Specifying a Prior Distribution in Structured Regression Problems

Oman, Samuel D.

doi:10.2307/2288070

Cited by 5 publications

(3 citation statements)

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“…(i) It protects against overshrinking by smoothly weighting â(k) and â according to the F-statistic we would use for making a preliminary test of model (1) vs model (2) (Sclove et al, 1972;Bock et al, 1973;Yancey & Judge, 1976). (ii) It is an empirical Bayes estimator which incorporates prior beliefs both in (2) and that the explanatory variables are intrinsically correlated as in the observed X (Raiffa & Schlaiffer, 1961;Tiao & Zellner, 1964;Efron & Morris, 1973;Zellner, 1983;Oman, 1984Oman, , 1985. (iii) Because â Ã (k) is a Stein estimator, PMSE( â Ã (k), â) , PMSE( â, â) for all â, where for an estimator â Ã , PMSE( â Ã , â) Ei X â Ã À X âi 2 .…”

Section: Additional Referencesmentioning

confidence: 99%

Multivariate Calibration — Direct and Indirect Regression Methodology

Sundberg

1999

Scandinavian J Statistics

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This paper tries ®rst to introduce and motivate the methodology of multivariate calibration. Next a review is given, mostly avoiding technicalities, of the somewhat messy theory of the subject. Two approaches are distinguished: the estimation approach (controlled calibration) and the prediction approach (natural calibration). Among problems discussed are the choice of estimator, the choice of con®dence region, methodology for handling situations with more variables than observations, near-collinearities (with countermeasures like ridge type regression, principal components regression, partial least squares regression and continuum regression), pretreatment of data, and cross-validation vs true prediction. Examples discussed in detail concern estimation of the age of a rhinoceros from its horn lengths (low-dimensional), and nitrate prediction in waste-water from high-dimensional spectroscopic measurements.

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Section: Additional Referencesmentioning

confidence: 99%

Multivariate Calibration — Direct and Indirect Regression Methodology

Sundberg

1999

Scandinavian J Statistics

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“…29 Bedrick et al 3 extended this approach to multiple covariates and to GLMs. In normal theory multiple regression, Kadane et al 30 and Oman 31 have also proposed choosing priors for speciÿed vectors of covariates. The AFT model has non-linear aspects similar to GLMs, but it also presents some distinct issues, namely, it is a location-scale family and often there is censoring.…”

Section: Specifying the Priormentioning

confidence: 99%

Bayesian accelerated failure time analysis with application to veterinary epidemiology

2000

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Standard methods for analysing survival data with covariates rely on asymptotic inferences. Bayesian methods can be performed using simple computations and are applicable for any sample size. We propose a practical method for making prior specifications and discuss a complete Bayesian analysis for parametric accelerated failure time regression models. We emphasize inferences for the survival curve rather than regression coefficients. A key feature of the Bayesian framework is that model comparisons for various choices of baseline distribution are easily handled by the calculation of Bayes factors. Such comparisons between non‐nested models are difficult in the frequentist setting. We illustrate diagnostic tools and examine the sensitivity of the Bayesian methods. Copyright © 2000 John Wiley & Sons, Ltd.

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“…Their approach is appealing but intractable for most GLM's. Oman (1985) suggested priors for linear models based on specifying a set of covariates and eliciting information on the corresponding mean vector. His approach is related to ours for that special case but does not easily generalize.…”

Section: Introductionmentioning

confidence: 99%

A New Perspective on Priors for Generalized Linear Models

Bedrick,

Christensen,

Johnson

1996

Journal of the American Statistical Association

217

202

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This article deals with specifications of informative prior distributions for generalized linear models. Our emphasis is on specifying distributions for selected points on the regression surface; the prior distribution on regression coefficients is induced from this specification. We believe that it is inherently easier to think about conditional means of observables given the regression variables than it is to think about model-dependent regression coefficients. Previous use of conditional means priors seems to be restricted to logistic regression with one predictor variable and to normal theory regression. We expand on the idea of conditional means priors and extend these to arbitrary generalized linear models. We also consider data augmentation priors where the prior is of the same form as the likelihood. We show that data augmentation priors are special cases of conditional means priors. With current Monte Carlo methodology, such as importance sampling and Gibbs sampling, our priors result in tractable posteriors.

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Specifying a Prior Distribution in Structured Regression Problems

Cited by 5 publications

References 0 publications

Multivariate Calibration — Direct and Indirect Regression Methodology

Multivariate Calibration — Direct and Indirect Regression Methodology

Bayesian accelerated failure time analysis with application to veterinary epidemiology

A New Perspective on Priors for Generalized Linear Models

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