Bayesian Hierarchical Modelling Frameworks for Flawed Data in Environment and Health
Date: 5 August 2019
University of Exeter
Doctor of Philosophy in Mathematics
In the fields of environment and health, available data is usually not a perfect representation of the quantity we are interested in, such as the number of people contracting a disease or the number of environmental hazards occurring in a given area or time period. Instead, data often suffer from a number of flaws, some of which can ...
In the fields of environment and health, available data is usually not a perfect representation of the quantity we are interested in, such as the number of people contracting a disease or the number of environmental hazards occurring in a given area or time period. Instead, data often suffer from a number of flaws, some of which can pose serious problems. For example, counts of disease cases or environmental hazards may suffer from under-reporting, such that the recorded count is less than or equal to the true count. In some cases, we will never know the true number. This inevitably convolutes our understanding of the risk the disease or natural hazard poses to society. A similar example is delayed reporting of counts, where we may eventually know the true count or something trivially close to it after a period of time. However, we often need to make important decisions, such as how to respond to a disease outbreak, before this certainty is available to us and based on any partial information we may instead have at our disposal. In this thesis we discuss different ways in which data may be flawed, which we refer to as flawed observation mechanisms, and the risks they pose to practitioners if ignored. Moving beyond previous approaches to tackling this issue, which mostly constitute bespoke solutions to individual problems, we present a conceptual framework for simultaneously modelling quantities we are interested in and any flawed observation mechanisms. We argue that the key strengths of this framework are its ability to rigorously quantify uncertainty, its flexibility and its interpretability. We spend the rest of the thesis demonstrating the power this framework offers to practitioners, with chapters dedicated to the general problems of under-reporting and delayed reporting, as well as a chapter dedicated to the exposition of a model which informs global health policy. Each of these chapters is broadly self contained, with individual discussions of the problems addressed. The thesis concludes with an overview of the effectiveness of our approach and some suggestions for future research.
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