Correlation in a Bayesian framework
Anirban Dasgupta, George Casella, Mohan Delampady, Christian Genest, William E. Strawderman, Herman Rubin · Canadian Journal of Statistics · 2000
The authors consider the correlation between two arbitrary functions of the data and a parameter when the parameter is regarded as a random variable with given prior distribution. They show how to compute such a correlation and use closed form expressions to assess the dependence between parameters and various classical or robust estimators thereof, as well as between p-values and posterior probabilities of the null hypothesis in the one-sided testing problem. Other applications involve the Dirichlet process and stationary Gaussian processes. Using this approach, the authors also derive a general nonparametric upper bound on Bayes risks.