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Evidential Calibration of Confidence Intervals
Methodology · Submitted 24 Jun 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We present a novel and easy-to-use method for calibrating error-rate based confidence intervals to evidence-based support intervals.
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The abstract, sentence by sentence
We present a novel and easy-to-use method for calibrating error-rate based confidence intervals to evidence-based support intervals. Support intervals are obtained from inverting Bayes factors based on a parameter estimate and its standard error. A $k$ support interval can be interpreted as "the observed data are at least $k$ times more likely under the included parameter values than under a specified alternative". Support intervals depend on the specification of prior distributions for the parameter under the alternative, and we present several types that allow different forms of external knowledge to be encoded. We also show how prior specification can to some extent be avoided by considering a class of prior distributions and then computing so-called minimum support intervals which, for a given class of priors, have a one-to-one mapping with confidence intervals. We also illustrate how the sample size of a future study can be determined based on the concept of support. Finally, we show how the bound for the type I error rate of Bayes factors leads to a bound for the coverage of support intervals. An application to data from a clinical trial illustrates how support intervals can lead to inferences that are both intuitive and informative.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a novel and easy-to-use method for calibrating error-rate based confidence intervals to evidence-based support intervals. | contribution 1.00 | 0.94 | 0.35 | asserted 1.00 |
| s1 | Support intervals are obtained from inverting Bayes factors based on a parameter estimate and its standard error. | method 0.98 | 0.63 | 0.07 | asserted 1.00 |
| s2 | A $k$ support interval can be interpreted as "the observed data are at least $k$ times more likely under the included parameter values than under a specified alternative". | interpretation 0.89 | 0.40 | 0.11 | asserted 0.99 |
| s3 | Support intervals depend on the specification of prior distributions for the parameter under the alternative, and we present several types that allow different forms of external knowledge to be encoded. | contribution 0.60 | 0.81 | 0.07 | asserted 0.98 |
| s4 | We also show how prior specification can to some extent be avoided by considering a class of prior distributions and then computing so-called minimum support intervals which, for a given class of priors, have a one-to-one mapping with confidence intervals. | contribution 0.73 | 0.94 | 0.12 | asserted 0.69 |
| s5 | We also illustrate how the sample size of a future study can be determined based on the concept of support. | contribution 0.97 | 0.92 | 0.06 | asserted 0.99 |
| s6 | Finally, we show how the bound for the type I error rate of Bayes factors leads to a bound for the coverage of support intervals. | contribution 0.50 | 0.91 | 0.12 | asserted 1.00 |
| s7 | An application to data from a clinical trial illustrates how support intervals can lead to inferences that are both intuitive and informative. | contribution 0.42 | 0.92 | 0.18 | asserted 0.99 |
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The paper
Original abstract
We present a novel and easy-to-use method for calibrating error-rate based confidence intervals to evidence-based support intervals. Support intervals are obtained from inverting Bayes factors based on a parameter estimate and its standard error. A $k$ support interval can be interpreted as "the observed data are at least $k$ times more likely under the included parameter values than under a specified alternative". Support intervals depend on the specification of prior distributions for the parameter under the alternative, and we present several types that allow different forms of external knowledge to be encoded. We also show how prior specification can to some extent be avoided by considering a class of prior distributions and then computing so-called minimum support intervals which, for a given class of priors, have a one-to-one mapping with confidence intervals. We also illustrate how the sample size of a future study can be determined based on the concept of support. Finally, we show how the bound for the type I error rate of Bayes factors leads to a bound for the coverage of support intervals. An application to data from a clinical trial illustrates how support intervals can lead to inferences that are both intuitive and informative.
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How the literature uses it
2 arXiv papers cite this in 4 sentences
Papers citing it · 3 sentences without a confident label
Cites it as background 1 paper
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[ref] study this e-variable, focusing on an `evidential' interpretation; it also figures prominently in [ref] and, under the name `prior-to-posterior e-variable', in [ref] .
The E-Posterior · Examples of E-Collections · 0.84
What it cites · 1 sentence without a confident label
Cites as support 1 paper
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[ref] proved that $k$ support sets with $k < 1$ are also valid $(1 - k)100%$ confidence sets.
Anytime-Valid Inference for Multinomial Count Data · Error control via the universal bound · 0.98
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