Statistical sequential hypotheses testing on parameters of probability distributions of random binary data

Abstract

An important mathematical problem of computer data analysis – the problem of statistical sequential testing of simple hypotheses on parameters of probability distributions of observed binary data – is considered in the paper. This problem is being solved for two models of observation: for independent observations and for homogeneous Markov chains. Ex­plicit expressions of the sequential tests statistics are derived, transparent for interpretation and convenient for computer realisation. An approach is developed to calculate the performance characteristics – error probabilities and mathematical expectations of the random number of observations required to guarantee the requested accuracy for decision rules. As­ymptotic expansions for the mentioned performance characteristics are constructed under «contamination» of the proba­ bility distributions of observed data.