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
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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)