Many biological systems are only partially observed, requiring statistical models that account for latent states, imperfect detection, and uncertainty in inference. Bayesian state-space models provide a flexible framework for addressing these challenges, but increasing model complexity often poses substantial computational challenges. In this talk, I present two methodological contributions that advance Bayesian inference for ecological and epidemiological applications. The first contribution develops a Bayesian multistate capture–recapture model to estimate demographic parameters in wildlife populations when individual identification is compromised by tag loss. Unlike existing approaches, the proposed framework explicitly incorporates retagging information to estimate survival, capture, and tag-retention probabilities without requiring permanent individual marks. The model is estimated using Markov chain Monte Carlo (MCMC) and accommodates both homogeneous and multi-regime tag-retention processes. Its performance is evaluated through extensive simulation studies and demonstrated using long-term Antarctic fur seal capture–recapture data.
The second contribution extends Bayesian inference to more complex multievent models with high-dimensional latent states, where conventional MCMC algorithms become computationally expensive. To overcome this limitation, I develop a variational Bayesian framework based on Automatic Differentiation Variational Inference (ADVI), enabling fast and scalable posterior approximation with minimal analytical derivation. The proposed methodology is evaluated through simulation studies and applied to COVID-19 testing data, demonstrating substantial gains in computational efficiency while maintaining accurate statistical inference. Together, these studies highlight how advances in Bayesian modelling and modern approximate inference can improve the analysis of complex biological systems, providing flexible and computationally efficient tools for inference under imperfect observation.
