Working with marginal distributions

[DavidBrainard]

I have been thinking that sometimes one might have a multi-dimensional psychometric function where the full parameterization is required to account for the data but where only a subset of the parameters are of interest to know.

So for example, one might include a lapse rate in the psychometric function but not have great interest in its value.

In this case, I think it would make sense to track the posterior over the full psychometric function, but evaluate the expected entropy over the marginal on the parameters of the distribution that are of interest.

Whether this would make the procedure considerably more efficient is hard for me to intuit. But in our work on color-material tradeoffs there is a 7 dimensional psychometric function and our main interest is in one of the parameters, and we want to make every trial count.

I think implementing this would mainly be a matter of careful bookkeeping plus structuring the data so that the computation of the relevant marginals was fast enough on a trial-by-trial basis. Plus, a lot of testing to make sure it is working right and to find out whether it is worth it.