The predictive nature of Bayesian inference

The specification of a prior probability on parameters of a likelihood function is the typical starting point, and unique characteristic, of Bayesian analysis. In this talk I will argue that a more distinctive feature of Bayesian reasoning is that Bayesian inference is inherently predictive of future observables (data), whereas methods such as maximum likelihood estimation are not. The predictive viewpoint provides insight on the uncertainty quantification defined by Bayesian credible versus frequentist confidence intervals.

I will illustrate the predictive view using simple, hypothetical, examples taken from the analysis of randomized controlled trials. I will argue that one can be `Bayesian’ without the need for a prior, but at a cost. Then, armed with this knowledge, we will address a question of modern AI, namely, are Large Language Models (LLMs) being Bayesian when performing in-context learning, and how might we know?

Holmes is Professor of Biostatistics at the University of Oxford with a joint appointment between the Nuffield Department of Medicine and the department of Statistics. He is a founding Fellow of ELLIS https://ellis.eu/ and founding editorial board member of the NEJM-AI. Holmes served as the inaugural Programme Director for Health at The Alan Turing Institute (2017-2023). His research focusses on the theory, methods and applications of statistical machine learning in health. 

University members only.