On optimal quantization rules for some sequential decision problems

We consider the problem of sequential decentralized detect ion, a problem that entails several interdependent choices: the choice of a stopping rule (specifyin g the sample size), a global decision function (a choice between two competing hypotheses), and a set of qua ntization rules (the local decisions on the basis of which the global decision is made). In this paper we esolve an open problem concerning whether optimal local decision functions for the Bayesian f ormulation of sequential decentralized detection can be found within the class of stationary rules. We dev elop an asymptotic approximation to the optimal cost of stationary quantization rules and show how t his approximation yields a negative answer to the stationarity question. We also consider the class of b lockwise stationary quantizers and show that asymptotically optimal quantizers are likelihood-based t hreshold rules. 1

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