Yes. This implies that today is a "coincidental similarity" day.
Since it is nearly midnight where you are, however, I offer that this similarity is actually not coincidental at all and is related to deep mathematical relationships between observed entropy and the chi-squared distribution. This connection is why Chernow's 1956 paper about the asymptotic form of the log-likelihood ratio is so significant. But that is a topic for tomorrow which is still more than 12 hours away for me. On Fri, Jul 15, 2011 at 11:47 AM, Sean Owen <[email protected]> wrote: > > This means that the maximum log likelihood is > > > > max_pi p(K | \vec \pi) = \sum k_i \log (k_i / N) + log Z > > > > The log-likelihood ratio involves three such expressions. > > > > The similarity to Shannon entropy here is either very deep or > coincidental, > > depending on the day of the week. > > That makes sense. It isn't necessarily entropy that this is > calculating, but something entropy-shaped that falls out of the max > likelihood for this multinomial distribution.
