Professor Deborah G. Mayo

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1 Professor Deborah G. Mayo Office Hrs: T405: TBA PH500 Ph.D Research Seminar in the Philosophy of Science: Autumn 2008: Topics in the Philosophy and History of Inductive/Statistical Inference and the Foundations of Statistical Science The Seminar is currently scheduled for 10:00-12:00, on the following Wednesdays: 15, 29 October; 12, 19 November; 10 December. This seminar will focus on central problems in contemporary philosophy of statistics, and their interrelationships with general problems of inference and evidence in philosophy of science. We will study some relevant work by statisticians, e.g., R.A. Fisher, J. Neyman, E.S. Pearson, L. J. Savage, G. Barnard, D.R. Cox, E. Lehmann, J. Berger, notable exchanges between them, and related arguments by philosophers of statistics and confirmation theory. We will trace out a handful of problems and principles that underlie contrasting philosophies about evidence and inference, as well as contemporary statistical foundations (frequentist, Bayesian,other). Questions we consider include: What are the roles of probability in uncertain inference in science? Which methods can be shown to ensure reliability? And How is control of long-run error probabilities relevant for warranting inductive inference in science? We will explore how contrasting answers to these questions directly connects to long-standing problems about inductive inference and methodological issues about data collection and hypotheses construction, e.g., data-dependent (versus predesignated) hypotheses, double-counting, data-mining, "stopping-rules", and "selection" effects. No knowledge of statistics is expected*, only an interest in learning something about its foundations from a philosophical perspective. The full syllabus lists some broad areas of possible discussion for general, (optional) additional, meetings to be held at agreed upon times, given interest (among seminar participants and/or non-participants). Input, as well as presentations by others, would be welcome. I expect to supply (hard copies or on line) all readings for the seminar, and ongoing notes and slides as the course proceeds, depending on the interests of participants. The material of this seminar will relate to a manuscript I am writing, Learning From Error. For more information and updates, please write to mayod@vt.edu or error@vt.edu. *However, if there is interest, I would expect to hold 1-2 optional sessions on some of the more formal aspects. 9/27/08 1

2 Tentative List of Topics 1. October 15: INTRODUCTION TO THE SEMINAR: Designing our Seminar. Introduction and Overview: (i) The relevance of philosophy of statistics to philosophy of science; (ii) 4 Waves of Controversy in the Philosophy of Statistics 2. October 29: Statistical Significance Tests: Family Feuds and 50+ years of fallout. Some Classical Exchanges between R. A. Fisher, J. Neyman, and E.S. Pearson 3. November 12: Some Problems of Frequentist Error Statistics (Behavioristic and Evidential Interpretations) and Bayesian Statistics (Subjective and Objective interpretations); Fallacies of Testing (and their avoidance) 4. November 19: Error Statistical and Bayesian Principles and Their Consequences: The (strong) Likelihood Principle; Optional Stopping, (and/or Double-Counting, Non-novel data, and Data-Dredging) 5. December 10: The O-Bayesian Movement: Bayesian-Frequentist "reconciliations" and methodological "unifications"; impersonal and reference Bayesians (and resulting Bayesian family feuds); Highy Probable vs Highly Probed hypotheses 9/27/08 2

