Re-visiting hypothesis testing

There are many approaches to hypothesis testing.  The well-known approach of p-values has been drawn into question and even controversy in more recent years, even though criticisms reportedly date back at least as far as 1954 (Dowe, 2008a, sec. 1, pp549-550).

Discussion of how to do this using the Bayesian information-theoretic minimum message length (MML) approach (Wallace and Boulton, 1968; Wallace and Dowe, 1999a; Wallace, 2005) are given in Dowe (2008a, section 0.2.5, page 539, and section 0.2.2, page 528), and Dowe (2011, pages 919 and 964).

References:

  D. L. Dowe (2008a), "Foreword re C. S. Wallace", Computer Journal, Vol. 51, No. 5 (Sept. 2008) [Christopher Stewart WALLACE (1933-2004) memorial special issue [and front cover and back cover]], pp523-560 (and here). www.doi.org: 10.1093/comjnl/bxm117

  D. L. Dowe (2011a), "MML, hybrid Bayesian network graphical models, statistical consistency, invariance and uniqueness", Handbook of the Philosophy of Science - (HPS Volume 7) Philosophy of Statistics, P.S. Bandyopadhyay and M.R. Forster (eds.), Elsevier, [ISBN: 978-0-444-51862-0 {ISBN 10: 0-444-51542-9 / ISBN 13: 978-0-444-51862-0}], pp901-982, 1/June/2011

  L Held (2020), "A new standard for the analysis and design of replication studies", J Royal Statist Soc. (A), vol. 183, no. 2, pp431-448

  K Rice, T Bonnett and C Krakauer (2020), "Knowing the signs: a direct and generalizable motivation of two‐sided tests", J Royal Statist Soc. (A), vol. 183, no. 2, pp411-430

  Wallace, C.S. (2005), ``Statistical and Inductive Inference by Minimum Message Length'', Springer  (Link to the preface [and p vi, also here])

  Wallace, C.S. and D.M. Boulton (1968), ``An information measure for classification'', Computer Journal, Vol 11, No 2, August 1968, pp 185-194

  Wallace, C.S. and D.L. Dowe (1999a). Minimum Message Length and Kolmogorov Complexity, Computer Journal (special issue on Kolmogorov complexity), Vol. 42, No. 4, pp270-283

    Wallace, C.S. and P.R. Freeman (1987).  Estimation and inference by compact coding. J. Royal Statist. Soc. B, 49, 240–252.

    Wen, Z. and D. L. Dowe (2024).  Zihao Wen and David L. Dowe’s contribution to the Discussion of ‘Safe testing’ by Grünwald, de Heide, and Koolen, Journal of the Royal Statistical Society Series B: Statistical Methodology (J RSS (B)), Volume 86, Issue 5, November 2024, Pages 1161–1162, https://doi.org/10.1093/jrsssb/qkae067 .