Bayesian statistical inference using a regression in electrical impedance tomography

Abstract

In this paper, we present the formulation of Bayesian statistical inference with respect to a posterior distribution using a regression model. So the unknown parameter is set as the dependent variable and the data measurement is set as the independent variable of the regression model. The regression model is built using joint samples of the unknown parameter and the data measurements drawn from the related likelihood function and prior distribution. The regression fits an operator constructed from the so-called optimal approximation method. Naturally, the regression model defines an approximated posterior distribution and, in this regards, we call it the posterior approximated regression model (PARM). The feasibility of making Bayesian statistical inference using PARM is tested numerically. We consider the electrical impedance tomography Bayesian inverse problem on a two dimensional domain with benchmark examples. Results with varying levels of practicality and intuitive discussions are presented.