Thank you for the reply. The AutoGuide machinery sounds useful, but I guess before learning to use it I would still like to understand how to hand-design a guide for MLE in the case where I have a latent variable, so that I can understand what the guide should contain in that case.
My model was a somewhat arbitrary one, constructed only for the sake of having both a latent variable and a parameter. Let me explain it in more detail, though:
Suppose we have three coins. Coins ‘A’ and ‘B’ are known to be fair, but coin ‘C’ has an unknown bias f. We don’t have a prior over f. (That is, f is a parameter rather than a latent variable.) We are given data from 10 trials of the following experiment:
- first flip coin ‘A’ (known to be fair)
- if ‘A’ comes up heads, flip coin ‘B’ (known to be fair) and return the result
- otherwise, flip coin ‘C’ (with unknown bias f) and return the result
So the result from each trial is either heads or tails, but we don’t know if it came from coin ‘B’ or coin ‘C’, which is to say, we don’t know the value of the latent variable ‘A’. The goal is to get a maximum likelihood estimate of the unknown parameter f, given this data.
So then my question is just, what should I put in the guide, in that case? I made a guess at that in my original post, but it doesn’t behave as expected and I conclude I must be doing something wrong, so I’m looking for feedback on what.