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168 Pages
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From the reviews:
"[This book is]... for anyone who lists "foundations of statistics" as an area of interesting, and it would make interesting reading for someone who wants to take some time to reflect on where the discipline stands." (Biometrics, 64, March 2008)
"This book seeks to answer the question: 'In what sense do statistical methods provide scientific evidence?' ... . The intended audience includes students, consultants, and researchers with a solid background in probability and mathematical statistics, experience using statistics in applied problems, and a willingness to question prevailing statistical methodology. ... Inquisitive statisticians may find this book an interesting read in which to put their theories and epistemology to the test. There is an appendix to help with the requisite logical reasoning." (Shaun S. Wulff, Journal of the American Statistical Association, Vol. 102 (480), 2007)
"This brief volume attempts an heroic tilt at the problem of identifying and elucidating the nexus between statistical and scientific pursuits. ... The breadth of the material covered is remarkable, considering the book's brevity; the book draws together an idiosyncratic collection of sources, ranging from Lehman and Kuhn to Persig and Ayer. ... Thompson does draw us through some interesting and challenging new ways of looking at existing concepts." (Andrew Robinson, Journal of Applied Statistics, Vol. 35 (3), 2008)
"Readership: Statisticians and other scientists interested in the foundations of statistical inference. This is a personal view of how statistical inference relates to scientific discovery. It seeks to link Bayesian statistics and p-values to 'one widely accepted view of science'. ... It is not too mathematical and does not require a deep prior grasp of the issues. ... The book is divided into three parts, the first setting the context, the second discussing interpretations of probability, and the thirdstatistical models for inference." (David J. Hand, International Statistical Review, Vol. 75 (2), 2007)
"The main purpose of this interesting book is to provide interpretations and explanations of different theories of statistical evidence. In particular, the methodologies based on the Bayesian approach and p-values are thoroughly examined. ... The book also contains an appendix on deductive logic, with a discussion on propositional calculus, conditional statements ... classical logic and many-valued logic." (Angelo Gilio, Mathematical Reviews, Issue 2008 h)
"The book analyses a set of well-known and related questions of any field of knowledge with respect to statistics. ... There are 14 brief chapters divided into three clusters ... . for statisticians interested in the wider context of their field, the book is highly recommended." (Goetz Uebe, Advances in Statistical Analysis, Vol. 92 (3), 2008)
"This book presents a series of intellectual discussions concerning some of the most basic topics in statistics ... . The book is a well-researched and thoroughly professional approach to the various dilemmas faced by statisticians in interpreting data. The author's knowledge of the literature as it pertains to the various issues discussed in the book is excellent ... . The wealth of knowledge present in this 152-page book is remarkable; the book is a worthy of addition to any library of statistical literature." (Jeffrey E. Jarrett, Technometrics, Vol. 50 (3), August, 2008)
| Overview | p. 1 |
| The Context | |
| Mathematics and Its Applications | p. 9 |
| Axiomatic Method and Mathematics | p. 9 |
| Prepositional Calculus as an Axiomatic System | p. 12 |
| The Euclidean Geometry Paradigm | p. 13 |
| Formal Science and Applied Mathematics | p. 15 |
| Notes on the Literature | p. 17 |
| The Evolution of Natural Scientists and Their Theories | p. 18 |
| Background | p. 18 |
| "Prediction = Science"? | p. 21 |
| External Aspects of Science | p. 24 |
| Conclusion Theory | p. 29 |
| Law and Learning | p. 33 |
| The Law | p. 33 |
| Learning Theory | p. 35 |
| Interpreting Probability | |
| Introduction to Probability | p. 41 |
| The Axiomatic Theory | p. 42 |
| Interpreting the Axiomatic Theory | p. 47 |
| Enumerative Probability | p. 49 |
| Frequency Probability | p. 50 |
| Propensity Probability-"Tendency to Happen" | p. 51 |
| The Fair Betting Utility Interpretation of Probability | p. 54 |
| Probability as Personal Price | p. 54 |
| Probability as Personal Degree of Belief | p. 58 |
| Conditional Subjective Probability | p. 59 |
| Attitudes Toward Chance | p. 61 |
| Indeterminism and Chance | p. 61 |
| The Location of Probability-Mind or Matter? | p. 62 |
| Equally Likely | p. 63 |
| Frequency and the Law of Large Numbers | p. 67 |
| The Single Instance | p. 69 |
| Locations of Some Kinds of Probabilities | p. 70 |
| Statistical Models of Induction | |
| A Framework for Statistical Evidence | p. 75 |
| Introduction | p. 75 |
| What Is an Experiment? | p. 76 |
| E[subscript v](E, y) Does Not Exist | p. 77 |
| The Fitted Parameter Model | p. 78 |
| Interlaboratory Experimentation | p. 79 |
| Conclusion | p. 83 |
| A Critique of Bayesian Inference | p. 84 |
| Randomness Needs Explaining | p. 84 |
| How to Adjust Your Belief | p. 86 |
| The Economic Approach to Group Belief | p. 88 |
| Objective Bayesian Statistics | p. 94 |
| The Long-Run Consequence of Behavior | p. 97 |
| Decision Theory | p. 97 |
| The Accept-Reject Theory | p. 98 |
| Frequency Interpretation of Confidence Intervals | p. 99 |
| A Critique of p-Values | p. 102 |
| The Context | p. 102 |
| Simple Hypotheses | p. 104 |
| Composite Hypotheses | p. 108 |
| Test of a Direction | p. 110 |
| Asymptotic Considerations | p. 112 |
| Intuitive Test Statistics | p. 113 |
| Discussion | p. 115 |
| The Nature of Statistical Evidence | p. 116 |
| Introduction | p. 116 |
| Birnbaum's Theorem | p. 117 |
| Counterexamples | p. 120 |
| The Science of Statistics | p. 122 |
| Meanings of "Science" | p. 122 |
| Concepts of Statistics | p. 124 |
| Is Statistics a Science? | p. 124 |
| Comparison of Evidential Theories | p. 126 |
| Evidential Models and Their Criteria | p. 126 |
| Two Interpretations of the Mathematics of Testing Are Needed | p. 126 |
| Evidential Meaning | p. 127 |
| Comparison of Bayesian, Likelihood, and "Show-Me" Evidence | p. 127 |
| An Example-Probability Evidence and the Law | p. 130 |
| Deductive Logic | p. 133 |
| The Prepositional Calculus | p. 133 |
| Truth Tables | p. 135 |
| Deductive Arguments and Conditional Statements | p. 136 |
| Critique of Classical Logic | p. 139 |
| Many-Valued Logic | p. 140 |
| Notes on the Literature | p. 142 |
| References | p. 143 |
| Author Index | p. 149 |
| Subject Index | p. 151 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780387400501
ISBN-10: 0387400508
Series: LECTURE NOTES IN STATISTICS
Published: 5th March 2007
Format: Paperback
Language: English
Number of Pages: 168
Audience: General Adult
Publisher: Springer Nature B.V.
Country of Publication: US
Dimensions (cm): 23.5 x 15.24 x 1.27
Weight (kg): 0.25
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