Elicitation of the Parameters of Multiple Linear Models

Abstract

Estimating the parameters of a multiple linear model is a common task in all areas of sciences. In order to obtain conjugate distributions, the Bayesian estimation of these parameters is usually carried out using noninformative priors. When informative priors are considered in the Bayesian estimation an important problem arises because techniques arerequired to extract information from experts and represent it in an informative prior distribution. Elicitation techniques can be used for suchpurpose even though they are more complex than the traditional methods. In this paper, we propose a technique to construct an informative prior distribution from expert knowledge using hypothetical samples. Our proposal involves building a mental picture of the population of responses at several specific points of the explanatory variables of a given model andindirectly eliciting the mean and the variance at each of these points. In addition, this proposal consists of two steps: the first step describes the elicitation process and the second step shows a simulation process to estimate the model parameters.