My PhD project is interdisciplinary between mathematics and mircobiology, focused on developing statistical models in the rapidly developing field of single molecule imaging. My project seeks to facilitate the automatic exploitation of spatial data derived from a single molecule imaging technique called Fluorescence Localisation Imaging with Photobleaching, or FLImP. This technique is used to measure the arrangement of EGFR protein clusters on the cell membrane which are known to play a role in the development of several types of cancer. The measurement of the population of shapes these protein clusters adopt can be used as a novel diagnostic test to determine the most appropriate treatment for cancers such as small cell lung carcinomas. By investigating methods in Bayesian statistics and efficient hidden Markov modelling approaches, this project aims to develop algorithms which are robust and computationally efficient to maximise information extraction.