3 PH500 Ph.D. Research Seminar in the Philosophy of Science: D. Mayo Room T405 Autumn 2008 Topics in the Philosophy and History of Inductive/Statistical Inference and the Foundations of Statistical Science Syllabus (first installment) 1. October 15 INTRODUCTION TO THE SEMINAR: Designing our Seminar Introduction and Overview: (i) The relevance of philosophy of statistics to philosophy of science; (ii) 4 Waves of Controversy in the Philosophy of Statistics 2. October 29 Statistical Significance Tests: Family Feuds and 50+ years of fallout Some Classical Exchanges between R. A. Fisher, J. Neyman, and E.S. Pearson The Triad (3 short, key, papers): Fisher, R. A. (1955), "Statistical Methods and Scientific Induction". Journal of The Royal Statistical Society (B) 17: Neyman, J. (1956), Note on an Article by Sir Ronald Fisher, Journal of the Royal Statistical Society. Series B (Methodological), 18: Pearson, E. S. (1955), "Statistical Concepts in Their Relation to Reality," Journal of the Royal Statistical Society, B, 17: One of the following a-c: a. Cox, D.R. (1982), Statistical Significance Tests, B. J. Clin. Pharmac. 14: b. Fisher, The Design of Experiments, Oliver & Boyd, Edinburgh (pp. 1-25). c. Historical overview: (pp from The Inference Experts ) Gigerenzer, G., Swijtink, Z., Porter, T., Daston, L., Beatty, J., and Krueger, L., (1989) The Empire of Chance, Cambridge University Press, Cambridge. (First half) Mayo, D. and Cox, D. (2006), Frequentist Statistics as a Theory of Inductive Inference, Optimality: The Second Erich L. Lehmann Symposium, (J. Rojo, ed.), Lecture Notes-Monograph Series, Inst. of Mathematical Stat. (IMS), Vol. 49: /27/08 3

4 3. November 12 Some Problems of Frequentist Error Statistics (Behavioristic and Evidential Interpretations) and Bayesian Statistics (Subjective and Objective interpretations) Fallacies of Testing (and their avoidance) Chapters 8 and 9 from C. Howson and P. Urbach, (1992), Scientific Reasoning: The Bayesian Approach, 2 nd edition, Fisher s Theory, and "The Neyman-Pearson Theory of Significance Tests" (pp ). a. Mayo, D. and Spanos, A. (2006), Severe Testing as a Basic Concept in a Neyman- Pearson Philosophy of Induction, British Journal of Philosophy of Science, 57: or b. Mayo, D. (2003), Severe Testing as a Guide for Inductive Learning, in H. Kyburg and M. Thalos (eds.), Probability Is the Very Guide in Life. Chicago: Open Court: Optional: one of the hidden Neyman papers: Neyman talks to Carnap: (pp ; 40-41) Neyman, J. (1955), The Problem of Inductive Inference, Communications on Pure and Applied Mathematics, VIII, Neyman, J. (1957), The Use of the Concept of Power in Agricultural Experimentation, Journal of the Indian Society of Agricultural Statistics, IX: November 19 Error Statistical and Bayesian Principles and Their Consequences: The (strong) Likelihood Principle; Optional Stopping, (and/or Double-Counting, Non-novel data, and Data-Dredging) Selected pages from: M Savage, L. (ed.) (1962), The Foundations of Statistical Inference: A Discussion. London, Methuen. Hacking, I. (1972), Likelihood, The British Journal for the Philosophy of Science 23: Mayo, D and Kruse, M. (2001), Principles of Inference and Their Consequences, with M. Kruse, in Foundations of Bayesianism, D. Cornfield and J. Williamson (eds.). Dordrecht: Kluwer Academic Publishers, 2001, /27/08 4

5 5. (i) December 10 The O-Bayesian Movement: Bayesian-Frequentist "reconciliations" and methodological "unifications"; impersonal and reference Bayesians (and resulting Bayesian family feuds); Highly Probable vs Highly Probed hypotheses in philosophy of science. a-1: Berger, J. (2003), Could Fisher, Jeffreys and Neyman Have Agreed Upon Testing? (and Commentary), Statistical Science 18, 2003: a-2: Kass, R. E. and Wasserman, L. (1996), The Selection of Prior Distributions by Formal Rules, J. Amer. Statist. Assoc. 91: a-2dawid, A.P. (1997), Comments on [Bernardo] Non-Informative Priors do not exist, Journal of Statistical Planning and Inference 65: Or, we might opt for a more informal discussion based on unpublished material and/or: b-1 Hacking, I. (1980), The Theory of Probable Inference: Neyman, Peirce and Braithwaite, in D. H. Mellor (ed.), Science, Belief and Behavior: Essays in Honour of R.B. Braithwaite, pp , Cambridge University Press, Cambridge. b-2 Mayo, D. (2005), "Evidence as Passing Severe Tests: Highly Probed vs. Highly Proved" in P. Achinstein (ed.), Scientific Evidence, Johns Hopkins, pp Other Gillies D. (2001), Bayesianism and the Fixity of the Theoretical Framework, in Corfield, D. and Williamson, J. (eds.), Foundations of Bayesianism, Kluwer, pp (ii) probably best done as an optional session, if there s interest Another look at a breakthrough : From the (weak) conditionality principle, and sufficiency to the (strong) likelihood principle? (and the 50th year birthday of Cox s 1958 example) (Selected pages from) Birnbaum, A. (1962), On the Foundations of Statistical Inference (with discussion), Journal of the American Statistical Association, 57: Robins, J. and L. Wasserman (2000), Conditioning, Likelihood, and Coherence: A Review of Some Foundational Concepts, Journal of the American Statistical Association, 95: (Selected pages from) Cox, D. R. and D. G. Mayo (2008), Objectivity and Conditionality in Frequentist Inference, Ch. 8 (II), An Error in the Argument From WCP and S to the SLP: Discussion, (Ch. 8 III) in Mayo, D. and Spanos, A.(eds.), (forthcoming) Error and Inference (Mayo, D. and Spanos, A. eds. Cambridge University Press, Cambridge.. 9/27/08 5

