ATD: Statistical methodology and algorithms for detection problems

Stanford University, Stanford CA

Investigators

Abstract

The investigator will develop new statistical methodology and algorithms for the quick detection of the abrupt emergence of a signal which is observed by a sensor in a noisy data stream or by an array of sensors in multiple data streams. A particular emphasis will be on the construction of techniques for effectively combining the information from several sensors. Such techniques are essential when the signal is weak and observed by only a small fraction of the sensors. Part of the proposed new methodology is based on recent advances in the statistical theory of multiscale analysis. Theoretical investigations of these recent advances in the abstract Gaussian White Noise model suggest that clear improvements in detection power are possible for the problem of a quick detection of a change point, and the investigator plans to adapt these ideas for this problem, to investigate its theoretical performance, and to develop efficient algorithms for its implementation. The second main emphasis is to develop improved statistical methodology to combine the information from several data streams using a novel criterion based on the average likelihood ratio. In preliminary work the investigator has shown that this criterion results in superior detection power in a large-scale multiple testing context, and the investigator will develop corresponding methodology for the detection of a signal in multiple data streams. Change-point detection plays an important role in a range of problems such as the detection of radioactive and biochemical threats, environmental monitoring, or the detection of recurrent DNA copy number variants in multiple samples in high-thoughput genomics. Advances in detection methodology have thus a direct impact on important problems in national security and in high-thoughput genomics, e.g. in terms of a shorter time to the detection of chemical agents and biological threats. The investigator will adapt recent results in statistical theory to these detection problems. The theoretical results suggest that clear improvements in detection power are possible in these important problems.