R help - Dec 2015 - If I have 3 parameters, is optim() doing the same thing as Gibbs sampling?

Hi R list,

I am using optim() to optimize a function with 3 parameters.

#My 1-d toy example: loglikelihood of normal with x=c(2,5,3,7,-3,-2,0),
find MLE of mean.

p1 <- function(theta){
    sum(log(dnorm(c(2,5,3,7,-3,-2,0), mean = theta, sd = 1))) +log(dnorm(
theta, mean = 0.8, sd = 2))
}
optimize(p1, c(-3, 5), maximum = TRUE)


My question:

If function p1 has 3 parameters, is it doing the same thing as Gibbs
sampling?

In Gibbs, we optimize parameter 1 while fixing parameter 2 and 3.  Then
optimize 2, fixing 1 and 3. Repeat until convergence.

How does optim() choose random numbers?  I am using the default,
Nelder-Mead.

Is optim() drawing numbers from uniform distribution?  Is it picking from
[-Inf, Inf]?  What if I want draw from a prior N(3, 1) instead?

Thanks so much!

Mike

	[[alternative HTML version deleted]]

> If function p1 has 3 parameters, is it doing the same thing as Gibbs
sampling?
No.
> How does optim() choose random numbers?  
It doesn't, for Nelder-Mead. Nelder-Mead is a deterministic algorithm that
does not need random numbers.

Read up on Nelder-Mead; it - and everything else in optim() - is pretty much
completely different from MCMC using a Gibbs sampling algorithm

S Ellison




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