Markov Chain Monte Carlo
Part 1
The R data set in the file
loaded by R command
load(url("http://www.stat.umn.edu/geyer/8054/hw/hw12/pois.rda"))
is data for Poisson regression.
The model of interest is fit by the command
out <- glm(y ~ (v1 + v2 + v3 + v4 + v5 + v6)^3,
family = poisson, data = dat, x = TRUE)
the argument x = TRUE saying that the model matrix should
be returned as part of the object, that is, as out$x.
Use the R function metrop in the mcmc library
to simulate the posterior distribution of the regression coefficients
for this model when a flat prior is used (flat on the regression coefficient
scale).
- Report the posterior mean of each regression coefficient.
- Report an estimate of the Monte Carlo standard error (MCSE) for each posterior mean estimated.
- Use a run long enough so that each MCSE is less than 0.01.
Part 2
Redo part 1 with everything the same except now we wish to simulate
conditional on the Intercept
regression coefficient being zero,
as would be appropriate when the sampling distribution is assumed multinomial
rather than Poisson.
The Intercept
is the first regression coefficient,
as can be seen by looking at colnames(out$x).
