## Archive for frequentist inference

## Bill’s 80th birthday

Posted in Statistics, Travel, University life with tags 80th birthday, Cornell University, flight, frequentist inference, James-Stein estimator, mathematical statistics, New York, Pitman nearness, Rutgers University, shrinkage estimation, William Strawderman on March 30, 2022 by xi'an## statistics for making decisions [book review]

Posted in Books, Statistics with tags book review, textbook, decision theory, CRC Press, testing of hypotheses, frequentist inference, Bayesian hypothesis testing, Bayesian paradigm, Neyman-Pearson tests, fiducial inference, decision making, client, elicitat on March 7, 2022 by xi'an**I** bought this book [or more precisely received it from CRC Press as a ({prospective} book) review reward] as I was interested in the author’s perspectives on actual decision making (and unaware of the earlier Statistical Decision Theory book he had written in 2013). It is intended for a postgraduate semester course and “not for a beginner in statistics”. Exercises with solutions are included in each chapter (with some R codes in the solutions). From Chapter 4 onwards, the “Further reading suggestions” are primarily referring to papers and books written by the author, as these chapters are based on his earlier papers.

*“I regard hypothesis testing as a distraction from and a barrier to good statistical practice. Its ritualised application should be resisted from the position of strength, by being well acquainted with all its theoretical and practical aspects. I very much hope (…) that the right place for hypothesis testing is in a museum, next to the steam engine.”*

The first chapter exposes the shortcomings of hypothesis testing for conducting decision making, in particular by ignoring the consequences of the decisions. A perspective with which I agree, but I fear the subsequent developments found in the book remain too formalised to be appealing, reverting to the over-simplification found in Neyman-Pearson theory. The second chapter is somewhat superfluous for a book assuming a prior exposure to statistics, with a quick exposition of the frequentist, Bayesian, and … fiducial paradigms. With estimators being first defined without referring to a specific loss function. And I find the presentation of the fiducial approach rather shaky (if usual). Esp. when considering fiducial perspective to be used as default Bayes in the subsequent chapters. I also do not understand the notation (p.31)

outside of a Bayesian (or fiducial?) framework. (I did not spot typos aside from the traditional “the the” duplicates, with at least six occurences!)

The aforementioned subsequent chapters are not particularly enticing as they cater to artificial loss functions and engage into detailed derivations that do not seem essential. At times they appear to be nothing more than simple calculus exercises. The very construction of the loss function, which I deem critical to implement statistical decision theory, is mostly bypassed. The overall setting is also frighteningly unidimensional. In the parameter, in the statistic, and in the decision. Covariates only appear in the final chapter which appears to have very little connection with decision making in that the loss function there is the standard quadratic loss, used to achieve the optimal composition of estimators, rather than selecting the best model. The book is also missing in practical or realistic illustrations.

“With a bit of immodesty and a tinge of obsession, I would like to refer to the principal theme of this book as a paradigm, ascribing to it as much importance and distinction as to the frequentist and Bayesian paradigms”

The book concludes with a short postscript (pp.247-249) reproducing the introducing paragraphs about the ill-suited nature of hypothesis testing for decision-making. Which would have been better supported by a stronger engagement into elicitating loss functions and quantifying the consequences of actions from the clients…

*[Disclaimer about potential self-plagiarism: this post or an edited version will eventually appear in my Book Review section in CHANCE.]*

## BFF⁷ postponed

Posted in Books, pictures, Statistics, Travel, University life with tags Bayesian foundations, BFF Statistics Conference, Canada, fiducial inference, Fields Institute, frequentist inference, Ontario, Philosophy of Science, Toronto on March 31, 2020 by xi'an## back to Ockham’s razor

Posted in Statistics with tags Bayesian model choice, candidate's formula, David MacKay, evidence, flexibility, frequentist inference, marginal likelihood, marginal likelihood identity, Ockham's razor, William of Ockham on July 31, 2019 by xi'an

“All in all, the Bayesian argument for selecting the MAP model as the single ‘best’ model is suggestive but not compelling.”

**L**ast month, Jonty Rougier and Carey Priebe arXived a paper on Ockham’s factor, with a generalisation of a prior distribution acting as a regulariser, R(θ). Calling on the late David MacKay to argue that the evidence involves the correct penalising factor although they acknowledge that his central argument is not absolutely convincing, being based on a first-order Laplace approximation to the posterior distribution and hence “dubious”. The current approach stems from the candidate’s formula that is already at the core of Sid Chib’s method. The log evidence then decomposes as the sum of the maximum log-likelihood minus the log of the posterior-to-prior ratio at the MAP estimator. Called the flexibility.

“Defining model complexity as flexibility unifies the Bayesian and Frequentist justifications for selecting a single model by maximizing the evidence.”

While they bring forward rational arguments to consider this as a measure model complexity, it remains at an informal level in that other functions of this ratio could be used as well. This is especially hard to accept by non-Bayesians in that it (seriously) depends on the choice of the prior distribution, as all transforms of the evidence would. I am thus skeptical about the reception of the argument by frequentists…

## O’Bayes 2019 conference program

Posted in Kids, pictures, Statistics, Travel, University life with tags Bayesian conference, Bayesian model selection, BNP12, England, frequentist inference, imprecise probabilities, ISBA, O'Bayes 2019, objective Bayes, prior selection, Statistical learning, University of Warwick on May 13, 2019 by xi'an**T**he full and definitive program of the O’Bayes 2019 conference in Warwick is now on line. Including discussants for all papers. And the three [and free] tutorials on Friday afternoon, 28 June, on model selection (M. Barbieri), MCMC recent advances (G.O. Roberts) and BART (E.I. George). Registration remains open at the reduced rate and submissions of posters can still be sent to me for all conference participants.