Dear list,
This is my first use of this list, so apologies if I don't follow protocols... I'm working on something completely new to me, and struggling to know how to search the web effectively due to my lack of knowledge of terminology. I would be grateful for any advice, including whether I should send my question to a different list!
I'm working on improving ML estimation (in R) of an individual-level parameter ('par') - which is based on the individual's genotype - for each of 1000 individuals. I know (because I simulated the data) that the distribution of true values of 'par' across the population is non-uniform. (In this particular data set, the set of true par values closely follow a bimodal double-normal distribution). If I understand, this should mean that the individual par values are partially cross-informative, because normalized entropy<1. So I've been wondering if I can use this cross-informative-ness to improve my individual-level estimates of 'par'?
So far I've tried a few methods of weighting the likelihoods depending on how well they fit the expected double-normal (my own guesses - not based on anything in the literature). I can alter the distribution of resulting ML par estimates (which is more or less uniform when I independently estimate each individual's par), but so far the overall fit of the MLs to the true values doesn't improve. If anyone is aware of anything in the literature that could help me, please let me know.
The other thing I want to try is related to parameter updating in the MCMC (hence the email title). The set of true parameter values are partially non-independent (because they are non-uniform), so I'm looking for a way of updating the existing set of par values each iteration, which retains the expected bimodal distribution. It seems like the updating rule should therefore somehow include frequency-dependence. E.g. each new par value is taken from a normal distribution with mean at the existing parameter value, but with the updating probability distribution somehow modified to account for all other (actual or probable) updated parameter values. Is anyone aware of this having been done before?
(With a real data set I also wouldn't perfectly know the best-fitting distribution of true par values, but that's another issue).
Thanks and best wishes,
Richard.
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