Sequential detection with limited memory

Sequential tests outperform fixed sample size tests by requiring fewer samples on average to achieve the same level of error performance. The sequential probability ratio test (SPRT) has been suggested by Wald (1947) for sequential binary hypothesis testing problems. SPRT recursively calculates the likelihood of an observed data stream and requires this likelihood to be stored in memory between samples. In this paper we study the design of sequential detection tests under memory constraints. We derive the optimal sequential test in the case where only a quantized version of the likelihood can be stored in memory. An application of the proposed techniques is large scale sensor networks where price and communication constraints dictate limited complexity devices, which store and transmit concise representations of the state of nature.