GravStat 2005: Loredo (again)

Spatial coincidence (with Wasserman). Consider 2 objects - frequentist nearest neighbour test p(Bayesian coincidence assessment. Compare models of no repetition and repetition. Odds favouring repetition = 4 pi Int dn L_1(n)L_2(n) ~ (2/sigma_12) exp(-theta_12^2/2sigma_12^2), sigma_12^2 = sigma_1^2+sigma_2^2. Generalizing to more events is tough - number of pairs to calculate goes as N^4.

Bayesian Adaptive Exploration (with Chernoff). Sequential analysis.
Observation -> Inference -> Design

Stopping problem: binomial (fixed # of obs) and negative binomial (fixed # of particular type of object) give different frequentist test results. A Bayesian comparison does not depend on the stopping condition.
Maximum entropy sampling: learn the most by observing where we know the least.