Recent work on the convergence of posterior distributions under Bayesian updating has established conditions under which the posterior will concentrate on the truth, if the latter is has a perfect representation within the support of the prior, and under various dynamical assumptions, such as the data-generating process being independent and identically distributed or a Markov process. Here I establish sufficient conditions for the convergence of the posterior distribution in non-parametric problems even when {\em all} of the hypotheses are wrong, and the data-generating process has a complicated dependence structure. The main dynamical assumption is the generalized asymptotic equipartition (or "Shannon-McMillan-Breiman") property of information theory. I derive a kind of large deviations principle for the posterior measure, and discuss the advantages of predicting using a combination of models known to be wrong. An appendix sketches connections between the present results and the "replicator dynamics" of evolutionary theory.
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