Statistical Information and Likelihood: A Collection of Critical Essays by Dr. D. BasuIt is an honor to be asked to write a foreword to this book, for I believe that it and other books to follow will eventually lead to a dramatic change in the current statistics curriculum in our universities. I spent the 1975-76 academic year at Florida State University in Tallahassee. My purpose was to complete a book on Statistical Reliability Theory with Frank Proschan. At the time, I was working on total time on test processes. At the same time, I started attending lectures by Dev Basu on statistical inference. It was Lehmann's hypothesis testing course and Lehmann's book was the text. However, I noticed something strange - Basu never opened the book. He was obviously not following it. Instead, he was giving a very elegant, measure theoretic treatment of the concepts of sufficiency, ancillarity, and invariance. He was interested in the concept of information - what it meant. - how it fitted in with contemporary statistics. As he looked at the fundamental ideas, the logic behind their use seemed to evaporate. I was shocked. I didn't like priors. I didn't like Bayesian statistics. But after the smoke had cleared, that was all that was left. Basu loves counterexamples. He is like an art critic in the field of statistical inference. He would find a counterexample to the Bayesian approach if he could. So far, he has failed in this respect. |
Contents
Recovery of Ancillary Information | 1 |
Conceptual Statistical Experiments | 16 |
Basic Definitions and Relations | 23 |
Copyright | |
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ancillarity ancillary statistic Barnard Basu Basu's Bayesian conditional distribution conditionality consider corresponding data analysis defined definition depends discussion e-oriented equal example exists experiment experimental factor fiducial argument finite Fisher fixed G-invariant given Godambe H-sufficient Hájek inference interval invariant label-set likelihood function likelihood principle logical marginal mathematical maximum likelihood mean method model-preserving transformations Neyman non-Bayesian notion nuisance parameter p-quantal p-quantity parameter of interest parameter space partial sufficiency particular pivotal quantity population posterior prior q probability distribution probability measures problem question R.A. Fisher random variable randomization test ratio relevant risk function S-ancillary sample space sampling plan scientist selection sense Sir Ronald situation specific sufficient statistical model statistician stochastically independent subset sufficient statistic sufficient sub-field Suppose survey sampling survey theory surveyor T₁ Theorem tion true unbiased estimator unit unknown variance vector X₁ Y₁