Paradoxes in scientific inference:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton
CRC Press
2013
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025872316&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025872316&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Includes bibliographical references |
| Umfang: | xviii, 273 S. |
| ISBN: | 9781466509863 |
Internformat
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| 650 | 4 | |a Inference | |
| 650 | 4 | |a Paradoxes | |
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Datensatz im Suchindex
| _version_ | 1819342240337625088 |
|---|---|
| adam_text | Contents
Preface
vii
1.
The Joy of Paradoxes: A Random Walk
1
1.1
Introduction to Paradox
...................... 1
1.1.1
Paradoxes about Life
.................... 2
1.1.2
Paradoxes of Self-Reference
................ 6
1.1.3
Six Degree of Separation
.................. 8
1.1.4
Paradox of Music and Noise
................ 9
1.1.5
Paradox of a Fair Game
.................. 10
1.1.6 DNA
Paradox in Justice System
.............. 11
1.2
Applications of Paradoxes
..................... 12
1.2.1
Benford s Law and Detecting Accounting Fraud
..... 12
1.2.2
Parrondo s
Paradox and Stock Diversification
...... 14
1.2.3
Arrow s Paradox in Social Economics
........... 16
1.2.4
Friendship Paradox and Disease Outbreak Prediction
. . 18
1.2.5
Paradox of Pesticides
.................... 20
1.2.6
Hat Puzzle and Coding Theory
.............. 21
1.2.7
Inspection Paradox and Machine Repair
......... 22
1.2.8
Paradox in Axiom System
................. 23
1.2.9
Paradox and Electric Bell
................. 24
1.2.10
Paradox and Message Encryption
............. 25
1.3
Mathematical Paradox
....................... 27
1.3.1
Achilles and The Tortoise
................. 27
1.3.2
Hubert s Paradox of Grand Hotel
............. 28
1.3.3
Berry s Paradox of the Smallest Integer
......... 28
1.3.4
Torricelli s Trumpet of Finiteness and Infinity
...... 29
1.3.5
Barber s Paradox in Naive Set Theory
.......... 30
xiv
Scientific Inference and Paradoxes
1.3.6
Fermaťs
Last Theorem
................... 32
1.3.7
Borel s Normal Number
.................. 32
1.3.8
Paradoxes of Enrichment
.................. 33
1.3.9
Logistic Model and Chaos
................. 34
1.3.10
Paradoxes Related to Fixed Points
............ 35
1.3.11
Paradox of
π:
Möbius Band................ 37
1.3.12
Dimensional Paradox and Network Robustness
..... 38
1.3.13
The Possibility of The Impossible
............. 40
1.4
Probabilistic and Statistical Paradoxes
.............. 41
1.4.1
Roulette Paradox
...................... 41
1.4.2
Birthday Paradox
...................... 42
1.4.3
Elevator Paradox (Chinese Box)
.............. 43
1.4.4
Paradox of A Drunken Man
................ 44
1.4.5
Saint Petersburg Paradox
................. 45
1.4.6
Paradox of the Family Tree
................ 45
1.4.7
Paradox of Choice
..................... 46
1.4.8
Paradox of Voting and Electing
.............. 48
1.4.9
Brownian Motion Paradox
................. 50
1.4.10
Paradox of Random Graphs
................ 51
1.4.11
A Ghost Number: Chaitin s Constant
.......... 52
1.5
Chapter Review
........................... 53
1.6
Exercises
.............................. 54
2.
Mathematical and Plausible Reasoning
57
2.1
Probability and Randomness
................... 57
2.1.1
Conceptual Unification of Probability
........... 58
2.1.2
The Boy or Girl Paradox
.................. 64
2.1.3
Coupon Collector s Problem
................ 64
2.1.4
Bertrand s Paradox
..................... 66
2.1.5
Monty Hall Dilemma
.................... 67
2.1.6
Tennis Game Paradox
................... 68
2.1.7
Paradox of
Nontransitive Dice:
Round Defeat
...... 69
2.1.8
Paradox of Ruining Time
................. 71
2.1.9
Paradoxes of Independence
................. 72
2.1.10
Randomness and Complexity
............... 74
2.1.11
Randomness and Disorder
................. 75
2.1.12
Quantum Probability
.................... 77
2.2
Mathematical Logic and Formal Reasoning
........... 78
2.2.1
Prepositional Calculus
................... 79
Contents xv
2.2.2
Elementary Laws in Prepositional Calculus
....... 80
2.2.3
Predicate Calculus
..................... 82
2.2.4
Mathematical Induction
.................. 82
2.2.5
Significance of Silence
................... 83
2.3
Plausible Reasoning
........................ 84
2.3.1
Bayesian Reasoning
..................... 85
2.3.2
Paradox of Lewis Carroll s Urn*
.............. 87
2.3.3
Two-Envelope Paradox*
.................. 89
2.3.4
Paradoxes of Random Variables
.............. 92
2.4
Chapter Review
........................... 93
2.5
Exercises
.............................. 95
3.
