The statistical tool box contains a wealth of methodology and theory, and reliability is widely assumed, but massive failures have also occurred! The tools range from standardized observed-minus-expected, to Bayes-distributions, to fiducial and confidence-type distributions, to decision methods, to AI and data mining, to Lasso and relatives, and much more. But do they work as implied? Do they do as they say? Calibration has been cited as a criterion but may be just confidence in disguise.
The profession and users need to know the behaviour of the tools they use, or respect for the profession could be tarnished and science too. We give a brief overview of core methods and how they fit calibration, and how they target what is intended.
Donald Fraser is Professor Emeritus of Statistics at the University of Toronto. He completed his undergraduate studies at the University of Toronto, where he won the Putnam competition in his graduating year. He did his doctoral studies at Princeton under the supervision of Turkey and Wilks, and took up his career at the University of Toronto in 1949. He is a founding member and former chair of the Department of Statistics, has published 5 books and nearly 300 papers, and has held visiting and adjunct appointments at several universities in North America and Europe. His research and teaching has had a profound influence on the way statistics is thought about and taught, particularly in Canadian universities. He is known for his development of structural inference, and this work has had considerable impact on his development of higher order asymptotic theory. His current research interests include higher order asymptotics, foundations of inference and their implications for Bayesian methodology, and properties of significance functions.
Professor Fraser is a Fellow of the Royal Society of Canada, the American Association for the Advancement of Science, the American Mathematical Society, the Institute of Mathematical Statistics and the American Statistical Association. He was the first gold medallist of the Statistical Society of Canada, and has honorary doctorates from the University of Waterloo and the University of Toronto. In 2012 he was appointed Officer of the Order of Canada.