Getting MAP estimate via MCMC

1

How can I get the MAP estimate via MCMC? After inference finishes, should I take all of my samples, run them through the likelihood function and choose the one that has the highest likelihood or Pyro has some functions that I should call for that?

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2

for MAP see here. the usual way to find MAP estimates is optimization, not MCMC.

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3

But is there a way to get an approximate MAP estimate using the samples that MCMC has produced?

4

as you noted you could take the MCMC samples you have and compute k = argmax_i log p(latent_i) + log p(data|latent_i). then
your approximate MAP estimate would be latent_k.

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