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Fall 2004
STATISTICS
COLLOQUIUM
Friday,October 1, 2004
2:30-3:00—Refreshments
3:00-4:00—Talk
Yost Hall, Room 300
Don Fraser
Department of Statistics,
University of Toronto
Is there statistical inference? The Bayesian frequentist divergence.
A model with data is a primary concern within statistics. It is of course not all of statistics but it has a central position and influences broad areas even algorithmic methods and exploratory analyses. The model can be approximately true or examined on a what-if basis, and the data come from the context being examined. Statistical inference is what the model with data says about the unknowns.
The decision orientation of the first half of the twentieth century was faced by two quite different alternatives in the late 1950s, the frequentist and the Bayesian: much of the frequentist approach evolved as decision material relabeled as inference; and the Bayesian was initially subjective but recently aggressively seeks default priors. Which is right? Or is there statistical inference?
A frequent pragmatic suggestion is to try them out and see which works. Sounds simple but it gives wrong answers; the suggestion doesn't take account of conditioning, an issue of long denied importance in statistics.
We give an overview of some of the issues involved and indicate that the future may hold a convergence.
Dr. Fraser, a fellow of the Royal Society of Canada, was the first winner of the Gold Medal of the Statistical Society of Canada for his many outstanding contributions to the field of statistical inference.
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