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Breaking News (September 23rd 2024): my single-authored paper Beyond Neyman-Pearson: e-value enable hypothesis testing with a data-driven alpha (arXiv version) has been published  in the Proceedings of the National Academy of Sciences of the USA (PNAS)!  G., 2023. Together with my earlier The E-Posterior. Philosophical Transactions of the Royal Society of London Series A, 2023 (arXiv version) ;  this paper puts forward a novel approach to statistical inference that provides a middle ground between (and is different from both) the two standard paradigms in statistics, i.e.  Bayesian and frequentist (Neyman-Pearson) approaches. Foto© Patrick Post.

Peter Grünwald is senior researcher in the machine learning group at CWI in Amsterdam, the Netherlands. He is also full professor of Statistical Learning at the mathematical institute of Leiden University.

Peter is the recipient of a prestigious ERC Advanced Grant (2024) (CWI announcement and interviews (in Dutch) in national newspapers De Volkskrant and Trouw– see here for more general biographical information and recent media exposure). The project, and Peter’s research in general,  is about creating a much more flexible theory of statistical inference,  based on the emerging theory of e-values and e-processes.  E-values (wikipedia) are an alternative to p-values that effortlessly deal with optional continuation: with e-value based tests and the corresponding always valid confidence intervals, one can always gather additional data, while keeping statistically valid conclusions. Until June 2019, publications on e-values were few and far between: the concept did not even have a name. Then, in the course of just six months, four papers by different research groups appeared on arXiv that firmly established them as an important statistical concept, leading to a plethora of novel results. Allowing for optional continuation is just one way in which e-values provide more flexibility than p-values –  they also allow to set a type of significance level after seeing the data, which is a mortal sin in classical testing. Recent publications and preprints include:

Introductions/Overviews/General Methodology/Code:

  • G. and Rianne de Heide and Wouter Koolen. Safe Testing. To appear in the Journal of the Royal Statistical Society, Series B, 2024, with discussion (link to preprint on RSS website).  The original arXiv version (which has been very, very substantially revised) is the first (2019) paper in which e-values were given a name (originally we called them s-value). January 24 I presented this paper in a discussion meeting at the Royal Statistical Society in London (youtube video).
  • A. Ly, U. Boehm, G., A. Ramdas, D. van Ravenzwaaij. Safe Anytime-Valid Inference: Practical Maximally Flexible Sampling Designs for Experiments Based on e-Values. PsyArXiv Preprint, available at doi.org/10.31234/osf.io/h5vae. This is an introductory paper written for social scientists,  focusing on how to apply e-values with R code (see below) and explaining how it relieves the burden of specifying a sampling plan.
  • A. Ly, R. Turner, J. ter Schure, M. Perez, G. CRAN R-package safestats. This includes R code for the e-value based approach to t-tests, contingency table tests, z-test and the logrank test. Here is a simple R markdown tutorial including installation instructions, written by Alexander Ly.
  • A. Ramdas, G., V. Vovk, G. Shafer Game-theoretic statistics and safe anytime-valid inference (SAVI). Statistical Science, 2023. (arXiv version). The first overview paper of this exciting new area, written by some of its most prolific contributors (each involved in one of the four initial 2019 papers).

Image ©Papernerd

Development of Specific E-Values and Applications:

  • J. ter Schure, M. F. Pérez-Ortiz, A. Ly, G.
    The Anytime-Valid Logrank Test: Error Control Under Continuous Monitoring with Unlimited Horizon. New England Journal for Statistics in Data Science 2(2), 2024.
  • Muriel Felipe Pérez-Ortiz, Tyron Lardy, Rianne de Heide, G.  E-Statistics, Group Invariance and Anytime Valid Testing. The Annals of Statistics, 52(4), 1410-1432, 2024, http://dx.doi.org/10.1214/24-AOS2394. (arXiv version).
  • G., Alexander Henzi, Tyron Lardy. Anytime Valid Tests of Conditional Independence Under Model-X . Journal of the American Statistical Association,  2023. (arXiv version).
  • Rosanne Turner and G. Safe Sequential Testing and Effect Estimation in Stratified Count Data (arXiv version), Proceedings 26th Intern. Conf. on AI and Statistics (AISTATS) 2023, Valencia, Spain, 2023 (among the 2.5% of submissions selected for oral presentation).
  • Judith ter Schure, A. Ly, <many others>, G. H. van Werkhoven. Bacillus Calmette-Guérin vaccine to reduce COVID-19 infections and hospitalisations in healthcare workers – a living systematic review and prospective ALL-IN meta-analysis of individual participant data from randomised controlled trials. medrxiv preprint, December 2022. This is the first time that the e-value based approach was (and is) actually used in a live meta-analysis.

Note: at the ML group at CWI we do not offer internships for master’s and bachelor’s students from outside of the Netherlands. We only have an international internship program for Ph.D. students that are in their second or later years (I get so many requests for internships these days that I cannot respond to each request individually).