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I'm fairly knowledgeable about Bayesian statistics, but I can't tell which technique you're referring to. It vaguely sounds like maximum likelihood, but ML doesn't iterate the model or priors. Could you explain further and give a reference?

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Iterative algorithms which attempt to solve maximum likelihood usually fall under the category of expectation maximization (a good example is K-means clustering).

http://en.wikipedia.org/wiki/Expectation-maximization_algori...

Ah, I'd always thought of EM as iterating over the parameters given a model, but I suppose it makes sense to see it as a search for a model, including parameters, that fits the data. Cool.

Perhaps he/she is referring to conjugate priors [1], where the prior and the posterior are of the same family of distributions. Once you compute the posterior using a likelihood and prior, you obtain a posterior that is of the same family of distribution as the prior. This posterior can then be used as a prior for more samples.

[1] http://en.wikipedia.org/wiki/Conjugate_prior

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