A multistage procedure for decentralized sequential multi-hypothesis testing problems

We studied the problem of sequentially testing M ≥ 2 hypotheses with a decentralized sensor network system. In such a system, the local sensors observe raw data and then send quantized observations to a fusion center, which makes a final decision regarding hypothesis is true. Motivated by the two-stage tests in Wang and Mei (2011), we propose a multistage decentralized sequential test that provides multiple opportunities for the local sensors to adjust to the optimal local quantizers. It is demonstrated that when the hypothesis testing problem is asymmetric, the multistage test is second-order asymptotically optimal. Even though this result constitutes an interesting theoretical improvement over twostage tests that can enjoy only first-order asymptotic optimality, the corresponding practical merits seem to be only marginal. Indeed, performance gains over two-stage procedures with carefully selected thresholds are small.