Hypothesis Testing With Dependent Observations

This paper considers the problem of detection in a network consisting of heterogeneous sensors collecting measurements which are dependent both among the samples collected by each sensor and among the data collected by different sensors. The dependence in the data is modeled by using copula theory. It is assumed that the statistics of the sensors' data is not completely known and that, in particular, the probability distribution of the sensors' data involves unknown parameters. Our goal is to estimate these parameters and to detect the state of nature. The expectation maximization algorithm is developed and solved for this problem. Then, a case study including the Gaussian and Student's t copulas is investigated. The proposed method is compared with similar methods which ignore the dependence among the data. Numerical results are presented from simulations showing the efficacy of the proposed method for both parameter estimation and hypothesis testing.