Perspectives on Randomness in Statistics

Welcome to the course website for the EDMA PhD course MATH-705, Perspectives on Randomness in Statistics. All relevant information and materials are collected and will be updated on this page.

• Location: EPFL, CM1 113
• Time: 10.00 - 11.30
• Email: tobias [dot] freidling [at] epfl [dot] ch

Description

In this weekly course, we read and discuss different papers that examine how randomness is conceptualized in statistics. There are two presentation formats: (1) We directly examine the reading material and different people can lead the discussion with their comments, questions, and opinions; (2) one of the participants starts the session with a 20-minute presentation introducing the main points and subsequently leading the discussion. See the schedule below for details about the topics and presentations. Regardless of the presentation format, participants enrolled for the module are expected to read the material before the session.

Free auditors are always welcome. :)

Schedule

Reading Materials

Randomness, Philosophically

• Introduction to the main philosophical views on randomness: Hájek, A. (2023) ‘Interpretations of Probability’, in E.N. Zalta and U. Nodelman (eds) The Stanford Encyclopedia of Philosophy. Winter 2023. Metaphysics Research Lab, Stanford University. link

Randomness, Probabilistically

• Review of the historical developments leading up to Kolmogorov’s axioms: Shafer, G. and Vovk, V. (2006) ‘The Sources of Kolmogorov’s Grundbegriffe’, Statistical Science, 21(1), pp. 70–98. link
• Modern retrospective on von Mises’ approach to probability: van Lambalgen, M. (1996) ‘Randomness and foundations of probability: von Mises’ axiomatisation of random sequences’, Statistics, probability and game theory. Institute of Mathematical Statistics, pp. 347–368. link

Optional reading:

• von Mises’ formulation of probability: von Mises, R. (1941) ‘On the Foundations of Probability and Statistics’, The Annals of Mathematical Statistics, 12(2), pp. 191–205. link

The Bayesian Perspective

• Historical Overview: Savage, L.J. (1961) ‘The Foundations of Statistics Reconsidered’, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics. University of California Press, pp. 575–587. link
• Modern and more statistical overview of the Bayesian approach: Gelman, A. and Shalizi, C.R. (2013) ‘Philosophy and the practice of Bayesian statistics’, British Journal of Mathematical and Statistical Psychology, 66(1), pp. 8–38 link

Optional reading:

• Non-technical exposition of the decision-theoretic approach: Savage, L.J. (1951) ‘The Theory of Statistical Decision’, Journal of the American Statistical Association, 46(253), pp. 55–67. link

• de Finetti’s contributions: De Finetti, B. (1992) ‘Foresight: Its Logical Laws, Its Subjective Sources’, in S. Kotz and N.L. Johnson (eds) Breakthroughs in Statistics. New York, NY: Springer New York (Springer Series in Statistics), pp. 134–174. link

• Model validation under the Bayesian and Frequentist paradigm: Freedman, D. (1995) ‘Some issues in the foundation of statistics’, Foundations of Science, 1(1), pp. 19–39. link

The Frequentist Perspective

• An argument for the likelihood principle: Birnbaum, A. (1962) ‘On the Foundations of Statistical Inference’, Journal of the American Statistical Association, 57(298), pp. 269–306. link

• Fisherian vs Neyman-Pearsonian point of view: Lehmann, E.L. (1993) ‘The Fisher, Neyman-Pearson Theories of Testing Hypotheses: One Theory or Two?’, Journal of the American Statistical Association, 88(424), pp. 1242–1249. link

Optional reading:

• An interpretation of the Neyman-Pearson theory: Birnbaum, A. (1977) ‘The Neyman-Pearson Theory as Decision Theory, and as Inference Theory; With a Criticism of the Lindley-Savage Argument for Bayesian Theory’, Synthese, 36(1), pp. 19–49. link

• Fisher on statistical errors: Fisher, R. (1955) ‘Statistical Methods and Scientific Induction’, Journal of the Royal Statistical Society: Series B (Methodological), 17(1), pp. 69–78. link

• Pearson’s response to Fisher’s paper: Pearson, E.S. (1955) ‘Statistical Concepts in the Relation to Reality’, Journal of the Royal Statistical Society. Series B (Methodological), 17(2), pp. 204–207. link

Finite and Infinite Populations I

• Fisher’s approach to inference (read in excerpts): Fisher, R.A. (1922) ‘On the mathematical foundations of theoretical statistics’, Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 222(594–604), pp. 309–368. link
• Retrospective on Fisher and Neyman’s contributions on sampling: Fienberg, S.E. and Tanur, J.M. (1996) ‘Reconsidering the Fundamental Contributions of Fisher and Neyman on Experimentation and Sampling’, International Statistical Review / Revue Internationale de Statistique, 64(3), p. 237. link
• Outline of Fisher’s idea with discussion (shared with the next session): Fisher, R.A. (1935) ‘The Logic of Inductive Inference’, Journal of the Royal Statistical Society, 98(1), pp. 39–82. link

