Abstract:
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Consider a stochastic system composed of multiple subsystems, where each subsystem can generate a binary response. The full system follows a general canonical exponential family distribution (e.g., Gaussian and multinomial) that depends on multiple parameters. This type of system has a wide range of applications in practice, such as systems reliability testing, sensor networks, target detection, fault diagnosis, and Internet-based systems control. Based on principles of maximum likelihood estimation, prior work introduces a method to estimate the mean output (reliability) of the full system and the "success" probabilities of the subsystems. This paper generalized the results to estimate all the unknown parameters in the exponential family distribution (e.g., means and variances of a Gaussian distribution). We derive an MLE formulation for general structural relationships between the subsystems and the full system along with the formal convergence proof of the MLEs. The asymptotic distributions of the MLEs are also given, which is then used to provide asymptotic confidence bounds through the Fisher information matrix.
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