On the Subexponential Decay of Detection Error Probabilities in Long Tandems

We consider the problem of Bayesian decentralized binary hypothesis testing in a network of sensors arranged in a tandem. We show that the rate of error probability decay is always subexponential, establishing the validity of a long-standing conjecture. Under the additional assumption of bounded Kullback-Leibler (KL) divergences, we show that for all <i>d</i> > 1/2, the error probability is Omega(<i>e</i> <sup>-</sup> <i>c</i> <i>nd</i>), where <i>c</i> is a positive constant. Furthermore, the bound Omega(<i>e</i> <sup>-</sup> <i>c</i> (log<i>n</i>)<i>d</i>) , for all <i>d</i> > 1, holds under an additional mild condition on the distributions. This latter bound is shown to be tight.

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