, similar to those on the sample space. When these properties are satisfied, parameter estimation may be performed locally, i.e. the estimators for certain subsets of the graph are determined entirely by the data corresponding to the subset. Firstly, I discuss the applications of these properties to the analysis of case-control studies. It has long been established that the maximum likelihood estimates for the odds-ratio may be found by logistic regression, in other words, the "incorrect" prospective model is equivalent to the correct retrospective model. I use a generalisation of the hyper Markov properties to identify necessary and sufficient conditions for the corresponding result in a Bayesian analysis, that is, the posterior distribution for the odds-ratio is the same under both the prospective and retrospective likelihoods. These conditions can be used to derive a parametric family of prior laws that may be used for such an analysis. The second part focuses on the problem of inferring the structure of the underlying graph. I propose an extension of the meta and hyper Markov properties, which I term structural Markov properties, for both undirected decomposable graphs and directed acyclic graphs. Roughly speaking, it requires that the structure of distinct components of the graph are conditionally independent given the existence of a separating component. This allows the analysis and comparison of multiple graphical structures, while being able to take advantage of the common conditional independence constraints. Moreover, I show that these properties characterise exponential families, which form conjugate priors under sampling from compatible Markov distributions