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An exposition of the false confidence theorem

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Iain Carmichael, Jonathan P Williams

Methodology · Submitted 17 Jul 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Our examples illustrate that models involving marginalization to non-linear, not one-to-one functions of multiple parameters play a key role in more extreme manifestations of false confidence.

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arXiv ID1807.06217 (version 1)
Pith IDK57DO5ZN, Pith's permanent record of this paper and its review
CitationIain Carmichael, Jonathan P Williams. "An exposition of the false confidence theorem." arXiv:1807.06217 (2018). https://pith.science/paper/K57DO5ZN
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,372 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.23 · human participants 0.03 · controlled comparison 0.02 · randomized assignment 0.02 · states quantitative result 0.07 · compares with prior results 0.19 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

A recent paper presents the "false confidence theorem" (FCT) which has potentially broad implications for statistical inference using Bayesian posterior uncertainty. This theorem says that with arbitrarily large (sampling/frequentist) probability, there exists a set which does \textit{not} contain the true parameter value, but which has arbitrarily large posterior probability. Since the use of Bayesian methods has become increasingly popular in applications of science, engineering, and business, it is critically important to understand when Bayesian procedures lead to problematic statistical inferences or interpretations. In this paper, we consider a number of examples demonstrating the paradoxical nature of false confidence to begin to understand the contexts in which the FCT does (and does not) play a meaningful role in statistical inference. Our examples illustrate that models involving marginalization to non-linear, not one-to-one functions of multiple parameters play a key role in more extreme manifestations of false confidence.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 A recent paper presents the "false confidence theorem" (FCT) which has potentially broad implications for statistical inference using Bayesian posterior uncertainty. background 1.00 0.05 0.05 hedged possibility 0.83
s1 This theorem says that with arbitrarily large (sampling/frequentist) probability, there exists a set which does \textit{not} contain the true parameter value, but which has arbitrarily large posterior probability. background 0.95 0.07 0.14 asserted 1.00
s2 Since the use of Bayesian methods has become increasingly popular in applications of science, engineering, and business, it is critically important to understand when Bayesian procedures lead to problematic statistical inferences or interpretations. background 1.00 0.04 0.03 asserted 0.99
s3 In this paper, we consider a number of examples demonstrating the paradoxical nature of false confidence to begin to understand the contexts in which the FCT does (and does not) play a meaningful role in statistical inference. contribution 0.95 0.90 0.11 asserted 0.86
s4 Our examples illustrate that models involving marginalization to non-linear, not one-to-one functions of multiple parameters play a key role in more extreme manifestations of false confidence. result 0.73 0.85 0.53 asserted 0.99

What kind of paper the classifier reports this is: position or commentary 0.80 · evidence from argument 0.50.

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  • references and citing sentences
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

A recent paper presents the "false confidence theorem" (FCT) which has potentially broad implications for statistical inference using Bayesian posterior uncertainty. This theorem says that with arbitrarily large (sampling/frequentist) probability, there exists a set which does \textit{not} contain the true parameter value, but which has arbitrarily large posterior probability. Since the use of Bayesian methods has become increasingly popular in applications of science, engineering, and business, it is critically important to understand when Bayesian procedures lead to problematic statistical inferences or interpretations. In this paper, we consider a number of examples demonstrating the paradoxical nature of false confidence to begin to understand the contexts in which the FCT does (and does not) play a meaningful role in statistical inference. Our examples illustrate that models involving marginalization to non-linear, not one-to-one functions of multiple parameters play a key role in more extreme manifestations of false confidence.

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