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Below results based on the criteria 'noninformative prior distribution'
Total number of records returned: 2

1
Paper
Prior Distributions for Variance Parameters in Hierarchical Models
Gelman, Andrew

Uploaded 03-28-2004
Keywords Bayesian inference
hierarchical model
multilevel model
noninformative prior distribution
weakly informative prior distribution
Abstract Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. We construct a new folded-noncentral-$t$ family of conditionally conjugate priors for hierarchical standard deviation parameters, and then consider noninformative and weakly informative priors in this family. We use an example to illustrate serious problems with the inverse-gamma family of "noninformative" prior distributions. We suggest instead to use a uniform prior on the hierarchical standard deviation, using the half-$t$ family when the number of groups is small and in other settings where a weakly informative prior is desired.

2
Paper
A default prior distribution for logistic and other regression models
Gelman, Andrew
Jakulin, Aleks
Pittau, Maria Grazia
Su, Yu-Sung

Uploaded 08-03-2007
Keywords Bayesian inference
generalized linear model
least squares
hierarchical model
linear regression
logistic regression
multilevel model
noninformative prior distribution
Abstract We propose a new prior distribution for classical (non-hierarchical) logistic regression models, constructed by first scaling all nonbinary variables to have mean 0 and standard deviation 0.5, and then placing independent Student-$t$ prior distributions on the coefficients. As a default choice, we recommend the Cauchy distribution with center 0 and scale 2.5, which in the simplest setting is a longer-tailed version of the distribution attained by assuming one-half additional success and one-half additional failure in a logistic regression. We implement a procedure to fit generalized linear models in R with this prior distribution by incorporating an approximate EM algorithm into the usual iteratively weighted least squares. We illustrate with several examples, including a series of logistic regressions predicting voting preferences, an imputation model for a public health data set, and a hierarchical logistic regression in epidemiology. We recommend this default prior distribution for routine applied use. It has the advantage of always giving answers, even when there is complete separation in logistic regression (a common problem, even when the sample size is large and the number of predictors is small) and also automatically applying more shrinkage to higher-order interactions. This can be useful in routine data analysis as well as in automated procedures such as chained equations for missing-data imputation.


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