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       Departments of Mathematical Sciences and Biostatistics
                    The Johns Hopkins University

                          JOINT SEMINAR

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Professor Richard Royall                          October 29, 1998
Department of Biostatistics                       304 Whitehead Hall
The Johns Hopkins University                      Preseminar: 3:00 p.m.
                                                  Refreshments: 3:45 p.m.
                                                  Seminar: 4:00 p.m.

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          THE LIKELIHOOD PARADIGM FOR STATISTICAL EVIDENCE

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                             ABSTRACT

Statistical methods aim to answer a variety of questions about observations.
A simple example occurs when a fairly reliable test for a condition or
substance, C, has given a positive result.  Three important types of
questions are

	 1. Should this observation lead me to believe that C is present?

	 2. Does this observation justify my acting as if C were present?

	 3. Is this observation evidence that C is present?

We distinguish among these three questions in terms of the variables and
principles that determine their answers.  Then we use this framework to
understand the scope and limitations of current methods for interpreting
statistical data as evidence.

Questions of the third type, concerning the "evidential interpretation" of
statistical data, are central to many applications of statistics in science.
We see that for answering them current statistical methods are seriously
flawed.  We find the source of the problems and propose a solution based on
the Law of Likelihood.  This law suggests how the dominant statistical
paradigm can be altered so as to generate appropriate methods for
(i) objective, quantitative representation of the evidence embodied in a
specific set of observations, as well as (ii) measurement and control of the
probabilities that a study will produce weak or misleading evidence.

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Forthcoming in Mathematical Sciences seminar series: Friday, November 6,
Fourth Mid-Atlantic Day for Combinatorics and Probability (MADCAP!)