Bayes Estimation Of The Variance And Covariance Components In The Two Types Of Statistical Models

In the regression model, the estimation of variance and covariance components is wider applied in the industrial, chemical, biological, behavioral sciences, and other fields. In this paper, the two kinds of statistical models are the nonlinear model and the mixed-integer linear model. The estimations of variance and covariance components which come from non-informative prior and inverted gamma prior are researched with the Bayesian approach in the two kinds of statistical models.In this paper, the Bayesian estimation of the variance and covariance components include the correlation coefficientρin the nonlinear model, but the Bayesian estimation of the variance and covariance components in the linear model is provided by other scholars just only a special situation. By an example , the feasibility of the Bayesian approach is demonstrated, and the result of inverted gamma prior is better than non-informative prior.The research of the mixed-integer linear model began with the GPS measurement (Xu peiliang, 2006), this issue is not studied in the statistics. The baseline vectorβ∈R~l and the difference-two whole ambiguityθ∈Z~m are studied in the GPS measurement, in which the variance and covariance components are not considered. From the view of statistics, the estimation of variance and covariance components is the same important as other estimations of unknown parameters. So another issue of research in this paper is the Bayesian estimation of variance in the mixed-integer linear model by satellites. Similarly, the result indicates that the result of inverted gamma prior is better than non-informative prior.