Quantization of Prior Probabilities for Hypothesis Testing

Bayesian hypothesis testing is investigated when the prior probabilities of the hypotheses, taken as a random vector, are quantized. Nearest neighbor and centroid conditions are derived using mean Bayes risk error as a distortion measure for quantization. A high-resolution approximation to the distortion-rate function is also obtained. Human decision making in segregated populations is studied assuming Bayesian hypothesis testing with quantized priors

Quantization of Prior Probabilities for Collaborative Distributed Hypothesis Testing

This paper studies the quantization of prior probabilities, drawn from an ensemble, for distributed detection and data fusion. Design and performance equivalences between a team of N agents tied by a fixed fusion rule and a more powerful single agent are obtained. Effects of identical quantization and diverse quantization are compared. Consideration of perceived common risk enables agents using diverse quantizers to collaborate in hypothesis testing, and it is proven that the minimum mean Bayes risk error is achieved by diverse quantization. The comparison shows that optimal diverse quantization with K cells per quantizer performs as well as optimal identical quantization with N(K-1)+1 cells per quantizer. Similar results are obtained for maximum Bayes risk error as the distortion criterion.Comment: 11 page

On optimal quantization rules for some problems in sequential decentralized detection

We consider the design of systems for sequential decentralized detection, a problem that entails several interdependent choices: the choice of a stopping rule (specifying the sample size), a global decision function (a choice between two competing hypotheses), and a set of quantization rules (the local decisions on the basis of which the global decision is made). This paper addresses an open problem of whether in the Bayesian formulation of sequential decentralized detection, optimal local decision functions can be found within the class of stationary rules. We develop an asymptotic approximation to the optimal cost of stationary quantization rules and exploit this approximation to show that stationary quantizers are not optimal in a broad class of settings. We also consider the class of blockwise stationary quantizers, and show that asymptotically optimal quantizers are likelihood-based threshold rules.Comment: Published as IEEE Transactions on Information Theory, Vol. 54(7), 3285-3295, 200