Statistical Methodology and Theory with Application to Microbiome Data Analysis

My research focuses on development of statistical methodology using abstract mathematical ideas, particularly with applications to microbiome data. Many of the methods developed in this proposal will have broad applicability to a wide range of data analysis problems including analysis of microbial abundance data, health data, house price data and others. There are three main themes in my research programme. The first theme is studying the temporal dynamics of microbial communities. Recent research has highlighted the importance of microbial communities to health, agriculture and the environment. However, knowledge of the importance is not enough to lead to new applications. In order to apply the knowledge, we need to both know which types of microbial communities are desirable, and how to achieve and maintain a desirable community. Studying how a microbial community changes over time, both with and without external influences is key to achieving and maintaining desirable community states. By appropriate modelling of time--series microbial abundance data, I will develop methods to predict the changes to microbial communities. The second theme deals with the measurement error problem. For many problems the available data is not measured accurately due to limitations of the measuring apparatus. Learning from the underlying data often requires developing corrections for this measurement error. With these corrections, the results of the data analysis can be improved. The third theme is developing a new approach to machine-learning methods based on assessing hypothetical examples. This is designed to mimic the human thought process, where in a lot of cases, we evaluate a particular problem by evaluating a similar but easier problem. For example to estimate a house price, we might say "if the kitchen were renovated, it would be worth $400,000: it is therefore worth $380,000." By making a series of small hypothetical changes, we find examples where we have more confidence in our assessment. We then assess the object of interest by adjusting assessment of the similar examples to take into account the small differences. It turns out that a number of widely used and very effective machine--learning methods are equivalent to certain methods of using hypothetical examples. Building this connection will help us to better understand the "thinking" of current AI methods, and will offer new approaches for improved AI methods.