Statistical modelling of lattice data with applications in flow cytometry

Statisticians are among the most in demand problem solvers in today's data driven world, with their expertise often employed to address emerging issues in other scientific fields by adopting, modifying and/or developing statistical methods. This application and redeployment of statistical methods allows statisticians to provide invaluable and actionable insights to scientific experts in the chosen field. This thesis provides statistical methodology for the gating of fow cytometry data. Flow cytometry is a technology that simultaneously measures and analyses multiple physical and chemical characteristics of single cells as they fow in a fuid stream through a beam of laser light. This technology has become an emerging state-of-the-art device in microbiology and dairy science, and is also used extensively in medical diagnostics. Unfortunately, the lack of a robust statistical analysis toolbox for flow cytometry has restricted the deployment of this world-leading sensor technology. Gating, the identification of homogeneous cell populations, of these complex data sets are performed using expert opinion or naive clustering algorithms rather than employing a specialised statistical framework. Gating is the equivalent of clustering however the data from flow cytometry lies on a structured lattice grid. The focus of this thesis is to provide a methodology for the gating of ow cytometry data which respects the underlying structure of the data. This research provides statistical methods for the analysis of binary lattice data, which are based on the statistical properties of the observed lattice. A Bernoulli outcome governs the binary value taken at each node. From this the energy distribution, a measure of similarity of nodes across the lattice, for each node can be specified, allowing the expected value and variance of the complete lattice energy to be calculated. For small lattices the complete probability distribution is provided, while the energy function for larger lattices is known for specific values. The novel probabilistic and statistical quantities lead to an algorithm for gating FCM data, which incorporates an improved Markov chain Monte Carlo and a hierarchical approach, that overcomes many of the limitations facing the deployment of this world leading sensor technology.