MAP estimation by optimisation fails when minimiser on boundary?

[dmcdougall]

I think I'm running into issues when the maximiser for the target pdf is on (or near) the boundary. I return GSL_NAN when gsl asks me to evaluate my target outside of the support, but I'm not actually sure it achieves anything. I think to fix this, we might have to append a penalty function to the end of the boundary so the target now has infinite support.

[dmcdougall]

This looks useful: http://dlib.net/optimization.html#find_min_box_constrained

[dmcdougall]

It seems returning INFINITY for a point requested outside of the domain makes gsl give up and stop at the previous good point. This seems to be 'good enough' for now. Anything we do here will be better than what we're currently doing (burning in the chain and praying it gets to a mode).