David Jones wrote: > Anon. wrote: >> Luna Moon wrote: >>> Hi all, >>> >>> If my model can be estimated using Maximum Likelihood estimation >>> (although the likelihood function is quite complicated where only >>> numerical evaluations are possible), are there still benefit of >>> turning to Bayesian estimation? >>> >> 1. The ability to add in prior information. 2. Estimation of >> uncertainty is part of the process, so you don't need to use any >> extra tools to do that. 3. The Angels will rejoice as someone else >> follows The Way. >> >> Bob > > But 2 and 3 are available for Maximum Likelihood. After all you don't > need either exact or approximate second derivatives to extract > uncertainty information from ML. And for 3, I was refering to a > different Way. > I was thinking in terms of the practicalities - typically one would use a maximisation routine to get the ML estimates, and then turn to something else (Fisher information, bootstrapping etc.) to estimate the standard error. In contrast, the Bayesian way would be to estimate the fill posterior through MCMC. Conceptually, of course, thereos' no difference either way.
> However, other differences include the way in which nuisance > parameters can be dealt with, and this can be of some importance. > True. Why didn't I mention that?
Oh yes, I should also point out that frequentists, by necessity, need an infinite number of angels. Bayesians get to decide how many they want to have.
-- Bob O'Hara
Dept. of Mathematics and Statistics P.O. Box 68 (Gustaf Hällströmin katu 2b) FIN-00014 University of Helsinki Finland