I am asking for estimating the location parameter of logistic distribution by Bayesian methods. I am in need of a proper prior distribution for µ , and how to know the prior is Normal ? or logistic ? Or how to know what is the result for posterior distribution for µ.
Abbas, I am not an expert so I will quote from "Doing Bayesian Data Analysis with Bugs" by Kruschke(p.408): " It is typical to put a normal prior on the mean of a normal likelihood, and a gamma prior on the precision of a normal likelihood". For example, you would have mu with dnorm(0,1.0E-10) and tau(precision) as dgamma(0.01,0.01).
I am not sure if this answers your question.
Olga
Didn't know much about the context of the problem.
In general, prior distribution just models the information already known before seeing the data (when new data comes, likelihood takes effect). So basically you decide which form of prior is appropriate according to the information you already knew before seeing the data. The posterior usually can be obtained by Monte Carlo sampling methods such as MCMC, Gibbs sampling.
See chapter 10 of:
Hoff, Peter D. A first course in Bayesian statistical methods. New York: Springer, 2009.
Except for the normal regression model, standard conjugate prior distributions for generalized linear models do not exist. The book recommends obtaining the posterior distribution in your situation with a Markov chain Monte Carlo (MCMC) method, the Metropolis algorithm.
- Badges
- Science topic
- Similar topics
- Statistics
- Survey