Large Language Bayes

Many domain experts do not have the time or training to write formal Bayesian models. This paper takes an informal problem description as input, and combines a large language model and a probabilistic programming language to create a joint distribution over formal models, latent variables, and data. A posterior over latent variables follows by conditioning on observed data and integrating over formal models. This presents a challenging inference problem. We suggest an inference recipe that amounts to generating many formal models from the large language model, performing approximate inference on each, and then doing a weighted average. This is justified an analyzed as a combination of self-normalized importance sampling, MCMC, and variational inference. We show that this produces sensible predictions without the need to specify a formal model.