Results 1  10
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20
Prior Probabilities
 IEEE Transactions on Systems Science and Cybernetics
, 1968
"... e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determ ..."
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Cited by 171 (3 self)
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e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determined by the prior information, independently of the choice of parameters. In a certain class of problems, therefore, the prior distributions may now be claimed to be fully as "objective" as the sampling distributions. I. Background of the problem Since the time of Laplace, applications of probability theory have been hampered by difficulties in the treatment of prior information. In realistic problems of decision or inference, we often have prior information which is highly relevant to the question being asked; to fail to take it into account is to commit the most obvious inconsistency of reasoning and may lead to absurd or dangerously misleading results. As an extreme examp
A WEAKLY INFORMATIVE DEFAULT PRIOR DISTRIBUTION FOR LOGISTIC AND OTHER REGRESSION MODELS
"... We propose a new prior distribution for classical (nonhierarchical) logistic regression models, constructed by first scaling all nonbinary variables to have mean 0 and standard deviation 0.5, and then placing independent Studentt prior distributions on the coefficients. As a default choice, we reco ..."
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Cited by 19 (7 self)
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We propose a new prior distribution for classical (nonhierarchical) logistic regression models, constructed by first scaling all nonbinary variables to have mean 0 and standard deviation 0.5, and then placing independent Studentt 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 longertailed version of the distribution attained by assuming onehalf additional success and onehalf additional failure in a logistic regression. Crossvalidation on a corpus of datasets shows the Cauchy class of prior distributions to outperform existing implementations of Gaussian and Laplace priors. We recommend this prior distribution as a default choice 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 higherorder interactions. This can
An introduction to Bayesian reference analysis: Inference on the ratio of multinomial parameters. The Statistician 47
, 1998
"... ..."
A Compendium of Conjugate Priors
, 1997
"... This report reviews conjugate priors and priors closed under sampling for a variety of data generating processes where the prior distributions are univariate, bivariate, and multivariate. The effects of transformations on conjugate prior relationships are considered and cases where conjugate prior r ..."
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Cited by 7 (0 self)
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This report reviews conjugate priors and priors closed under sampling for a variety of data generating processes where the prior distributions are univariate, bivariate, and multivariate. The effects of transformations on conjugate prior relationships are considered and cases where conjugate prior relationships can be applied under transformations are identified. Univariate and bivariate prior relationships are verified using Monte Carlo methods. Contents 1
RESURRECTING LOGICAL PROBABILITY
 ERKENNTNIS
, 2001
"... The logical interpretation of probability, or “objective Bayesianism” – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine t ..."
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Cited by 3 (0 self)
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The logical interpretation of probability, or “objective Bayesianism” – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a “principle of insufficient reason” inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; that it is possible to distinguish reasonable from unreasonable priors on logical grounds; and that in real cases disagreement about priors can usually be explained by differences in the background information. It is argued also that proponents of alternative conceptions of probability, such as frequentists, Bayesians and Popperians, are unable to avoid committing themselves to the basic principles of logical probability.
A noninformative prior for neural networks
 Machine Learning
, 2000
"... Neural networks are commonly used for classification and regression. The Bayesian approach may be employed, but choosing a prior for the parameters presents challenges. This paper reviews several priors in the literature and introduces Jeffreys priors for neural network models. The effect on the pos ..."
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Cited by 3 (0 self)
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Neural networks are commonly used for classification and regression. The Bayesian approach may be employed, but choosing a prior for the parameters presents challenges. This paper reviews several priors in the literature and introduces Jeffreys priors for neural network models. The effect on the posterior is demonstrated through an example. Key Words: nonparametric classification; nonparametric regression; Bayesian statistics; prior sensitivity 1
Parametric bootstrap approximation to the distribution of EBLUP, and related prediction intervals in linear mixed models. Annals of Statisitcs
, 2008
"... Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed model in combining information from different sources of information. This method is particularly useful in small area problems. The variability of an EBLUP is traditionally measured by the mean squared prediction error (MS ..."
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Cited by 3 (1 self)
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Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed model in combining information from different sources of information. This method is particularly useful in small area problems. The variability of an EBLUP is traditionally measured by the mean squared prediction error (MSPE), and interval estimates are generally constructed using estimates of the MSPE. Such methods have shortcomings like undercoverage or overcoverage, excessive length and lack of interpretability. We propose a parametric bootstrap approach to estimate the entire distribution of a suitably centered and scaled EBLUP. The bootstrap histogram is highly accurate, and differs from the true EBLUP distribution by only O(d 3 n −3/2), where d is the number of parameters and n the number of observations. This result is used to obtain highly accurate prediction intervals. Simulation results demonstrate the superiority of this method over existing techniques of constructing prediction intervals in linear mixed models. 1. Introduction. Large
A representation theorem and applications to measure selection and noninformative priors
"... We introduce a set of transformations on the set of all probability distributions over a finite state space, and show that these transformations are the only ones that preserve certain elementary probabilistic relationships. This result provides a new perspective on a variety of probabilistic infere ..."
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Cited by 2 (1 self)
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We introduce a set of transformations on the set of all probability distributions over a finite state space, and show that these transformations are the only ones that preserve certain elementary probabilistic relationships. This result provides a new perspective on a variety of probabilistic inference problems in which invariance considerations play a role. Two particular applications we consider in this paper are the development of an equivariancebased approach to the problem of measure selection, and a new justification for Haldane’s prior as the distribution that encodes prior ignorance about the parameter of a multinomial distribution. 1.
A representation theorem and applications
 in ‘Proceedings of the Seventh European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU)’, Lecture Notes in Artificial Intelligence
, 2003
"... Abstract. We introduce a set of transformations on the set of all probability distributions over a finite state space, and show that these transformations are the only ones that preserve certain elementary probabilistic relationships. This result provides a new perspective on a variety of probabilis ..."
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Cited by 2 (2 self)
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Abstract. We introduce a set of transformations on the set of all probability distributions over a finite state space, and show that these transformations are the only ones that preserve certain elementary probabilistic relationships. This result provides a new perspective on a variety of probabilistic inference problems in which invariance considerations play a role. Two particular applications we consider in this paper are the development of an equivariancebased approach to the problem of measure selection, and a new justification for Haldane’s prior as the distribution that encodes prior ignorance about the parameter of a multinomial distribution. 1
Default Priors for Neural Network Classification
, 2005
"... Feedforward neural networks are a popular tool for classification, offering a method for fully flexible modeling. This paper looks at the underlying probability model, so as to understand statistically what is going on in order to facilitate an intelligent choice of prior for a fully Bayesian analys ..."
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Cited by 1 (0 self)
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Feedforward neural networks are a popular tool for classification, offering a method for fully flexible modeling. This paper looks at the underlying probability model, so as to understand statistically what is going on in order to facilitate an intelligent choice of prior for a fully Bayesian analysis. The parameters turn out to be difficult or impossible to interpret, and yet a coherent prior requires a quantification of this inherent uncertainty. Several approaches are discussed, including flat priors, Jeffreys priors and reference priors. Key Words: Bayesian neural network; nonparametric classification; noninformative prior