Prior Elicitation, Assessment and Inference with a Dirichlet Prior

Evans, Michael; Guttman, Irwin; Li, Peiying

doi:10.3390/e19100564

Cited by 13 publications

(25 citation statements)

References 15 publications

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“…, x n ) is a sample from the Bernoulli(θ) with θ ∈ [0, 1] unknown so nx ∼ binomial(n, θ) and interest is in θ. For the prior, let θ ∼ beta(α 0 , β 0 ) where the hyperparameters are elicited as in, for example [34], so…”

Section: Example 4 Binomial Proportionmentioning

confidence: 99%

Measuring and Controlling Bias for Some Bayesian Inferences and the Relation to Frequentist Criteria

Evans

Guo

2021

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A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in favor. Based upon the principle of evidence, it is shown how to measure and control these biases for both hypothesis assessment and estimation problems. Optimality results are established for the principle of evidence as the basis of the approach to these problems. A close relationship is established between measuring bias in Bayesian inferences and frequentist properties that hold for any proper prior. This leads to a possible resolution to an apparent conflict between these approaches to statistical reasoning. Frequentism is seen as establishing figures of merit for a statistical study, while Bayes determines the inferences based upon statistical evidence.

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Section: Example 4 Binomial Proportionmentioning

confidence: 99%

Measuring and Controlling Bias for Some Bayesian Inferences and the Relation to Frequentist Criteria

Evans

Guo

2021

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“…Moreover, P is treated quite differently than other probabilities (see, for example, Evans, Guttman, and Li ( 2017)). Alternative methods are, of course, suggested in the literature (see Zapata-Vázquez, O'Hagan, and Bastos (2014) and Evans et al (2017)) to deal with the elicitation of Dirichlet parameters efficiently but we stick to the method of Dorp and Mazzuchi (2003) simply because of its inherent ease. Moreover, since our illustration in the next section considers a large data size, it is expected that a slight deviation in elicited prior will not affect our final inferences.…”

Section: Subjective Elicitation Of Priormentioning

confidence: 99%

Subjective Elicitation of Dirichlet Hyperparameters Using Past Data: A Study of Ovarian Cancer Patients

Gupta

Upadhyay

2019

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Elicitation of prior plays a very important role in Bayesian paradigm especially when dealing with rare disease problems in medical field. The reason being that we do not get enough data to draw valid inferences always. Since the subject of study is human population, one cannot do experiments with their health. The prior distribution supports the final results by some additional information gained from the experts. In any case if an appropriate expert is not available, we can use past data to get information about the prior and its hyperparameters. The present paper provides a technique of elicitation of prior hyperparameters based on a well known multinomial-Dirichlet model. Since the main focus is on medical data problems, the inferences on odds ratios and interaction parameters are also provided. Numerical illustration is based on a real dataset from Israel on patients having ovarian cancer. Although the details have been given in the context of ovarian cancer patients, the development in the paper is equally well applicable for any such disease.

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“…Early work focused on representing expert opinion by a Dirichlet distribution, which is the natural conjugate prior distribution for multinomial sampling; reviews of this work may be found in Garthwaite et al (2005) andO'Hagan et al (2006). Modelling opinion by a Dirichlet distribution has continued to attract attention (Zapata-Vázquez et al, 2014;Evans et al, 2017), but methods for eliciting more flexible prior distributions have also been proposed. Elfadaly and Garthwaite (2013) give a method for quantifying expert opinion as both a Dirichlet distribution and a Connor-Mosimann distribution, and give an example to illustrate the greater flexibility of the latter.…”

Section: Introductionmentioning

confidence: 99%