Frequentist Inference without Repeated Sampling

Don Holbert; Paul Vos

arxiv: 1906.08360 · v1 · pith:DD2IXGQOnew · submitted 2019-06-19 · 📊 stat.OT · stat.AP

Frequentist Inference without Repeated Sampling

Paul Vos , Don Holbert This is my paper

Pith reviewed 2026-05-25 20:14 UTC · model grok-4.3

classification 📊 stat.OT stat.AP

keywords inferenceclassicalrandomfrequentistinterpretationprobabilitiesrepeatedsample

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The pith

Frequentist inference is reinterpreted via classical probability on a single sample using urn models instead of repeated sampling.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Frequentist statistics is often taught by imagining what would happen if the same experiment were repeated many times under identical conditions. This paper proposes using the classical probability view instead, where the population is modeled as an urn containing balls of different types, and a single draw represents the sample. The probability is simply the proportion of favorable balls in the urn. The authors apply this to describe p-values as the probability of drawing a result at least as extreme as observed, confidence intervals as ranges consistent with the single draw, and power as the probability of drawing a result that leads to rejecting the null. They note that both the single-sample classical view and the traditional repeated-sampling view can be used to communicate results, and discuss their relative effectiveness.

Core claim

Load-bearing premise

That an urn model can accurately represent the population and sampling process such that classical probabilities defined on a single draw directly support valid frequentist inference procedures for p-values, confidence intervals, and power.

read the original abstract

Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random phenomena are interpreted as classical probabilities, and this interpretation is applied to statistical inference using urn models. Both classical and limiting relative frequency interpretations can be used to communicate statistical inference, and the effectiveness of each is discussed. Recent descriptions of p-values, confidence intervals, and power are viewed through the lens of classical probability based on a single random sample from the population.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that urn models can serve as faithful representations of statistical populations for the purpose of defining inference quantities via classical probability.

axioms (1)

domain assumption Classical probability defined on a single draw from an urn model can be used to interpret frequentist procedures such as p-values and confidence intervals.
Invoked throughout the abstract to replace the repeated-sampling interpretation.

pith-pipeline@v0.9.0 · 5599 in / 1150 out tokens · 54017 ms · 2026-05-25T20:14:48.477833+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample... using urn models
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The proportion... is the p-value... Pr[T≥t] = |{b∈⌊X⌋n_θ : T(b)≥t}| / |⌊X⌋n_θ|

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.