Adaptive Statistical Inferential Methods For Information Processing

Modern sensors produce increasingly high volume of data that requires efficient and reliable statistical methods for information processing. We consider frequent problems of information processing which can be cast into the framework of parameter estimation and multihypothesis testing. We propose a unified approach for statistical inference of information processing by introducing the inclusion principle, confidence process, unimodal likelihood estimator, and time-uniform concentration inequalities. Our methods attempt to make decision based on observing data in an adaptive and sequential way so that the decision can be made as quick as possible, while the probability of committing mistakes is acceptably small.