Conditional mean estimates and Bayesian hypothesis testing (Corresp.)

For conditional probability density functions (pdf\´s) drawn from the exponential family, it is shown that the marginal pdf is completely determined by a posterior conditional mean estimate (CME). This result implies that likelihood ratios involving these marginals have the estimator-correlator structure in the following sense: if the noise is drawn from an exponential pdf, then independent of the signal (prior pdf), the optimum detector correlates the estimate with the data. A generalization of Esposito\´s result on "pseudoestimates" is also given.