Although large language models (LLMs) are becoming increasingly capable of solving challenging real-world tasks, accurately quantifying their uncertainty remains a critical open problem, which limits their applicability in high-stakes domains. This challenge is further compounded by the closed-source, black-box nature of many state-of-the-art LLMs. Moreover, LLM-based systems can be highly sensitive to the prompts that bind them together, which often require significant manual tuning (i.e., prompt engineering). In this work, we address these challenges by viewing LLM-based systems through a Bayesian lens. We interpret prompts as textual parameters in a statistical model, allowing us to use a small training dataset to perform Bayesian inference over these prompts. This novel perspective enables principled uncertainty quantification over both the model's textual parameters and its downstream predictions, while also incorporating prior beliefs about these parameters expressed in free-form text. To perform Bayesian inference, a difficult problem even for well-studied data modalities, we introduce Metropolis-Hastings through LLM Proposals (MHLP), a novel Markov chain Monte Carlo (MCMC) algorithm that combines prompt optimization techniques with standard MCMC methods. MHLP is a turnkey modification to existing LLM pipelines, including those that rely exclusively on closed-source models. Empirically, we demonstrate that our method yields improvements in both predictive accuracy and uncertainty quantification (UQ) on a range of LLM benchmarks and UQ tasks. More broadly, our work demonstrates a viable path for incorporating methods from the rich Bayesian literature into the era of LLMs, paving the way for more reliable and calibrated LLM-based systems.

Photo-identification (photo-id) is one of the main non-invasive capture-recapture methods utilised by marine researchers for monitoring cetacean (dolphin, whale, and porpoise) populations. This method has historically been performed manually resulting in high workload and cost due to the vast number of images collected. Recently automated aids have been developed to help speed-up photo-id, although they are often disjoint in their processing and do not utilise all available identifying information. Work presented in this paper aims to create a fully automatic photo-id aid capable of providing most likely matches based on all available information without the need for data pre-processing such as cropping. This is achieved through a pipeline of computer vision models and post-processing techniques aimed at detecting cetaceans in unedited field imagery before passing them downstream for individual level catalogue matching. The system is capable of handling previously uncatalogued individuals and flagging these for investigation thanks to catalogue similarity comparison. We evaluate the system against multiple real-life photo-id catalogues, achieving mAP@IOU[0.5] = 0.91, 0.96 for the task of dorsal fin detection on catalogues from Tanzania and the UK respectively and 83.1, 97.5% top-10 accuracy for the task of individual classification on catalogues from the UK and USA.