Published
2017-12-23

Elicitación de una distribución a priori para el modelo logístico

Eliciting an a priori distribution for a logistic model

DOI: https://doi.org/10.15332/2422474x.3175
Jenny Andrea Tangarife Quintero
Juan Carlos Correa Morales

Abstract (en)

In many situations it is useful to quantify subjective information that one or more experts know about a topic of interest, therefore, an important part of Bayesian statistics is building elicitation methods for finding probability distributions. In order to contribute to the development in this field, a methodology was developed to elicit the parameters of the logistic regression with a single covariate. The proposed method requires to determite the levels of the covarible, at each level a binomial distribution is assumed and the parameter of interest is elicited by using the indirect method hypothetical samples.

 

 

Keywords (en): a priori distribution, bayesian statistic, beta distribution, binomial distribution, indirect methodology.

Abstract (es)

En muchas situaciones resulta util cuanticar informacion subjetiva que uno o varios expertos conocen acerca de un tema de interes, por esto, una parte importante dentro de la estadstica Bayesiana es la construccion de metodos de elicitacion para hallar distribuciones de probabilidad. Con el fin de contribuir al desarrollo en este campo,se desarrollo una metodología para elicitar los parametros de la regresion logstica con una sola covariable. El metodo que se plantea requiere que se jen unos niveles de la covarible y en estos se asume una distribucion Binomial, para cada nivel se elicita el parametro de interes mediante la metodologa indirecta de muestras hipoteticas.

 

Keywords (es): distribución a priori, distribución beta, distribución binomial, estadísica bayesiana, metodología indirecta.

References

Barrera, C. (2015), ‘Analysis of the elicited prior distributions using tools of functional’,Tesis Doctoral, Universidad Nacional de Colombia .

Bedrick, E., Christensen, R. & Johnson, W. (1996), ‘A new perspective on priors for generalized linear models’, The American Statistical Association 91, 1450–1460.

Bedrick, E., Christensen, R. & Johnson, W. (1997), ‘Bayesian binomial regression: Predicting survival at a trauma center’, the American Statistical Association 51, 211–218.

Burgman, M., Fidler, F., McBride, M., Walshe, T. & Wintle, B. (2007), ‘Eliciting expert judgments: Literature review’, University of Melbourne .

Cannell, C. (1977), ‘A summary of studies of interviewingmethodology’, Vital and Health Statistics 2, 69–72.

Chaloner, K. & Duncan, T. (1983), ‘Assessment of a beta prior distribution: Pmelicitation’, The Statistician pp. 174–180.

Chaloner, K. & Larntz, K. (1989), ‘Optimal bayesian design applied to logistic regression experiments’, Statistical Planning and Inference 21, 191–208.

Chesley, G. (1975), ‘Elicitation of sub active probabilities: A review’, The Accounting Review 50, 325–337.

Choy, L., James, A. & Mengersen, K. (2009), ‘Expert elicitation and its interface with technology: a review with a view to designing elicitator’, The Accounting Review 18, 13–17.

De Finetti, B. (1937), ‘La prevision: ses lois logigues, ses sources subjectives’, Annal es de l’Institut Henri Poincard 7, 1–68.

Denham, R. & Mengersen, K. (2007), ‘Geographically assisted elicitation of expert opinion for regression models’, Bayesian Analysis 2, 99–136.

Garthwaite, P. & Al-Awadhi, S. (2006), ‘Quantifying opinion about a logistic regression using interactive graphics’, Statistics Group 6.

Garthwaite, P. & Dickey, J. (1988), ‘Quantifying expert opinion in linear regression problems’, The Royal Statistical Society 29, 462–474.

Garthwaite, P. & O’Hagan, A. (2005), ‘Statistical methods for eliciting probability distributions’, The American Statistical Association 100, 680–700.

Hamada, M., Martz, H. F., Reese, C. S. & Wilson, A. G. (2001), ‘Finding nearoptimal bayesian experimental designs via genetic algorithms’, The American Statistician 55, 175–181.

Hora, S. (2007), ‘Advances in desicion analysis: From foundations to applications’, Cambridge University Press pp. 129–153.

Huson, L. & Kinnersley, N. (2008), ‘ayesian fitting of a logistic dose-response curve with numerically derived priors’, John Wiley and Sons Inc .

James, A., Low Choy, S. & Mengersen, K. (2010), ‘Elicitator: an expert elicitation tool for regression in ecology’, Environmental Modelling and Software 25, 129– 145.

Kadane, J. & Wolfson, L. (1998), ‘Experiencies in elicitation’, The Statistician 47, 3–19.

Kynn, M. (2005), ‘Designing elicitor: Software to graphically elicit expert priors for logistic regression models in ecology’, Department of Mathematics and Statistics, Fylde College, Lancaster University .

Kynn, M. (2008), ‘The heuristics and biases bias in expert elicitation’, The Royal Statistical Society 171, 239–264.

Martin, T., Kuhnert, P., Mengersen, K. & Possingham, H. (2005), ‘he power of expert opinion in ecological models: a bayesian approach examining the impact of livestock grazing on birds’, Ecological Applications 15, 266–280.

O’Leary, R., Low Choy, S., Mengersen, K., Kynn, M., Kuhnert, P., Denham, R.,Martin, T. & Murray, J. (2008), ‘Comparison of expert elicitation methods for logistic regression for presence of endangered brush-tailed rock-wallaby petrolage penicillata’, Environmetrics.

Sedlmeier, P. (1999), ‘Improving statistical reasoning: theoretical models and practical’, implications, Lawrence Erlbaum, Mahwah, NJ.

Shephard, G. & Kirkwood, C. (1994), ‘Managing the judgmental probability elicitation process: A casestudy of analyst/manager interaction’, IEEE Transactions on Engineering Management 41, 414–425.

Umesh, G. (1998), ‘Comparison of two elicitation methods for a prior for a binomial parameter’, Management Science 34, 784–790.

Dimensions

PlumX

Visitas

750

Downloads

Download data is not yet available.

How to Cite

Tangarife Quintero, J. A., & Correa Morales, J. C. (2017). Eliciting an a priori distribution for a logistic model. Comunicaciones En Estadística, 10(2), 225-246. https://doi.org/10.15332/2422474x.3175