Parameter estimation for systems with binary subsystems

Consider a stochastic system of multiple subsystems, each subsystem having binary (“0 or 1”) output. The full system may have general binary or non-binary (e.g., Gaussian) output. Such systems are widely encountered in practice, and include engineering systems for reliability, communications and sensor networks, the collection of patients in a clinical trial, and Internet-based control systems. This paper considers the identification of parameters for such systems for general structural relationships between the subsystems and the full system. Maximum likelihood estimation (MLE) is used to estimate the mean output for the full system and the “success” probabilities for the subsystems. The MLE approach is well suited to providing asymptotic or finite-sample confidence bounds through the use of Fisher information or bootstrap Monte Carlo-based sampling. Three examples are presented to illustrate the method.