Ideas Page

This page contains ideas and suggestions I or others have made but which have not yet been acted on.

3/3/14 (due to John Lafferty): Could try assuming that g is a log-concave density instead of unimodal. [my thought on this: I think it is a nice idea, but it isn't obvious how to do it. I don't know much about the fitting methods for log-concave densities, but they seem to exploit the fact that the knots are at observed points. In our case the fact that beta are observed with error means that we don't know where the knots should be. Maybe one could do a stochastic EM to fix this? Stochastic EM could maybe also be applied to obtaining the NPMLE for g under the assumption that it is a unimodal density.]

3/4/14 (arising from conversations with Lei Sun): I should check how the q-value style "non-parametric" estimates of FDR given pi0 compare with ash estimates of FDR. Maybe also add to my talk or the paper a plot of how ash splits the p value distribution into null and alternative components.

3/14/14 (arising from conversations with Wei Wang): It should be easy to modify ash to also estimate a non-zero mean to which to shrink. I think this could be quite easy in the normal case. That is, do joint maximum likelihood of pi, mu for g(.) = sum_k pi_k N(.,mu, sigma_k) I conjecture that for the normal case there will be a simple EM update for mu. For the uniform case, we might have to do numerical optimization of mu...I'm not sure. But we should try the normal case first.