Xi'an's Og

While (still!) looking at questions on Cross Validated on Saturday morning, just before going out for a chilly run in the park, I noticed an interesting question about a light bulb problem. Once you get the story out of the way, it boils down to the fact that, when comparing two binomial probabilities, p₁ and p₂, based on a Bernoulli sample of size n, and when selecting the MAP probability, having either n=2k-1 or n=2k observations lead to the same (frequentist) probability of making the right choice. The details are provided in my answers here and there. It is a rather simple combinatoric proof, once you have the starting identity [W. Feller, An Introduction to Probability Theory and Its Applications, vol. 1, 1968, [II.8], eqn (8.6)]

but I wonder if there exists a more statistical explanation to this weak information paradox…

This entry was posted on December 2, 2011 at 12:11 am and is filed under pictures, Running, Statistics, University life with tags binomial coefficient, binomial distribution, combinatorics, cross validated, elm tree, MAP estimators, William Feller. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.