Statistical Measures of Scientific Evidence
99
3.1
Introduction to Statistical Methods
................100
3.1.1
Statistics versus Probability
................100
3.1.2
Statistical Paradigms
....................100
3.1.3
Statistical Models
......................102
3.1.4
Paradox of Classification
..................103
3.1.5
Hypothesis Testing
.....................104
3.1.6
Spring Water Paradox
...................107
3.2
Statistical Principles
........................108
3.2.1
Conditionality Principle
..................108
3.2.2
Sufficiency Principle
....................110
3.2.3
Likelihood Principle
....................113
3.2.4
Law of Likelihood
......................117
3.2.5
Bayes s Law
.........................119
3.3
Decision Theory Approach
.....................124
3.3.1
Paradox of Saving Lives
..................125
3.3.2
Paradoxes of Group Decisions
...............126
3.4
Controversies in Evidence Measures
...............128
3.4.1
Paradox of Model Fitting and Validation
......... 128
3.4.2
Robbins s Paradox
..................... 128
3.4.3
Simpson s Paradox
..................... 130
3.4.4
Regression to the Mean
.................. 131
3.4.5
Paradox of Confounding
.................. 133
3.5
Causal Space Theory: Unification of Paradigms
......... 135
3.5.1
Paradox of Mixed Experiment
...............136
3.5.2
Paradox of the
Birnbaum
Experiment*
..........137
3.5.3
Paradoxes of Causal Space
.................139
xvi
Scientific Inference and Paradoxes
3.5.4
Causal Space Schema of Statistical Paradigms
...... 140
3.6
Multiplicity: The Black Hole of Scientific Discovery
....... 142
3.6.1
Description of Multiplicity Issues
............. 143
3.6.2
Frequentisi
Approach to Multiplicity Problems
..... 145
3.6.3
Sequential Probability Ratio Test
............. 149
3.6.4
Bayesian Approach to Multiplicity Problems*
...... 150
3.6.5
Controversies in Multiplicity
................ 153
3.7
Chapter Review
........................... 155
3.8
Exercises
.............................. 158
4.
Scientific Principles and Inferences
161
4.1
Epistemology
............................ 162
4.1.1
Science
............................ 162
4.1.2
Meaning of Understanding
................. 163
4.1.3
Theories of Truth
...................... 164
4.1.4
Discovery or Invention
................... 166
4.1.5
Occam s Razor
....................... 167
4.1.6
Analogies and Metaphors in Scientific Research
..... 169
4.1.7
Paradoxes of Scientific Reasoning
............. 171
4.1.8
Buridan s Ass: Paradox of Bias
.............. 173
4.1.9
Scientific Method and Experiment
............ 175
4.1.10
Thought Experiment
.................... 177
4.2
Controversies in Scientific Philosophy
............... 178
4.2.1
Determinism Versus Free Will
............... 178
4.2.2
Paradox of Causality
.................... 181
4.2.3
Chicken or Egg
....................... 182
4.2.4
Maxwell s Demon
...................... 183
4.2.5
Paradox of Speed and Space
................ 184
4.2.6
Modern Conception of Time and Space
.......... 185
4.2.7
Time Travel: The Twin and Grandfather Paradoxes
. . 187
4.2.8
Concept of Infinity
..................... 189
4.2.9
Einstein-Podolsky-Rosen Paradox*
............ 190
4.3
Paradox of a Logical System
.................... 192
4.3.1
Axiom Systems
....................... 192
4.3.2
Fitch s Paradox of Knowability*
.............. 194
4.3.3
Gödel s
Incompleteness Theorem*
............. 195
4.3.4
Goodstein s Theorem
.................... 196
4.3.5
Continuum Hypothesis
................... 197
4.3.6
Paradoxes of Truth and Belief
............... 198
Contents xvii
4.3.7
Pigeonhole Principle
....................199
4.3.8
Paradox of Reductio
ad Absurdum
............200
4.4
Paradox and Game Theory
....................202
4.4.1
Prisoner s Paradox
..................... 202
4.4.2
Braess s Paradox
...................... 204
4.4.3
Newcomb s Paradox
.................... 206
4.4.4
Stable Marriage Problem
.................. 208
4.5
Chapter Review
........................... 209
4.6
Exercises
..............................212
5.
