The Kid, the Clerk, and the Gambler: Critical Studies in Statistics and Cognitive Science [PhD Thesis]

231 Pages·2015·5.123 MB·English

by  Mathias Winther Madsen

· The Kid, the Clerk, and the Gambler ·
Critical Studies in Statistics
and Cognitive Science
Mathias Winther Madsen

· The Kid, the Clerk, and the Gambler ·
Critical Studies in Statistics
and Cognitive Science
ILLC Dissertation Series DS-2015-02
For further information about ILLC-publications, please contact
Institute for Logic, Language and Computation
Universiteit van Amsterdam
Science Park 107
1098 XG Amsterdam
phone: [phone]
e-mail: [email protected]
homepage: http://www.illc.uva.nl/
Copyright (cid:13)c 2015 by Mathias Winther Madsen
Cover design by Julie Cetti and Marie-Anne Soyez
after a watercolor by Mathias Winther Madsen.
Printed and bound by Ipskamp Drukkers, Enschede.
ISBN: 978-94-6259-947-5
· The Kid, the Clerk, and the Gambler ·
Critical Studies in Statistics
and Cognitive Science
Academisch Proefschrift
ter verkrijging van de graad van doctor aan de
Universiteit van Amsterdam
op gezag van de Rector Magnificus
prof.dr. D.C. van den Boom
ten overstaan van een door het college voor
promoties ingestelde commissie, in het openbaar
te verdedigen in de Agnietenkapel
op diensdag 1 december 2015, te 10:00 uur
door
Mathias Winther Madsen
geboren te Kopenhagen, Denemarken.
Promotores: Prof. dr. M.J.B. Stokhof
Prof. dr. M. van Lambalgen
Overige leden: Prof. dr. A. Betti, Unversiteit van Amsterdam
Prof. dr. G.J. Steen, Unversiteit van Amsterdam
Dr. W.H. Zuidema, Unversiteit van Amsterdam
Prof. dr. J.W. Romeijn, Rijksunversiteit Groningen
Prof. dr. R.A. Zwaan, Erasmus Unversiteit Rotterdam
Dr. D.H. Lassiter, Stanford University
Faculteit der Geesteswetenschappen
v
Contents
Acknowledgments and Sources ix
1 Introduction 1
2 Cognitive Metaphor Theory and
the Metaphysics of Immediacy 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Reliability Issues in Metaphor Identification . . . . . . . . . . . . 11
2.3 Further Problems for Word Sense Ordering . . . . . . . . . . . . . 19
2.4 Differences in Immediacy . . . . . . . . . . . . . . . . . . . . . . . 23
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 Back in Time is Not Back in Space:
New Evidence from Spontaneous Gesture 35
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.7 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4 Brain Potentials and the
Syntax-Semantics Distinction 53
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 The N400 and the P600 . . . . . . . . . . . . . . . . . . . . . . . 54
4.3 The Frayed Ends of Syntax . . . . . . . . . . . . . . . . . . . . . 57
4.4 The Statistics of Decoding . . . . . . . . . . . . . . . . . . . . . . 62
4.5 An Application to Locally Noisy Strings . . . . . . . . . . . . . . 69
4.6 Linguistic Plausibility . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.7 Physiological Plausibility . . . . . . . . . . . . . . . . . . . . . . . 81
4.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
vi
5 A Quantitative Measure of Relevance
Based on Kelly Gambling Theory 87
5.1 Doubling Rates and Kelly Gambling . . . . . . . . . . . . . . . . 88
5.2 Relevant Information and Relevance Rates . . . . . . . . . . . . . 92
5.3 Examples of Relevance Measurements . . . . . . . . . . . . . . . . 96
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6 Multi-Agent Probability Models
of Social Cognition 107
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.2 Multi-Agent Uncertainty Representation . . . . . . . . . . . . . . 109
6.3 Example 1: Preference Attribution . . . . . . . . . . . . . . . . . 116
6.4 Example 2: The Sally-Anne Task . . . . . . . . . . . . . . . . . . 120
6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7 On the Consistency of Approximate
Multi-Agent Probability Theory 131
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.2 Probabilistic Reasoning in Church . . . . . . . . . . . . . . . . . . 132
7.3 Multi-Agent Probability Theory . . . . . . . . . . . . . . . . . . . 135
7.4 Aymptotic Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8 An Epistemological Meditation
on the Bias-Variance Trade-off 147
8.1 The Bias-Variance Trade-off . . . . . . . . . . . . . . . . . . . . . 148
8.2 Example: Beta Estimators . . . . . . . . . . . . . . . . . . . . . . 149
8.3 The Frequentist Dilemma . . . . . . . . . . . . . . . . . . . . . . 150
8.4 Two Examples with “Gaps” . . . . . . . . . . . . . . . . . . . . . 152
8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
9 Fear and Loathing in Statistics 155
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
9.2 Mathematical Background . . . . . . . . . . . . . . . . . . . . . . 156
9.3 Aftermath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.4 A History of Rationality . . . . . . . . . . . . . . . . . . . . . . . 169
9.5 Two Paradigms of Rationality . . . . . . . . . . . . . . . . . . . . 176
9.6 Estimates and Estimators . . . . . . . . . . . . . . . . . . . . . . 182
9.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Summary 193
Samenvatting 195
vii