Bayesian estimation of variance factorin the nonlinear model

Motivated by the theory of Bayesian estimation of variance factor for the linear model.An attempt is made to establish a corresponding estimation theory for the nonlinear model.Under the principle of the minimization of the mean square error,the Bayesian estimation of variance factor for the nonlinear model is systematically studied.Best Bayesian estimation and best-unbiased Bayesian estimation of variance factor with conjugate and no informative priors are presented.The best conditionally unbiased Bayesian estimation of variance factor is developed.To compare with above estimations,the maximum posterior estimations of variance factor with conjugate and no informative priors are presented.Finally,a simple example is given to illuminate above feasibility.