Hypothesis Tests and Corroboration

2019 ◽  
pp. 227-260
Author(s):  
Jan Sprenger ◽  
Stephan Hartmann
Keyword(s):  
Hypothesis Testing ◽  
Scientific Knowledge ◽  
Statistical Significance ◽  
Axiomatic Characterization ◽  
Hypothesis Tests ◽  
Predictive Success ◽  
Impossibility Results ◽  
Philosophical Challenge

According to Popper and other influential philosophers and scientists, scientific knowledge grows by repeatedly testing our best hypotheses. However, the interpretation of non-significant results—those that do not lead to a “rejection” of the tested hypothesis—poses a major philosophical challenge. To what extent do they corroborate the tested hypothesis or provide a reason to accept it? In this chapter, we prove two impossibility results for measures of corroboration that follow Popper’s criterion of measuring both predictive success and the testability of a hypothesis. Then we provide an axiomatic characterization of a more promising and scientifically useful concept of corroboration and discuss implications for the practice of hypothesis testing and the concept of statistical significance.

scholarly journals Pragmatic Hypotheses in the Evolution of Science

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 883 ◽  
Author(s):  
Luis Gustavo Esteves ◽  
Rafael Izbicki ◽  
Julio Michael Stern ◽  
Rafael Bassi Stern
Keyword(s):  
Hypothesis Testing ◽  
Statistical Hypothesis ◽  
Scientific Theories ◽  
Statistical Hypothesis Testing ◽  
Hypothesis Tests ◽  
Experimental Conditions ◽  
Modal Operators ◽  
Evolution Of Science ◽  
Consistent Tests

This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators obtained from this test can be represented in the hexagon of oppositions. However, despite the importance of precise hypothesis in science, they cannot be accepted by logically consistent tests. Here, we show that this dilemma can be overcome by the use of pragmatic versions of precise hypotheses. These pragmatic versions allow a level of imprecision in the hypothesis that is small relative to other experimental conditions. The introduction of pragmatic hypotheses allows the evolution of scientific theories based on statistical hypothesis testing to be interpreted using the narratological structure of hexagonal spirals, as defined by Pierre Gallais.

scholarly journals How Demanding Is the Revealed Preference Approach to Demand?

2011 ◽  
Vol 101 (6) ◽  
pp. 2782-2795 ◽  
Author(s):  
Timothy K. M Beatty ◽  
Ian A Crawford
Keyword(s):  
Economic Theory ◽  
Revealed Preference ◽  
Axiomatic Characterization ◽  
Predictive Success ◽  
Empirical Performance ◽  
Revealed Preference Approach

A well-known problem with revealed preference methods is that when data are found to satisfy their restrictions it is hard to know whether this should be viewed as a triumph for economic theory, or a warning that these conditions are so undemanding that almost anything goes. This paper allows researchers to make this distinction. Our approach uses an axiomatic characterization of a measure of predictive success due to Selten (1991). We illustrate the idea using a panel dataset. The results show that this approach can lead us to radically reassess our view of the empirical performance of economic theory. JEL: D11, D12

An Axiomatic Characterization of a Class of Petri Nets

1991 ◽  
Vol 14 (4) ◽  
pp. 477-491
Author(s):  
Waldemar Korczynski
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Axiomatic Characterization ◽  
Algebraic Characterization

In this paper an algebraic characterization of a class of Petri nets is given. The nets are characterized by a kind of algebras, which can be considered as a generalization of the concept of the case graph of a (marked) Petri net.

Significance tests: Necessary but not sufficient

1998 ◽  
Vol 21 (2) ◽  
pp. 221-222
Author(s):  
Louis G. Tassinary
Keyword(s):  
Effect Size ◽  
Scientific Community ◽  
Statistical Significance ◽  
Significance Tests ◽  
Experimental Control

Chow (1996) offers a reconceptualization of statistical significance that is reasoned and comprehensive. Despite a somewhat rough presentation, his arguments are compelling and deserve to be taken seriously by the scientific community. It is argued that his characterization of literal replication, types of research, effect size, and experimental control are in need of revision.

scholarly journals Axiomatization and Measurement of Quasi-Hyperbolic Discounting *

2014 ◽  
Vol 129 (3) ◽  
pp. 1449-1499 ◽  
Author(s):  
José Luis Montiel Olea ◽  
Tomasz Strzalecki
Keyword(s):  
Hyperbolic Discounting ◽  
Partial Identification ◽  
Axiomatic Characterization ◽  
Discount Factors ◽  
Elasticity Of Intertemporal Substitution ◽  
Trade Offs ◽  
Subject Pool ◽  
Identification Approach ◽  
The Subject

Abstract This article provides an axiomatic characterization of quasi-hyperbolic discounting and a more general class of semi-hyperbolic preferences. We impose consistency restrictions directly on the intertemporal trade-offs by relying on what we call “annuity compensations.” Our axiomatization leads naturally to an experimental design that disentangles discounting from the elasticity of intertemporal substitution. In a pilot experiment we use the partial identification approach to estimate bounds for the distributions of discount factors in the subject pool. Consistent with previous studies, we find evidence for both present and future bias.

scholarly journals Axiomatic characterization of the interval function of a graph

2009 ◽  
Vol 30 (5) ◽  
pp. 1172-1185 ◽  
Author(s):  
Henry Martyn Mulder ◽  
Ladislav Nebeský
Keyword(s):  
Axiomatic Characterization ◽  
Interval Function

scholarly journals Asymptotic relative submajorization of multiple-state boxes

2021 ◽  
Vol 111 (4) ◽  
Author(s):  
Gergely Bunth ◽  
Péter Vrana
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Standard Form ◽  
Point Of View ◽  
State Discrimination ◽  
Simple Alternative ◽  
Multiple State ◽  
Error Probabilities

AbstractPairs of states, or “boxes” are the basic objects in the resource theory of asymmetric distinguishability (Wang and Wilde in Phys Rev Res 1(3):033170, 2019. 10.1103/PhysRevResearch.1.033170), where free operations are arbitrary quantum channels that are applied to both states. From this point of view, hypothesis testing is seen as a process by which a standard form of distinguishability is distilled. Motivated by the more general problem of quantum state discrimination, we consider boxes of a fixed finite number of states and study an extension of the relative submajorization preorder to such objects. In this relation, a tuple of positive operators is greater than another if there is a completely positive trace nonincreasing map under which the image of the first tuple satisfies certain semidefinite constraints relative to the other one. This preorder characterizes error probabilities in the case of testing a composite null hypothesis against a simple alternative hypothesis, as well as certain error probabilities in state discrimination. We present a sufficient condition for the existence of catalytic transformations between boxes, and a characterization of an associated asymptotic preorder, both expressed in terms of sandwiched Rényi divergences. This characterization of the asymptotic preorder directly shows that the strong converse exponent for a composite null hypothesis is equal to the maximum of the corresponding exponents for the pairwise simple hypothesis testing tasks.

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