ruth@utstat.uucp (Ruth Croxford) (09/19/89)
Colloquium, Department of Statistics, University of Toronto Topic: Non-informative priors for one parameter of many Speaker: Robert Tibshirani, Dept. of Statistics, U. of Toronto Date: Thursday, September 21, 1989, 4:00 p.m. Place: Room 1085, Sidney Smith Hall, 100 St. George Street, U of T Abstract: We consider the problem of constructing a ``non- informative'' prior for a single parameter in the presence of nuisance parameters. Our approach is to require that the resulting marginal posterior intervals have accurate fre- quentist coverage. Stein (1985) derived non-rigorously a sufficient condition for such a prior. Through the use of orthogonal parameters, we give a general form for the class of priors satisfying Stein's condition. The priors are proportional to the square root of the information element for the parameter of interest times an arbitrary function of the nuisance parameters. This is in contrast to Jeffreys' invariant prior for the overall parameter, which is propor- tional to the square root of the determinant of the informa- tion matrix. Several examples are given and comparisons are made to the reference priors of Bernardo (1979). -------------------------- Coffee and tea will be served in the DeLury Lounge (SS6006) at 3:30 p.m.