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Bayesian Testing for Nested Hypotheses under Partial Observability

Abstract:

Florens, Richard and Rolin (2003) proposed a specification test of a parametric hypothesis against a nonparametric one, in the framework of a Bayesian encompassing test. Building on that work, this paper elaborates the procedure under a condition of partial observability. The general procedure is illustrated with the case where only the sign is observable, and more generally when the available data come from a binary reduction of a vector of latent variables. This example is also used to point out some difficulties when implementing the proposed procedure.