1. maximizing a complex likelihood
2. MCMC sampling
3. random number generator
1. maximizing a complex likelihood
when the likelihood (or posterior) is high dimensional, giving a proper
starting value for ms is a problem. nlminb needs the boundary which also
requires the knowledge of the unknown parameters. Therefore, MCMC seems the
solution.
2. MCMC sampling
The followings are found to be of concern in sampling
a. acceptance rate; adjusting the proposal distribution variance to have a
acceptance rate at around 30% (don't know why, but it converges faster)
b. speed: in practice, the sampling speed is of concern. For N=10000,
dimension=10, S runs about 2 hours on HP 9000/780/180. So I rewrite S codes
in C.
c. When to stop
I run 1e4 - 1e6 and display the multiple chains together.
3. random number generator
In transforming the codes into C, I need a random number generator.
a. c built-in generator are said to to non-random. (rand, random, drand48)
b. randlib is recommended. I tried it to generate normals and it is fine.
Site: http://odin.mdacc.tmc.edu/anonftp/
Xu
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