If I multiply the two PDFs, does the variance of the result PDF becomes narrower than the two PDFs always? In other words, if I multiply likelihood and prior to get the posterior, is the variance of the posterior narrower than that of the likelihood and prior?
Asked
Active
Viewed 107 times
1
-
It doesn't make sense to compare the variance of the posterior to the variance of the likelihood distribution (as you're then comparing the parameter's variance with the observable variable's). See Andrew Gelman's blog post for a very brief discussion of your question: http://andrewgelman.com/2011/07/20/adding_more_inf/. – hejseb May 07 '14 at 18:34