De Finetti promoted the importance of predictive models for observables as the basis for Bayesian inference. The assumption of exchangeability, implying aspects of symmetry in the predictive model, motivates the usual likelihood-prior construction and with it the traditional learning approach involving a prior to posterior update using Bayes’ rule. We discuss an alternative approach, treating Bayesian inference as a missing data problem for observables not yet obtained from the population needed to estimate a parameter precisely or make a decision correctly. This motivates the direct use of predictive models for inference, relaxing exchangeability to start modelling from the data in hand (with or without a prior). Martingales play a key role in the construction. This is joint work with Stephen Walker and Edwin Fong, based on the paper “Martingale Posteriors” to appear with discussion JRSS Series B.