Multiple-model hypothesis testing using adaptive representative model

This paper presents a multiple-model hypothesis testing (MMHT) approach using a representative model (RM) for detecting unknown events that may have multiple distributions. It addresses various difficulties of MMHT for composite, multivariate, nondisjoint, and mis-specified hypothesis sets with correlated observations, and decides which region of the mode space covered by the model set is better. The model-set likelihood (MSL) based MMHT method (MMHT-MSL) is promising because of its efficiency and theoretical validity. The MSL is dominated by the likelihood of the closest-to-truth model in the model set as the sample size increases. However, the multiple-model approach usually intends to deal with all possible modes in the convex hull of the model set rather than only the models in the model set. Consequently, when mis-specification exists, this dominating model is not necessarily representative; that is, it is inappropriate for the model set rather than the region of the mode space covered by the model set. Our approach utilizes model-set adaptation (e.g., expected-mode augmentation and best model augmentation) to improve coverage ability of the model set, and then searches for the model which is closest to the truth under some criterion in the model-set-covered region as the RM. The RM based MMHT method (MMHT-RM) can be expected to provide a more efficient detection in the sense of minimizing the expected sample size subject to the error probability constraints. Moreover, in contrast to the MMHT-MSL, MMHT-RM is highly computationally efficient and easy to implement. Performance of MMHT-RM is evaluated for model-set selection problems in several scenarios. Simulation results demonstrate the effectiveness of the proposed MMHT-RM compared with MMHT-MSL.