Hi
I have hierarchical Bayesian model with 32 unknown parameters (alpha_1, alpha_2,..., alpha_30, mu, .sigma^2).
conditional posterior distributions of mu and sigma^2 have closed forms, but conditional posterior distributions of ( alpha_1, alpha_2,..., alpha_30 ) are not closed form, so I need to use Metropolis Hastings sampler within Gibbs sampler.
My question what is an algorithm and R code of Metropolis Hastings sampler of 30 parameters?
Dear Zainab Al-kaabawi,
If the alphas were real numbers (you can transforme them), you can try the following strategy:
1. Implement the -log (f (alpha | rest)) (i.e., minus the logarithm of the posterior conditional density).
2. Find the mode of f(alpha| Rest) using the function
optim (param, fun, hessian = TRUE) ,
where param are the initial values and fun = -log (f (alpha rest)).
3. The result above will return the hessian matrix of fun. This matrix is the observed Fisher Information (IF)
4. You can use the following distribution as a proposal in Metropolis-Hastings:
(alpha | rest) approx N (alpha [k], tau *IF ^ (-1))
where N(.,.) is the multivariate normal (you can sample from N(.,.) with rmvnor function in mvtnorm package) and tau is tunning parameter.
You can get more details on this implementation by referring to Chapter 3 of:
[1] Marin, Jean-Michel, and Christian Robert. Bayesian core: a practical approach to computational Bayesian statistics. Springer Science & Business Media, 2007.
Sinceraly,
James D. Santos.
Dear James D. Santos
Thank you for your reply. The steps to choose proposal distribution is clear and this will be very helpful of me , but I need to reference that build R codes in more detail , also my model is not linear regression model.
Go Through
http://www.stat.ufl.edu/archived/casella/ShortCourse/MCMC-UseR.pdf
Page 93 onwards - MH Algo.
An Idea with codes
The Metropolis–Hastings algorithm C.P. Robert1,2,3
1Universit ́e Paris-Dauphine, 2University of Warwick, and 3CREST
Rgds,
Abhay
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Statistical Software
- R