Probability matching priors: a review

Scricciolo, Catia

doi:10.1007/bf03178943

Cited by 4 publications

(2 citation statements)

References 48 publications

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“…Here, we derived a probability matching prior, distribution for H ( p ) for a discrete binary population, which is free from any hyper-parameter. In principle, a probability matching prior holds the promise of providing a possible agreement between frequentist and Bayesian inferential procedures, which can be used for routine use in Bayesian inference [ 10 , 11 ].…”

Section: Methodsmentioning

confidence: 99%

Diversity in substance use behaviour among street children of Delhi under Bayesian paradigm

Verma

Mishra

Dhawan

et al. 2020

BMC Med Res Methodol

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Background Shannon’s index is one of the measures of biodiversity, which is intended to quantify both richness and evenness of the species/individuals in the ecosystem or community. However, application of Shannon’s index in the field of substance use among the street children has not been done till date. Methods This paper is concerned with methods of estimating Shannon’s diversity index (SDI), which can be used to capture the variation in the population due to certain characteristics. Under the consideration that the probability of abundance, based on certain characteristics in the population, is a random phenomenon, we derive a Bayesian estimate in connection with Shannon’s information measure and their properties (mean and variance), by using a probability matching prior, through simulation and compared it with those of the classical estimates of Shannon. The theoretical framework has been applied to the primary survey data of substance use among the street children in Delhi, collected during 2015. The measure of diversity was estimated across different age profiles and districts. Results The results unrevealing the diversity estimate for street children corresponding to each region of Delhi, under both the classical and Bayesian paradigms. Although the estimates were close to one another, a striking difference was noted in the age profile of children. Conclusions The Bayesian methodology provided evidence for a greater likelihood of finding substance-using street children, belonging to the lower age group (7-10, maximum Bayesian entropy-3.73), followed by the middle (11-14) and upper age group (15-18). Moreover, the estimated variance under the Bayesian paradigm was lesser than that of the classical estimate. There is ample scope for further refinement in these estimates, by considering more covariates that may have a possible role in initiating substance use among street children in developing countries like India.

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Section: Methodsmentioning

confidence: 99%

Diversity in substance use behaviour among street children of Delhi under Bayesian paradigm

Verma

Mishra

Dhawan

et al. 2020

BMC Med Res Methodol

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“…WALDO addresses this by recalibrating the posterior using Neyman inversion. An alternative approach is to choose the prior so that the conditional coverage of posterior inferences is improved [5,7,31,50,17]. However, these modified prior distributions need to be created using properties of the likelihood instead of actual prior information, a limitation that is not present in WALDO.…”

Section: Relation To Other Workmentioning

confidence: 99%

Simulation-Based Inference with Waldo: Confidence Regions by Leveraging Prediction Algorithms or Posterior Estimators for Inverse Problems

Masserano¹,

Dorigo²,

Izbicki³

et al. 2022

Preprint

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The vast majority of modern machine learning targets prediction problems, with algorithms such as Deep Neural Networks revolutionizing the accuracy of point predictions for high-dimensional complex data. Predictive approaches are now used in many domain sciences to directly estimate internal parameters of interest in theoretical simulator-based models. In parallel, common alternatives focus on estimating the full posterior using modern neural density estimators such as normalizing flows. However, an open problem in simulation-based inference (SBI) is how to construct properly calibrated confidence regions for internal parameters with nominal conditional coverage and high power. Many SBI methods are indeed known to produce overly confident posterior approximations, yielding misleading uncertainty estimates. Similarly, existing approaches for uncertainty quantification in deep learning provide no guarantees on conditional coverage. In this work, we present WALDO, a novel method for constructing correctly calibrated confidence regions in SBI. WALDO reframes the well-known Wald test and uses Neyman inversion to convert point predictions and posteriors from any prediction or posterior estimation algorithm to confidence sets with correct conditional coverage, even for finite sample sizes. As a concrete example, we demonstrate how a recently proposed deep learning prediction approach for particle energies in high-energy physics can be recalibrated using WALDO to produce confidence intervals with correct coverage and high power.Preprint. Under review.

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Reference Analysis

Bernardo¹

2005

Handbook of Statistics

146

112

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Probability matching priors: a review

Abstract: First-order probability matching prior, Jeifreys’ prior, Noninformative prior, Posterior quantile, Reference prior, Second-order probability matching prior,

Cited by 4 publications

References 48 publications

Diversity in substance use behaviour among street children of Delhi under Bayesian paradigm

Diversity in substance use behaviour among street children of Delhi under Bayesian paradigm

Simulation-Based Inference with Waldo: Confidence Regions by Leveraging Prediction Algorithms or Posterior Estimators for Inverse Problems

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