Title:
Bayesian Analysis of One-Way Layouts
Abstract:
The one-way layout MLE solution has the unfortunate characteristic that the estimated variance between members of a block can be negative. This forces the
arbitrary designation that this variance is 0 and this gives a solution to the problem. One can instead formulate the problem from an uninformed Bayesian
point of view and determine a joint distribution for all the parameters of the problem. Doing this gives one freedom to choose some initial distribution for
the correlation (since the problem is overspecified, the priors cannot be forced through some group invariance) which one can set to be flat (if that indeed is
decided to be uninformative in this case). The solution gives a constraint on the correlation forced by the data for the posterior to be a distribution and
some intuitive notion of the spread of the parameters.