Elicitation of the Parameters of Multiple Linear Models

  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 estimat...

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Bibliographic Details
Published in:Revista Colombiana de estadística 2021, Vol.44 (1), p.159-170
Main Authors: Barrera-Causil, Carlos Javier, Correa-Morales, Juan Carlos
Format: Article
Language:English
Subjects:
Bayesian analysis
Cognition & reasoning
Estimation
Knowledge
Mathematical models
Parameters
Population
Probability
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Summary:  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.
ISSN:0120-1751
2389-8976
DOI:10.15446/rce.v44n1.83525