Prior‐based model checking

Al-Labadi, Luai; Evans, Michael

doi:10.1002/cjs.11457

Cited by 22 publications

(13 citation statements)

References 27 publications

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“…So the approach discussed in Al Labadi et al. ( 2017a ) and Al Labadi and Evans ( 2018 ) is used in such situations. A distance measure d on is specified so measures the distance is from which will be denoted hereafter as the set is implicit.…”

Section: Checking the Modelmentioning

confidence: 99%

Checking for model failure and for prior-data conflict with the constrained multinomial model

Englert

Evans

Jang

et al. 2021

Metrika

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Multinomial models can be difficult to use when constraints are placed on the probabilities. An exact model checking procedure for such models is developed based on a uniform prior on the full multinomial model. For inference, a nonuniform prior can be used and a consistency theorem is proved concerning a check for prior-data conflict with the chosen prior. Applications are presented and a new elicitation methodology is developed for multinomial models with ordered probabilities.

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Section: Checking the Modelmentioning

confidence: 99%

Checking for model failure and for prior-data conflict with the constrained multinomial model

Englert

Evans

Jang

et al. 2021

Metrika

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“…When RB Ψ (ψ 0 | x) < 1, there is evidence against ψ 0 , then a small value for (2) indicates a large posterior probability that the true value has a relative belief ratio greater than RB Ψ (ψ 0 | x) and so there is strong evidence against ψ 0 . When…”

Section: Inferences Using Relative Beliefmentioning

confidence: 99%

“…there is evidence in favour of ψ 0 , then a large value for (2) indicates a small posterior probability that the true value has a relative belief ratio greater than RB Ψ (ψ 0 | x)). Therefore, there is strong evidence in favour of ψ 0 , while a small value of (2) only indicates weak evidence in favour of ψ 0 .…”

Section: Inferences Using Relative Beliefmentioning

confidence: 99%

On one-sample Bayesian tests for the mean

2020

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This paper deals with a new Bayesian approach to the standard onesample z-and t-tests. More specifically, let x1, . . . , xn be an independent random sample from a normal distribution with mean µ and variance σ 2 .The goal is to test the null hypothesis H0 : µ = µ1 against all possible alternatives. The approach is based on using the well-known formula of the Kullbak-Leibler divergence between two normal distributions (sampling and hypothesized distributions selected in an appropriate way). The change of the distance from a priori to a posteriori is compared through the relative belief ratio (a measure of evidence). Eliciting the prior, checking for prior-data conflict and bias are also considered. Many theoretical On one-sample Bayesian tests 2 properties of the procedure have been developed. Besides it's simplicity, and unlike the classical approach, the new approach possesses attractive and distinctive features such as giving evidence in favor of the null hypothesis. It also avoids several undesirable paradoxes, such as Lindley's paradox that may be encountered by some existing Bayesian methods.The use of the approach has been illustrated through several examples.

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“…Further, they recommended that a should be chosen so that its value does not exceed 0.5n as otherwise the prior may become too influential. In light of this under the context of entropy estimation, any choice of a such that a/n is close to zero should be compatible with any choice of G. This follows from ( 6) as the sample will dominate the prior guess G. For example, setting a = 0.05 and n = 10 in (6) gives…”

Section: Bayesian Estimation Of the Entropymentioning

confidence: 99%

A Bayesian Nonparametric Estimation to Entropy

Al-Labadi

Patel

Vakiloroayaei

et al. 2019

Preprint

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A Bayesian nonparametric estimator to entropy is proposed. The derivation of the new estimator relies on using the Dirichlet process and adapting the well-known frequentist estimators of Vasicek (1976) and Ebrahimi, Pflughoeft and Soofi (1994). Several theoretical properties, such as consistency, of the proposed estimator are obtained. The quality of the proposed estimator has been investigated through several examples, in which it exhibits excellent performance.

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Prior‐based model checking

Cited by 22 publications

References 27 publications

Checking for model failure and for prior-data conflict with the constrained multinomial model

Checking for model failure and for prior-data conflict with the constrained multinomial model

On one-sample Bayesian tests for the mean

A Bayesian Nonparametric Estimation to Entropy

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