In my Bayesian class, I assigned a problem (exercise 8.3 from BCWR) where one is using logistic regression to model the trajectory of Mike Schmidt’s home run rates.
First, I have written a function to compute the log posterior for a logistic regression model with a vague prior placed on the regression vector. The function together with a short example how it works can be found here.
Second, it seems that there is a problem getting the laplace function to converge if you don’t use a really good starting value. Here is an alternative way of getting the posterior mode.
Suppose y is a vector containing the home run counts and n is a vector with the sample sizes. Let age be the vector of ages and age2 be the vector of ages squared. Define the response to be a matrix containing the vectors of successes and failures.
Then the mle of beta is found using the glm command with the family=binomial option
The posterior mode is the mle:
The approximation to the posterior variance-covariance matrix is found by
Now you should be able to use the random walk metropolis algorithm to simulate from the posterior.