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Revista Colombiana de Estadística
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Other literature type . 2021
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Elicitation of the Parameters of Multiple Linear Models

استنباط معلمات النماذج الخطية المتعددة
Authors: Carlos Barrera-Causil; Juan Carlos Correa;

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.

Keywords

conjugate distribution, Artificial intelligence, Conjugate prior, Learning and Inference in Bayesian Networks, Construct (python library), Linear model, Bayesian inference, Social Sciences, Expert Judgment, Management Science and Operations Research, Informative distribution, Bayesian statistics, Nonparametric Methods, Bayesian probability, Elicitación, Decision Sciences, Gaussian Processes in Machine Learning, Variance (accounting), Artificial Intelligence, Prior probability, Accounting, Machine learning, FOS: Mathematics, Business, Estadística Bayesiana, Data mining, Probabilistic Models, elicitation, Probabilistic Graphical Models, Linear regression; mixed models, Probabilistic Learning, Statistics, Elicitation, Conjugate distribution, Computer science, Distribución informativa, Process (computing), Programming language, Operating system, Computer Science, Physical Sciences, Time Series Forecasting Methods, Distribución conjugada, informative distribution, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
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gold
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