# The Neyman-Pearson theory as decision theory, and as inference theory; with a criticism of the Lindley-savage argument for Bayesian theory

@article{Birnbaum2004TheNT, title={The Neyman-Pearson theory as decision theory, and as inference theory; with a criticism of the Lindley-savage argument for Bayesian theory}, author={Allan Birnbaum}, journal={Synthese}, year={2004}, volume={36}, pages={19-49} }

The concept of a decision, which is basic in the theories of Neyman Pearson, Wald, and Savage, has been judged obscure or inappropriate when applied to interpretations of data in scientific research, by Fisher, Cox, Tukey, and other writers. This point is basic for most statistical practice, which is based on applications of methods derived in the Neyman-Pearson theory or analogous applications of such methods as least squares and maximum likelihood. Two contrasting interpretations of the…

## 51 Citations

### The analogy between decision and inference

- PhilosophySynthese
- 2004

Professor Birnbaum, in his paper (1976), makes a reasonable and valid distinction between 'evidence', i.e. information affecting beliefs, and 'decision', i.e. choice of course of action. He claims…

### Severe Testing as a Basic Concept in a Neyman–Pearson Philosophy of Induction

- PsychologyThe British Journal for the Philosophy of Science
- 2006

Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of…

### Toward Error-Statistical Principles of Evidence in Statistical Inference

- Philosophy
- 2014

The context for this research is statistical inference, the process of making predictions or inferences about a population from observation and analyses of a sample. In this context, many researchers…

### Frequentist statistics as a theory of inductive inference

- Philosophy
- 2006

After some general remarks about the interrelation between philosophical and statistical thinking, the discussion centres largely on significance tests. These are defined as the calculation of…

### Decisions as statistical evidence and Birnbaum's ‘confidence concept’

- PsychologySynthese
- 2004

ConclusionTo whatever extent the use of a behavioral, not an evidential, interpretation of decisions in the Lindley-Savage argument for Bayesian theory undermines its cogency as a criticism of…

### Why the Decision Theoretic Perspective Misrepresents Frequentist Inference: 'Nuts and Bolts' vs. Learning from Data

- Computer Science
- 2012

The paper calls into question the appropriateness of admissibility and reassesses Stein's paradox as it relates to the capacity of frequentist estimators to pinpoint the true theta.

### Did Pearson reject the Neyman-Pearson philosophy of statistics?

- PsychologySynthese
- 2004

I document some of the main evidence showing that E. S. Pearson rejected the key features of the behavioral-decision philosophy that became associated with the Neyman-Pearson Theory of statistics…

### Combining statistical inference and decisions in ecology.

- BiologyEcological applications : a publication of the Ecological Society of America
- 2016

An introduction to SDT for ecologists is provided and its utility for linking the conventionally separate tasks of statistical investigation and decision making in a single framework is described.

### Why the Decision‐Theoretic Perspective Misrepresents Frequentist Inference: Revisiting Stein’s Paradox and Admissibility

- Mathematics
- 2017

The primary objective of this paper is to make a case that R.A. Fisher ’ s objections to the decision-theoretic framing of frequentist inference are not without merit. It is argued that this framing…

### The nature of scientific evidence : statistical, philosophical, and empirical considerations

- Psychology
- 2004

An exploration of the statistical foundations of scientific inference, "The Nature of Scientific Evidence" asks what constitutes scientific evidence and whether scientific evidence can be quantified…

## References

SHOWING 1-10 OF 47 REFERENCES

### ON THE USE AND INTERPRETATION OF CERTAIN TEST CRITERIA FOR PURPOSES OF STATISTICAL INFERENCE PART I

- Geology
- 1928

In an earlier paper* we have endeavoured to emphasise the importance of placing in a logical sequence the stages of reasoning adopted in the solution of certain statistical problems, which may be…

### THE LOGIC OF STATISTICAL INFERENCE1

- MathematicsThe British Journal for the Philosophy of Science
- 1972

Re-reading the book one is again impressed with its easy-flowing style, full of felicitous phrases—such as 'cheerful concordat' to describe the current state of divided opinion on the foundations of set theory—but with careful attention to logical niceties.

### On the Problem of the Most Efficient Tests of Statistical Hypotheses

- Mathematics
- 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…

### More on Concepts of Statistical Evidence

- Economics
- 1972

Abstract A self-contained account is given of the implications among the sufficiency, conditionality and likelihood axioms of statistical evidence for the discrete case. These include a previously…

### Expected Significance Level as a Sensitivity Index for Test Statistics

- Mathematics
- 1965

Abstract After a brief motivating discussion, of approaches to significance tests in Section 1, the concept of expected significance level (esl) is defined and its basic properties are presented in…

### Scientific Explanation

- Philosophy, Education
- 2005

The three cardinal aims of science are prediction, control, and explanation; but the greatest of these is explanation. Also the most inscrutable: prediction aims at truth, and control at happiness,…

### The random phenotype concept, with applications.

- Computer ScienceGenetics
- 1972

A random phenotype is defined as a probability distribution over any given set of phenotypes. This includes as special cases the kinds of phenotypes usually considered (qualitative, quantitative, and…

### On Durbin's Modified Principle of Conditionally

- Economics
- 1970

Abstract The conditionality (ancillarity) concept is discussed with particular reference to Durbin's proposed reformulation (C') of Birnbaum's formulation (C) and Fisher's original formulations [6,…

### Sequential tests for the detection of linkage.

- MathematicsAmerican journal of human genetics
- 1955

INFORMATION ON LINKAGE in man is accumulated as a succession of samples, each of which is typically small relative to the amount of data required to detect even moderately close linkage. The best…

### Logic of Statistical Inference

- Mathematics
- 1965

This chapter discusses the long run frequencies, statistical tests, and theories of testing that led to Bayes' theory, as well as the subjective theory.