Collaboration in Distributed Hypothesis Testing with Quantized Prior Probabilities

The effect of quantization of prior probabilities in a collection of distributed Bayesian binary hypothesis testing problems over which the priors themselves vary is studied. In a setting with fusion of local binary decisions by majority rule, optimal local decision rules are discussed. Quantization is first considered under the constraint that agents employ identical quantizers. A method for design is presented that exploits an equivalence to a single-agent problem with a different likelihood function, the optimal quantizers are thus different than in the single-agent case. Removing the constraint of identical quantizers is demonstrated to improve performance. A method for design is presented that exploits an equivalence between agents having diverse K-level quantizers and agents having identical (3K-2)-level quantizers.