On Human Assisted Decision Making for Machines Using Correlated Observations

In this paper, the aim is to model the dependence between a continuous machine observation and a discrete human decision maker using copula theory for a binary hypothesis testing problem. We use a copula-based Likelihood Ratio Test (LRT) and derive expressions for the probability of false alarm and the probability of detection when the Signal-to-Noise ratio (SNR) is sufficiently large. When the machine observations are Gaussian with shifted means under the two hypotheses, we show the nature of the region in which the machine's observation falls, where there is no need for human assistance. We show that if the SNR is sufficiently large, the region that requires the human decision is a continuous interval.