A Comparison of Bayes–Laplace, Jeffreys, and Other Priors

Tuyl, Frank; Gerlach, Richard; Mengersen, Kerrie

doi:10.1198/000313008x267839

Cited by 70 publications

(49 citation statements)

References 25 publications

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“…This could be the reason behind why the uniform or Bayes-Laplace prior appears preferable, as a representation of prior ignorance and thus for the purpose of scientific communication and sensitivity analysis, to the reference/Jeffreys prior Be(θ | 1/2, 1/2). This can be most easily shown by considering x = 0 (x = n) (Tuyl et al 2008). As a related illustration, consider the Bayesian Rule of Three which states that, based on x = 0 and an informative prior Be(θ | 1, b) (b > 1), the 95% one-sided upper credible limit may be approximated by 3/(n + b) when n is large (Jovanovic and Levy, 1997).…”

Section: Jan Sprenger (Tilburg University the Netherlands)mentioning

confidence: 99%

Integrated Objective Bayesian Estimation and Hypothesis Testing

Bernardo

2011

Bayesian Statistics 9

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SummaryThe complete final product of Bayesian inference is the posterior distribution of the quantity of interest. Important inference summaries include point estimation, region estimation, and precise hypotheses testing. Those summaries may appropriately be described as the solution to specific decision problems which depend on the particular loss function chosen. The use of a continuous loss function leads to an integrated set of solutions where the same prior distribution may be used throughout. Objective Bayesian methods are those which use a prior distribution which only depends on the assumed model and the quantity of interest. As a consequence, objective Bayesian methods produce results which only depend on the assumed model and the data obtained. The combined use of the intrinsic discrepancy, an invariant information-based loss function, and appropriately defined reference priors, provides an integrated objective Bayesian solution to both estimation and hypothesis testing problems. The ideas are illustrated with a large collection of non-trivial examples.

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Section: Jan Sprenger (Tilburg University the Netherlands)mentioning

confidence: 99%

Integrated Objective Bayesian Estimation and Hypothesis Testing

Bernardo

2011

Bayesian Statistics 9

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“…Bayesian models may offer an instructive approach to estimate rates in the zero-event situation. Geisser (1984) and Tuyl, Gerlach, and Mengersen (2008) have suggested the use of the Bayes-Laplace prior beta (1,1) as noninformative prior in the zero event situation, whereas Kerman (2011) finds argument for a neutral prior beta (1/3,1/3) in the rare event setting. Alternatively, Chen and McGee (2008) examined different Bayesian hierarchical models, and reported consistent results with the Bayes-Laplace estimate, regardless of choice of hyperprior distributions.…”

Section: Zero-event Situation: the Rule Ofmentioning

confidence: 97%

Current Practices, Challenges, and Statistical Issues With Product Safety Labeling

Crowe

Brueckner

Beasley

et al. 2013

Statistics in Biopharmaceutical Research

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Prescribing health care professionals are dependent on product labels to give them the information they need to appropriately prescribe drugs and monitor patients. A well-constructed label with accurate, meaningful, and easy-to-understand information is important for understanding the benefit-risk profile of the compound. Statisticians are uniquely qualified to help. Historically, statisticians have played a major role in defining the efficacy information provided in the label. Similar leadership is needed to develop safety information for products. Statisticians should play a key role in making sure that the safety information from clinical trials is accurate and provides adequate information to health care professionals regarding the likely and potential effects of a drug. In this regard, giving careful thought to (a) the way safety information is defined and collected, (b) the way in which different adverse events (AEs) are categorized and combined over multiple studies, (c) the statistical methods used to analyze the safety data, and (d) the tables and graphs in which safety information is presented is needed. We have touched on aspects of each of these in this article. Though product labeling has improved greatly in the past 20 years, there are still many issues that need statisticians' leadership and thought processes. In this article, we consider some of the important issues and make recommendations to address them. These include passive versus active elicitation of AEs, grouping of terms for labeling purposes, definitions of treatment-emergent AEs, meta-analytical principles, and analytical methods for estimating incidence and rates. Consideration of these issues can benefit health care professionals and ultimately patients who take medicines.

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“…Tuyl, Gerlach, and Mengerson [14] recommended the B-L prior as a consensus prior when x=0 is observed, and this approach yields the following 100 (1-α)% upper confidence limit:…”

Section: Bayes-laplace Hpd Intervalmentioning

confidence: 99%

“…Observing X=0 in a binomial sample lends itself to the Bayesian approach since one can condition on the observed data, and several authors have considered this approach [13][14][15][16]. In the present article, we approach the problem from a frequentist point of view; however, we also include a Bayesian approach for comparison purposes.…”

Section: Introductionmentioning

confidence: 99%

On Finding the Upper Confidence Limit for a Binomial Proportion when Zero Successes are Observed

Looney¹

2017

J Biom Biostat

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We consider confidence interval estimation for a binomial proportion when the data have already been observed and x, the observed number of successes in a sample of size n, is zero. In this case, the main objective of the investigator is usually to obtain a reasonable upper bound for the true probability of success, i.e., the upper limit of a one-sided confidence interval. In this article, we use observed interval length and p-confidence to evaluate eight methods for finding the upper limit of a confidence interval for a binomial proportion when x is known to be zero. Long-run properties such as expected interval length and coverage probability are not applicable because the sample data have already been observed. We show that many popular approximate methods that are known to have good long-run properties in the general setting perform poorly when x=0 and recommend that the Clopper-Pearson exact method be used instead.Citation: McCracken CE, Looney SW (2017) On Finding the Upper Confidence Limit for a Binomial Proportion when Zero Successes are Observed.

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A Comparison of Bayes–Laplace, Jeffreys, and Other Priors

Cited by 70 publications

References 25 publications

Integrated Objective Bayesian Estimation and Hypothesis Testing

Integrated Objective Bayesian Estimation and Hypothesis Testing

Current Practices, Challenges, and Statistical Issues With Product Safety Labeling

On Finding the Upper Confidence Limit for a Binomial Proportion when Zero Successes are Observed

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