MCMC Model Composition Search Strategy in a Hierarchical Model . by Susan J. Simmons University of North Carolina Wilmington. Variable selection. In many hierarchical settings, it is of interest to be able to identify important features or variables
by Susan J. Simmons
University of North Carolina Wilmington
yij ~ N(qi, si2) and qi ~ N(Xi´b,t2)
Where X is P x L matrix of explanatory variables (P=#variables and L=# obsn)
bj ~ N(0,100) t2 ~ Inv-c2(1)
si2 ~ Inv-c2(1)
Combining the data and prior distributions give us an implicit posterior distribution, but the full conditional posterior distributions have a nice form
Repeat (1) – (5).
Where P(bj ≠0|D,M(k)) = 0 if feature j is not in the model and 1 if feature jis in the model, and P(M(k)|D) is calculated as
There are 165 different lines (or clusters) and in this simulation, ni=10 for i=1,…,165. We generated 60 different simulations scenarios.
where aj is the effect of marker j, m is the overall mean and eij is the error (gamma)