On the Problem of the Most Efficient Tests of Statistical Hypotheses

By J. Neyman, E. S. Pearson. 1933

The problem of testing statistical hypotheses is an old one. Its origins are usually connected with the name of Thomas Bayes, who gave the well-known theorem on the probabilities a posteriori of the possible “causes” of a given event.* Since then it has been discussed by many writers of whom we shall here mention two only, Bertrand† and Borel,‡ whose differing views serve well to illustrate the point from which we shall approach the subject.

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Citations in the corpus

Deep Imitative Models for Flexible Inference, Planning, and Control (2018, methodology): “R2P2’s use of pushforward distributions (McCann et al., 1995), employed in other invertible generative models (Rezende & Mohamed, 2015; Dinh et al., 2016) allows it to efﬁciently minimize both false positives and false negatives (type I and type II errors) (Neyman & Pearson, 1933).”
Experimental Design and Data Analysis for Biologists (2002, background): “Jerzy Neyman and Egon Pearson (Neyman & Pearson 1928, 1933) offered a related but slightly different approach, which has sometimes been called statistical hypothesis testing.”
A Comparison of Three Methods of Estimation in the Context of Spatial Modeling (2009, methodology): “Building on seminal texts like Fisher (1925, 1935) and Neyman and Pearson (1933), Classical methods have historically predominated.”
Constraining anomalous Higgs boson couplings to the heavy flavor fermions using matrix element techniques (2016, background): “For a simple discrimination of two hypotheses, the Neyman-Pearson lemma [93] guarantees that the ratio of probabilities P for the two hypotheses provides an optimal discrimination power.”
Likelihood-free MCMC with Approximate Likelihood Ratios (2019, methodology): “When comparing two hypotheses θ 0 and θ 1 under a set of observations O , the most powerful test-statistic [5] is the likelihood ratio .”
Text-Independent Writer Identification and Verification Using Textural and Allographic Features (2007, methodology): “Writer verification, as all biometric verification tasks, can be perfectly placed into the classical Neyman-Pearson framework of statistical decision theory [54].”
Statistical Rituals: The Replication Delusion and How We Got There (2018, background): “(Fisher, 1956, p. 42)2 Using a conventional 5% level of significance is also alien to Neyman and Pearson, who in their earliest writings already emphasized that their tests should be “used with discretion and understanding,” depending on the context (Neyman & Pearson, 1933, p. 296).”
Information, Divergence and Risk for Binary Experiments (2009, background): “Their only common point is when the respective convex functions satisfy f(t) = φ(t) = t ln t − at + b (for a, b ∈ R) in which case both If and Bφ are the KL divergence.”
Performance Trajectories and Performance Gaps as Achievement Effect-Size Benchmarks for Educational Interventions (2008, background): “…which focuses on testing a specific null hypothesis of zero effect against a general alternative hypothesis of nonzero effect, versus the framework developed by Neyman and Pearson (1928, 1933), which focuses on both a specific null hypothesis and a specific alternative hypothesis (or effect size).”