Optional reading:

• Fisher’s foundational work on random experiments: Fisher, R.A. (1935) ‘The design of experiments.’ link
• A Bayesian perspective on finite populations: Ericson, W.A. (1969) ‘Subjective Bayesian Models in Sampling Finite Populations’, Journal of the Royal Statistical Society: Series B (Methodological), 31(2), pp. 195–224. link

Finite and Infinite Populations II

• Outline of Fisher’s idea with discussion (shared with the previous session): Fisher, R.A. (1935) ‘The Logic of Inductive Inference’, Journal of the Royal Statistical Society, 98(1), pp. 39–82. link
• Neyman on sample surveys (read in excerpts): Neyman, J. (1934) ‘On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection’, Journal of the Royal Statistical Society, 97(4), p. 558. link
• An early interpretation of census data: Deming, W.E. and Stephan, F.F. (1941) ‘On the Interpretation of Censuses as Samples’, Journal of the American Statistical Association, 36(213), pp. 45–49. link

Optional reading:

• Theoretical paper on finite population inference: Pitman, E.J.G. (1937) ‘Significance Tests Which May be Applied to Samples from Any Populations’, Journal of the Royal Statistical Society Series B: Statistical Methodology, 4(1), pp. 119–130. link

Sampling with and without Replacement

• Distance of Distributions (in excerpts): Dümbgen, L., Samworth, R.J. and Wellner, J.A. (2021) ‘Bounding distributional errors via density ratios’, Bernoulli, 27(2). link
• Concentration Inequalities (focus on results): Bardenet, R. and Maillard, O.-A. (2015) ‘Concentration inequalities for sampling without replacement’, Bernoulli, 21(3), pp. 1361–1385. link
• Finite population Central Limit Theorems (focus on simple setting): Li, X. and Ding, P. (2017) ‘General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference’, Journal of the American Statistical Association, 112(520), pp. 1759–1769. link

Modelling in Survey Statistics

• Emergence of survey statistics and early results: Smith, T.M.F. (1976) ‘The Foundations of Survey Sampling: A Review’, Royal Statistical Society. Journal. Series A: General, 139(2), pp. 183–195. link
• Article and discussion about the use of models in survey statistics: Särndal, C.-E. et al. (1978) ‘Design-Based and Model-Based Inference in Survey Sampling [with Discussion and Reply]’, Scandinavian Journal of Statistics, 5(1), pp. 27–52. link

Optional reading:

• Review on sample surveys in the 20th century: Smith, T.M.F. (2001) ‘Biometrika Centenary: Sample surveys’, Biometrika, 88(1), pp. 167–243. link
• More modern and partly Bayesian contribution on the modelling debate: Little, R.J. (2004) ‘To Model or Not To Model? Competing Modes of Inference for Finite Population Sampling’, Journal of the American Statistical Association, 99(466), pp. 546–556. link

Finite Populations in Causal Inference

• Introduction if needed (Chapters 4 to 6): Imbens, G.W. and Rubin, D.B. (2015) Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction. Cambridge: Cambridge University Press. link

• Bridging finite and infinite population inference: Ding, P., Li, X. and Miratrix, L.W. (2017) ‘Bridging Finite and Super Population Causal Inference’, Journal of Causal Inference, 5(2). link

• From sample to population effects: Miratrix, L.W. et al. (2018) ‘Worth Weighting? How to Think About and Use Weights in Survey Experiments’, Political Analysis, 26(3), pp. 275–291. link

Optional reading:

• Regression in finite populations: Abadie, A. et al. (2020) ‘Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis’, Econometrica, 88(1), pp. 265–296. link

• Applied paper that discusses finite vs super-population: Manski, C.F. and Pepper, J.V. (2018) ‘How Do Right-to-Carry Laws Affect Crime Rates? Coping with Ambiguity Using Bounded-Variation Assumptions’, Review of Economics and Statistics, 100(2), pp. 232–244. link

Generalizability and Transportability

• Different kinds of deviation of observed and target population: Egami, N. and Hartman, E. (2023) ‘Elements of External Validity: Framework, Design, and Analysis’, American Political Science Review, 117(3), pp. 1070–1088. link
• Application-focused perspective on generalizability in different models: Berk, R.A. and Freedman, D.A. (2009) ‘Statistical Assumptions as Empirical Commitments’, in Statistical Models and Causal Inference. 1st edn. Edited by D. Collier, J. S. Sekhon, and P. B. Stark. Cambridge University Press, pp. 23–44. link

Optional reading:

• Less technical overview of external validity: Findley, M.G., Kikuta, K. and Denly, M. (2021) ‘External Validity’, Annual Review of Political Science, 24(1), pp. 365–393. link

Bonus Material

• What is good statistical evidence?: Chugg, B., Ramdas, A. and Grünwald, P. (2026) ‘E-values as statistical evidence: a comparison to Bayes factors, likelihoods, and p-values’, Synthese, 208(3), p. 130. link