Bayesian inference for the Errors-In-Variables model

Abstract

We discuss the Bayesian inference based on the Errors-In-Variables (EIV) model. The proposed estimators are developed not only for the unknown parameters but also for the variance factor with or without prior information. The proposed Total Least-Squares (TLS) estimators of the unknown parameter are deemed as the quasi Least-Squares (LS) and quasi maximum a posterior (MAP) solution. In addition, the variance factor of the EIV model is proven to be always smaller than the variance factor of the traditional linear model. A numerical example demonstrates the performance of the proposed solutions.