Learning Statistics From Counterexamples

James Berger ()
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James Berger: Duke University

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 3, 13-42

Abstract: Abstract The title of this article is (essentially) the same as the famous paper Basu (2011b). Basu often opined that counterexamples were the best way to learn limitations of theories or methods and I have followed his directive in my own teaching. A number of counterexamples I use extensively in teaching are collected here.

Keywords: Horvitz-Thompson estimator; ancillarity; likelihood principle; stopping rule principle; conditioning; shrinkage estimation; Jeffreys-Lindley paradox; p-values and error rates; understanding p-values; underestimating variances in elicitation; difficulties with conjugate priors; Neyman-Scott problem; difficulties with the multivariate Jeffreys prior; empirical Bayes counterexample; justifying improper priors; multinomial counterexample; Bartlett counterexample; median probability model; epistemic and aleatoric probability; robust Bayesian analysis; imprecise probability (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13171-024-00356-8

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