Abstract:

Wiener process is widely applied to model the performance degradation of products, and the conjugate prior distributions of random parameters are commonly adopted to facilitate the Bayesian inference. Due to the problem that the accuracy of the prior estimates of hyper parameters obtained by the twostep method is not high, the application of the expectation maximization (EM)algorithm to the prior estimation of hyper parameters of Wiener processes is studied. The EM algorithm takes the random parameters as hidden variables to deal with prior information as a whole, replaces the estimates of the random parameters with the expectations, and obtains the prior estimates of hyper parameters by the recursive iteration process which consists of expectation and maximization. Simulation tests show that the EM algorithm improves the estimation accuracy compared to the two-step method and has a relatively large advantage in estimation accuracy when the number of sampling is low. The case application of GaAs laser indicates that the EM algorithm not only has a good convergence but also provides a good engineering application value.