On the choice of the prior distribution in hypergeometric sampling

Dyer, Danny; Pierce, Rebecca L.

doi:10.1080/03610929308831139

Cited by 15 publications

(11 citation statements)

References 21 publications

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“…The posterior distribution of the number of overpaid claims in the population, K , in a particular stratum can be evaluated by using the hypergeometric distribution. As suggested by Dyer and Pierce, p ( K ) is assumed to have a beta‐binomial (hyper‐binomial) prior distribution, ie,

p false(K false) = \frac{N}{K} \frac{normalΓ false(K + α false) normalΓ false(N - K + β false)}{normalΓ false(N + α + β false)} \frac{normalΓ false(α false) normalΓ false(β false)}{normalΓ false(α + β false)},

where the gamma function, Γ( c ), is defined as

\int_{0}^{\infty} e^{- u} u^{c - 1} normald u

. We describe the likelihood of k conditional on K using the hypergeometric distribution, ie,

p false(k false| K false) = \frac{((), \frac{0}{K}) ((), \frac{0}{N - K})}{((), \frac{0}{N})} .

…”

Section: Methodology For a Stratified Sampling Frameworkmentioning

confidence: 99%

“…For a particular stratum h , this can be written as p ( K h | k h , n h ). Furthermore, it is shown in the work of Dyer and Pierce that the distribution of k given n and ω is

p false(k false| n false) = ((), \frac{0}{n}) \frac{normalΓ false(α + 1 false) normalΓ false(β + n - k false) normalΓ false(α + β false)}{normalΓ false(α false) normalΓ false(β false) normalΓ false(α + β + 1 false)} .

…”

Section: Methodology For a Stratified Sampling Frameworkmentioning

confidence: 99%

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Information‐theoretic multistage sampling framework for medical audits

Musal

Ekin

2018

Appl Stoch Models Bus & Ind

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The sampling resource allocation decisions for medical audits of outpatient procedures are crucial and challenging because of the large payment amounts and heterogeneity of the claims. A number of frameworks are utilized to help auditors address the trade-offs between efficiency and cost while having valid overpayment amount estimates. As a potential improvement, this paper presents a novel information-theoretic multistage sampling framework. In particular, we propose an iterative stratified sampling method that uses Lindley's entropy measure to evaluate the expected amount of information. We use US Medicare Part B claims outpatient payment data and investigate the versatility of the framework for different overpayment scenarios and resource allocation designs. The proposed method results in reasonable coverage and lower estimation errors for the proportion of overpaid claims and overpayment recovery amounts. Our sampling method is shown to outperform the current stratification method of practice, ie, Neyman allocation, for many scenarios. The framework also can be used to make probability statements on variables of interest, such as the number of overpaid claims.

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p false(K false) = \frac{N}{K} \frac{normalΓ false(K + α false) normalΓ false(N - K + β false)}{normalΓ false(N + α + β false)} \frac{normalΓ false(α false) normalΓ false(β false)}{normalΓ false(α + β false)},

where the gamma function, Γ( c ), is defined as

\int_{0}^{\infty} e^{- u} u^{c - 1} normald u

. We describe the likelihood of k conditional on K using the hypergeometric distribution, ie,

p false(k false| K false) = \frac{((), \frac{0}{K}) ((), \frac{0}{N - K})}{((), \frac{0}{N})} .

…”

Section: Methodology For a Stratified Sampling Frameworkmentioning

confidence: 99%

“…For a particular stratum h , this can be written as p ( K h | k h , n h ). Furthermore, it is shown in the work of Dyer and Pierce that the distribution of k given n and ω is

p false(k false| n false) = ((), \frac{0}{n}) \frac{normalΓ false(α + 1 false) normalΓ false(β + n - k false) normalΓ false(α + β false)}{normalΓ false(α false) normalΓ false(β false) normalΓ false(α + β + 1 false)} .

