Interrelated Bernoulli Processes

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Abstract
If the joint prior distribution of the parameters and of two Bernoulli processes exhibits dependence, we will say the processes are “interrelated.” This article motivates and studies a family of closed-under-sampling prior distributions, called the Dirichlet-beta family, for interrelated Bernoulli processes. This family arises naturally from consideration of bivariate Bernoulli processes on which some observations are incomplete. Since Dirichlet-beta distributions are intractable, several Dirichlet approximations are proposed. The quality of one of these approximations is investigated and appears to be quite good. Several possible applications are suggested.

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