This may appear to be totally off-topic but it's not entirely so,
given that we've had a "feature request" at sourceforge for a Gibbs
sampler implementation. Anyway, does anyone have a recommendation
for a sort of "Markov Chain Monte Carlo for dummies" -- a useful
book, article or website?
I understand the principles of Monte Carlo analysis pretty well;
I've read some interesting arguments in favour of a Bayesian
approach in statistics (though I'm basically a frequentist); and I
have some notion of what Markov chains are; but I'm having trouble
putting the whole picture together.
That is, if we start from some econometric problem, and we assume
some relevant data are available -- and maybe we also assume that I
have some prior beliefs about the problem in question that could be
quantified to some extent, in some way -- how exactly could I use
MCMC to arrive at "better" (in what sense?) parameter estimates,
confidence intervals for these estimates, forecasts, and confidence
intervals for the forecasts, than I could obtain via regular OLS,
GLS, MLE, or GMM?
I'm not asking people to explain this to me here, just to give any
references that they have found particularly useful.
Thanks.
Allin Cottrell