NDLI: On the probability of a model

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On the probability of a model

Content Provider	Springer Nature Link
Author	Villegas, Cesareo Swartz, Tim Martínez, Carmillo
Copyright Year	2002
Abstract	The posterior probabilities ofK given models when improper priors are used depend on the proportionality constants assigned to the prior densities corresponding to each of the models. It is shown that this assignment can be done using natural geometric priors in multiple regression problems if the normal distribution of the residual errors is truncated. This truncation is a realistic modification of the regression models, and since it will be made far away from the mean, it has no other effect beyond the determination of the proportionality constants, provided that the sample size is not too large. In the caseK=2, the posterior odds ratio is related to the usualF statistic in “classical” statistics. Assuming zero-one losses the optimal selection of a regression model is achieved by maximizing the posterior probability of a submodel. It is shown that the geometric criterion obtained in this way is asymptotically equivalent to Schwarz’s asymptotic Bayesian criterion, sometimes called the BIC criterion. An example of polynomial regression is used to provide numerical comparisons between the new geometric criterion, the BIC criterion and the Akaike information criterion.
Starting Page	413
Ending Page	438
Page Count	26
File Format	PDF
ISSN	11330686
Journal	Test
Volume Number	11
Issue Number	2
e-ISSN	18638260
Language	English
Publisher	Springer-Verlag
Publisher Date	2002-01-01
Publisher Institution	Spanish Society of Statistics and Operations Research
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Bayesian testing geometric Bayesian inference geometric priors, model selection probability of a model sharp hypotheses variable selection Diagnostics Statistics Statistical Theory and Methods Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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