Data selection in binary hypothesis testing

Abstract

Traditionally, statistical signal processing algorithms are developed from probabilistic models for data. The design of the algorithms and their ultimate performance depend upon these assumed models. In certain situations, collecting or processing all available measurements may be inefficient or prohibitively costly. A potential technique to cope with such situations is data selection, where a subset of the measurements that can be collected and processed in a cost-effective manner is used as input to the signal processing algorithm. Careful evaluation of the selection procedure is important, since the probabilistic description of distinct data subsets can vary significantly. An algorithm designed for the probabilistic description of a poorly chosen data subset can lose much of the potential performance available to a well-chosen subset. This thesis considers algorithms for data selection combined with binary hypothesis testing. We develop models for data selection in several cases, considering both random and deterministic approaches. Our considerations are divided into two classes depending upon the amount of information available about the competing hypotheses. In the first class, the target signal is precisely known, and data selection is done deterministically. In the second class, the target signal belongs to a large class of random signals, selection is performed randomly, and semi-parametric detectors are developed.