In a recent issue of The Economist, there is a very nice article (see here) about how everyday reasoning can be compared to Bayesian inference.
This article is based on a recent paper by Griffiths and Tenenbaum (see here). What they have done is to ask questions such as "How long do you think a man who is xx years old will live?" to several people. It turns out that the answers matched very well with those which would have been obtained by applying Bayes rule. Even more, they tried this with several different types of questions, for which the implicit priors are very different (Gaussian, Erlang or power-law distributions) and in all cases, the intuitive answers given by people had the right form (in terms of distribution).
What they conclude from this is that the way people intuitively reason about the world is quite similar to applying Bayesian inference.
What is intriguing is that the article in The Economist tries to see there a proof of domination of the Bayesian over the frequentist point of view. Also in the paper of Griffith and Tenenbaum, they use the term "optimal" when they talk about Bayes rule. I think this is very misleading and inaccurate.
Indeed, the only conclusion one should draw from this study is that the way people naturally make inferences about events in the world is very much rational and this confirms the fact that has been observed many times before that the intuitive notion of rationality we have match very well with the rules of the calculus of probabilities.
But this is no surprise because these rules were designed in order to be intuitively rational (what else?). What is interesting is that rationality leads necessarily to these rules and no other, but this has been known for years.
I do not see what this study has to do with the debate between Bayesian vs frequentist. First of all, there is no real opposition between these points of view. Indeed, they lead to the same rules for combining probabilities, the only difference is in the meaning that is associated to these probabilities. So this debate is mostly philosophical and should not interfere with cognitive science studies, nor (even less) with machine learning.