…”

Section: Methodology For a Stratified Sampling Frameworkmentioning

confidence: 99%

Information‐theoretic multistage sampling framework for medical audits

Musal

Ekin

2018

Appl Stoch Models Bus & Ind

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“…An alternative non-informative prior is the most conservative prior, which maximizes the expected information gain from the observed data, as measured by the Kullback-Leibler divergence between prior and posterior distributions [Dyer and Chiou 1984]. Dyer and Pierce [1993] show that the expected information gain for the beta-binomial prior to the hypergeometric is: [1993], which has n x instead of N r in the final line). Dyer and Pierce [1993] also demonstrate that Equation 18 is concave and symmetric in α and β, so the maximum occurs where α = β.…”

Section: Beta-binomial As Prior To Hypergeometricmentioning

confidence: 99%

“…Dyer and Pierce [1993] show that the expected information gain for the beta-binomial prior to the hypergeometric is: [1993], which has n x instead of N r in the final line). Dyer and Pierce [1993] also demonstrate that Equation 18 is concave and symmetric in α and β, so the maximum occurs where α = β. Finding the value α = β which maximizes Equation 18 provides the most conservative prior [Dyer and Pierce 1993].…”

Section: Beta-binomial As Prior To Hypergeometricmentioning

confidence: 99%

Approximate Recall Confidence Intervals

Webber

2013

ACM Trans. Inf. Syst.

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Recall, the proportion of relevant documents retrieved, is an important measure of effectiveness in information retrieval, particularly in the legal, patent, and medical domains. Where document sets are too large for exhaustive relevance assessment, recall can be estimated by assessing a random sample of documents, but an indication of the reliability of this estimate is also required. In this article, we examine several methods for estimating two-tailed recall confidence intervals. We find that the normal approximation in current use provides poor coverage in many circumstances, even when adjusted to correct its inappropriate symmetry. Analytic and Bayesian methods based on the ratio of binomials are generally more accurate but are inaccurate on small populations. The method we recommend derives beta-binomial posteriors on retrieved and unretrieved yield, with fixed hyperparameters, and a Monte Carlo estimate of the posterior distribution of recall. We demonstrate that this method gives mean coverage at or near the nominal level, across several scenarios, while being balanced and stable. We offer advice on sampling design, including the allocation of assessments to the retrieved and unretrieved segments, and compare the proposed beta-binomial with the officially reported normal intervals for recent TREC Legal Track iterations.

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“…There is a considerable literature treating Bayesiam implementations of markrecapture models using hypergeometric and multinomial likelihoods (Dyer and Pierce 1993, Dupuis 1995, Chavez-Demoulin 1999, Wade 2001. Bayesian solutions have also been developed for the problem of estimating the number of trials in a binomial (Wiper and Pettit 1994).…”

Section: Inferencementioning

confidence: 99%

Methods for Joint Inference From Multiple Data Sources for Improved Estimates of Population Size and Survival Rates

Goodman¹

2004

Marine Mammal Science

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Critical conservation decisions often hinge on estimates of population size, population growth rate, and survival rates, but as a practical matter it is difficult to obtain enough data to provide precise estimates. Here we discuss Bayesian methods for simultaneously drawing on the information content from multiple sorts of data to get as much precision as possible for the estimates. The basic idea is that an underlying population model can connect the various sorts of observations, so this can be elaborated into a joint likelihood function for joint estimation of the respective parameters. The potential for improved estimates derives from the potentially greater effective sample size of the aggregate of data, even though some of the data types may only bear directly on a subset of the parameters. The achieved improvement depends on specifics of the interactions among parameters in the underlying model, and on the actual content of the data. Assuming the respective data sets are unbiased, notwithstanding the fact that they may be noisy, we may gauge the average improvement in the estimates of the parameters of interest from the reduction, if any, in the standard deviations of their posterior marginal distributions. Prospective designs may be evaluated from analysis of simulated data. Here this approach is illustrated with an assessment of the potential value in various ways of merging mark‐resight and carcass‐survey data for the Florida manatee, as could be made possible by various modifications in the data collection protocols in both programs.

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On the choice of the prior distribution in hypergeometric sampling

Cited by 15 publications

References 21 publications

Information‐theoretic multistage sampling framework for medical audits

Information‐theoretic multistage sampling framework for medical audits

Approximate Recall Confidence Intervals

Methods for Joint Inference From Multiple Data Sources for Improved Estimates of Population Size and Survival Rates

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