6 Other: Cox, D. R. (1958), Some Problems Connected with Statistical Inference, Annals of Mathematical Statistics, 29: Lehmann, E. L. (1993), "The Fisher and Neyman-Pearson Theories of Testing Hypotheses: One Theory or Two?" Journal of the American Statistical Association, 88: Durbin, J. (1970), On Birnbaum s Theorem and the Relation between Sufficiency, Conditionality and Likelihood, Journal of the American Statistical Association, 65: Bjornstand, J. (1992), Introduction to Birnbaum (1962) On the Foundations of Statistical Inference, in Breakthroughs in Statistics, Vol I, Kotz and Johnson eds., pp Other possible additional discussions (if there is interest): -Recipes and calculations (significance levels, power, confidence levels, severity): TBA -Testing assumptions of statistical tests: misspecification testing Mayo, D. G. and Spanos, A. (2004), Methodology in Practice: Statistical Misspecification Testing, Philosophy of Science, 71: Some problems about novelty and predesignation: TBA Worrall, J. Error, Tests and Theory-Confirmation, and D. Mayo Exchange (chapter 5), forthcoming in Mayo, D. and Spanos, A. (eds.), Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science, CUP. Some Background Texts: Barnett, V. (1999), Comparative Statistical Inference, 3rd edition, Wiley, New York. Berger, J. and Wolpert, R. (1984), The Likelihood Principle. IMS. Cox, D. R. (2006), Principles of Statistical Inference, Cambridge: Cambridge University Press. Cox, D. R. and D. V. Hinkley (1974), Theoretical Statistics, Chapman & Hall, London. Hacking, I. (1965), Logic of Statistical Inference, Cambridge University Press, Cambridge. Mayo, D. G. (1996), Error and the Growth of Experimental Knowledge, The University of Chicago Press, Chicago. Salmon, W. (1966), The Foundations of Scientific Inference. Pittsburgh, University of Pittsburgh Press. Some Collections of Papers from Philosophy of Statistics Conferences: Godambe, V. and Sprott, D. (eds.) (1971), Foundations of Statistical Inference, Holt, Rinehart and Harper, W. L. and C. A. Hooker (eds.) (1976), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol II, D. Reidel, Dordrecht, Holland. Morrison, D. and Henkel, R. (eds.) (1970), The Significance Test Controversy, Aldine, Chicago. 9/27/08 6

7 Introductory Workbooks Gonick, L. and W. Smith (1993), The Cartoon Guide to Statistics, HarperCollins Publishers, NY. Peck, R., Olsen, C. and Devore, J., Introduction to Statistics and Data Analysis, Duxbury. 9/27/08 7

Commentary on A. Gelman and C. Robert: Not only defended but also applied : The perceived absurdity of Bayesian inference

Commentary on A. Gelman and C. Robert: Not only defended but also applied : The perceived absurdity of Bayesian inference 1. Introduction Deborah G. Mayo Philosophy Virginia Tech (Oct 3, 2012) I am grateful