Multiple-model hypothesis testing based on 2-SPRT

Abstract

Double sequential probability ratio test (2-SPRT), as an extended version of SPRT to cope with the no-upper-bound problem, is extended to the multiple-model hypothesis testing (MMHT) approach, called 2-MMSPRT, for detecting unknown events that may have multiple prior distributions. Not only does it address the mis-specified problem of the SPRT based MMHT method (MMSPRT), but it also can be expected to provide most efficient detection in the sense of minimizing the maximum expected sample size subject to error probability constraints. Specifically, we proved the theoretical validity of 2-SPRT for the problem of testing hypotheses with multivariate normal densities. Moreover, we present a method of forced independence and identical distribution (i.i.d.) to optimally map the non-i.i.d. likelihood ratio sequence to an i.i.d. one, by which we solve the problem of SPRT and 2-SPRT for dynamic systems with a non-identical distribution. Finally, 2-MMSPRT's asymptotic efficiency is also verified. Performance of 2-MMSPRT is evaluated for model-set selection problems in several scenarios. Simulation results demonstrate the asymptotic effectiveness of the proposed 2-MMSPRT compared with the MMSPRT.