evaluating 0 * log(0) in log probabilities

[Daniel Lee]

In c++ math, this evaluates to NaN. Since this represents log(0^0), I
think this should evaluate to 0.

Is there anything subtle to worry about with this calculation? If
there isn't, I'll start incorporating it into the distributions.

Daniel

[Matt Hoffman]

0*log(0) comes up all the time (e.g. when assigning 0 probability to
an unobserved event), and we almost always want it to be 0, since for
most distributions we care about it makes no practical difference if
θ=0 or θ=1e-100, and the limit when approaching 0*log(0)=0.

I don't know of any (non-pathological) subtleties to do with this that
could bite us; if any exist, my opinion is that they're unlikely to
cause us more trouble than letting 0*log(0)=NaN.

Matt