Statistical models for infectious disease dynamics play a central role in understanding how outbreaks unfold and in supporting public health decision-making. Statistical inference and the assessment of model adequacy in this setting are inherently challenging: outbreak data are typically dependent, the infection process is only partially observed, and an epidemic is realised only once. Addressing these challenges requires statistical methods that are both principled and flexible—an approach that aligns closely with the interests and contributions of Professor Richard Boys.

In this talk, I will give an overview of my recent work on Bayesian inference for stochastic infectious disease models. I will discuss (i) how Bayesian non-parametric methods can be used to relax restrictive modelling assumptions; (ii) how the underlying structure of epidemic models can be exploited, together with recent developments in deep learning and neural networks, to enable practical likelihood-based inference; and (iii) how goodness of fit and model adequacy can be assessed in this challenging setting.

Throughout the talk, I will use simple examples from infectious disease modelling to emphasise intuition rather than technical detail, and to highlight connections with themes central to Richard Boys’ statistical work.