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2020
Selecting a prior distribution is integral to Bayesian analyses. In this chapter, we discuss several approaches to specifying priors. First, we discuss the concept of “noninformative” priors. Next we introduce improper priors. Following this, we define conjugate priors. We conclude with a brief discussion of how a scientist might specify an informative
Edwin J. Green +2 more
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Selecting a prior distribution is integral to Bayesian analyses. In this chapter, we discuss several approaches to specifying priors. First, we discuss the concept of “noninformative” priors. Next we introduce improper priors. Following this, we define conjugate priors. We conclude with a brief discussion of how a scientist might specify an informative
Edwin J. Green +2 more
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Sensitivity of a Bayesian analysis to the prior distribution
IEEE Transactions on Systems, Man, and Cybernetics, 1994Consider the problem of eliciting and specifying a prior probability distribution for a Bayesian analysis. There will generally be some uncertainty in the choice of prior, especially when there is little information from which to construct such a distribution, or when there are several priors elicited, say, from different experts.
Stacy D. Hill, James C. Spall
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From Prior Information to Prior Distributions
1994Undoubtedly, the most critical and most criticized point of Bayesian analysis deals with the choice of the prior distribution. Indeed, in practice, it seldom occurs that the available prior information is precise enough to lead to an exact determination of the prior distribution, in the sense that many probability distributions are compatible with this
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Selecting the Prior Distribution in Bayesian Estimation
IEEE Transactions on Reliability, 1977A major problem associated with Bayesian estimation is selecting the prior distribution. Fisher's information measure is extended to cover prior distributions so that a comparative measure of the amount of information in the sample and in the prior is obtained. The amount of information is used as an intuitive measure of the relative value or weight of
Canfield, Ronald V., Teed, John C.
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Assigning a Prior Distribution
2020There is no such thing as the prior probability distribution of a parameter or a set of models. A prior expresses uncertainty arising from incomplete knowledge, and whatever the subject is, people have different knowledge and expertise. So instead of speaking of “the prior probability of \(x\)”, each of us should say “my prior probability for \(x ...
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Distribution-Dependent PAC-Bayes Priors
2010We develop the idea that the PAC-Bayes prior can be informed by the data-generating distribution. We prove sharp bounds for an existing framework, and develop insights into function class complexity in this model and suggest means of controlling it with new algorithms.
Guy Lever +2 more
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Compatible Prior Distributions for DAG models
2004The application of certain Bayesian techniques, such as the Bayes factor and model averaging, requires the specification of prior distributions on the parameters of alternative models. We propose a new method for constructing compatible priors on the parameters of models nested in a given directed acyclic graph model, using a conditioning approach.
ROVERATO, ALBERTO, G. Consonni
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