Artificial Intelligence
215
5.1
Paradoxes in Artificial Intelligence
................216
5.1.1
From Turing Machine to Artificial Intelligence
...... 216
5.1.2
Brain and Mind Identity Theory
............. 217
5.1.3
Machine-Race Human
................... 219
5.1.4
The Ship of Theseus: Identity Paradox
.......... 219
5.1.5
Paradox of Emotion
.................... 220
5.1.6
Paradox of Understanding
................. 221
5.1.7
Paradox of Discovery
.................... 222
5.1.8
Paradox of Dreaming
.................... 223
5.1.9
Paradox of Meta-Cognition
................ 224
5.1.10
Swarm Intelligence
..................... 224
5.1.11
Man in World in Man
................... 226
5.1.12
Crafting a Child or an Adult Agent
............ 228
5.1.13
Commonsense Knowledge Base and
AI
Agent
...... 229
5.2
Architecture of Artificial Intelligent Agent
............ 231
5.2.1
The
AI
Framework
..................... 231
5.2.2
Agent s Intrinsic Abilities and Concepts
......... 232
5.2.3
Representation of Knowledge
............... 235
5.2.4
Learning Rules
....................... 236
5.2.5
Response Rules
....................... 238
5.3
Learning and Teaching
....................... 239
5.3.1
Patternization
........................239
5.3.2
Pattern Optimization
....................243
5.3.3
Progressive Teaching
....................244
5.3.4
Intelligent Agent Evolution
................246
5.4
Chapter Review
...........................247
5.5
Exercises
..............................248
Appendix A Mathematical Notations
251
xviii
Scientific Inference and Paradoxes
Bibliography
253
Index
265
Statistics
Paradoxes are poems of science and philosophy that collectively allow
us to address broad multidisciplinary issues within a microcosm. A true
paradox is a source of creativity and a concise expression that delivers
a profound idea and provokes a wild and endless imagination. The study
of paradoxes leads to ultimate clarity and. at the same time, indisputably
challenges your mind.
Paradoxes in Scientific Inference analyzes paradoxes from many
different perspectives: statistics, mathematics, philosophy, science,
artificial intelligence, and more. The book elaborates on findings and
reaches new and exciting conclusions. It challenges your knowledge,
intuition, and conventional wisdom, compelling you to adjust your way
of thinking. Ultimately, you will learn effective scientific inference through
studying the paradoxes.
Features
1
Presents large collections of paradoxes in sciences and statistics
Provides broad and interesting applications of paradoxes
Offers a new. effective way of learning scientific inference
1
Analyzes controversies in statistical measures of scientific evidence
n Discusses principles and the conceptual unification of statistical
paradigms
Develops new architectures for creating artificial intelligent agents
Includes a quick study guide and exercises in each chapter
About the Author
Mark Chang is vice president of biometrics at AMAG Pharmaceuticals
and an adjunct professor at Boston University. Dr. Chang is a co-founder
of the International Society for Biopharmaceutical Statistics and an elected
fellow of the American Statistical Association. He serves on the editorial
boards of several statistical journals and has published five books on
biostatistics and clinical trial designs.
CRC
Press
Taylor
£»
Francis Group
an
informa
business
www.
с
re
pre s s.
com
6000
Broken Sound Parkw
.,.
Suite
300,
Boca Raton, FL
33487
71
Τ
Thira Avenue
NewYoffc. NY100T7
2
Park Square, Milton Park
Abingdon. Oxon OX14 4RN, UK
К1Ч7ЧЧ
9 781466 509863
|
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| institution | BVB |
| isbn | 9781466509863 |
| language | English |
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| spellingShingle | Chang, Mark 1955- Paradoxes in scientific inference Naturwissenschaft Science / Methodology Inference Paradoxes |
| title | Paradoxes in scientific inference |
| title_auth | Paradoxes in scientific inference |
| title_exact_search | Paradoxes in scientific inference |
| title_full | Paradoxes in scientific inference Mark Chang |
| title_fullStr | Paradoxes in scientific inference Mark Chang |
| title_full_unstemmed | Paradoxes in scientific inference Mark Chang |
| title_short | Paradoxes in scientific inference |
| title_sort | paradoxes in scientific inference |
| topic | Naturwissenschaft Science / Methodology Inference Paradoxes |
| topic_facet | Naturwissenschaft Science / Methodology Inference Paradoxes |
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