Tutorial Workshop

Differential Geometry with Applications to

Measurement and Statistics

Time: 9:00am-5:15pm, July 29, 2004
Place: 4448 East Hall, University of Michigan, Ann Arbor

Organizers: Richard Golden (University of Texas at Dallas)

and Jun Zhang (University of Michigan at Ann Arbor)

Workshop Registration Fee: $20 (covers coffee breaks, lunch and reception)

Click Here to Register

Click Here for Abstracts

Abstract

Although statistical theory and measurement play central roles in mathematical psychology, the application of differential geometry methods to problems in asymptotic statistical theory and measurement is much less prevalent among mathematical psychologists. This workshop will focus upon the application of differential geometry methods to problems in measurement and statistics. The tutorial workshop will immediately precede the regular sessions of the Annual Meeting of the Society for Mathematical Psychology.

Typically, workshop talks consist of an approximate 45-60 minutes of tutorial material followed by 15-30 minutes of recent state-of-the-art research in the area targeted by the invited speaker. Like last year, we have an exciting line-up of invited speakers!

About the Invited Speakers

• Professor Paul Vos (Department of Biostatistics, East Carolina University) has studied differential geometry of parametric statistical models. He is the co-author (with Robert Kass) of the book Geometrical Foundations of Asymptotic Inference (Wiley, 1997).
• Professor Paul Marriott (Department of Statistics, National University of Singapore and Duke University) has applied differential geometry methods to theoretical statistics and investigated the class of preferred point geometry (with his collaborators F. Critchley and M. Salmon). More recently, he studied the geometry of mixture models and the geometry of measurement error models.
• Professor Zhongmin Shen (Department of Mathematics, Indiana University-Purdue University Indianapolis) is an expert on Finsler geometry. He has authored and co-authors a number of monographs and graduate textbooks on Finsler geometry, including An introduction to Finsler geometry (GTM, Springer-Verlag, 2002), Lectures on Finsler Geometry (World Scientific Publishing, 2001), Differential Geometry of Spray and Finsler Spaces (Kluwer, 2001).
• Professor Hiroshi Matsuzoe (Department of Information Science, Saga University, Japan) has recently applied information geometric methods to Bayesian statistics and investigated the class of invariant priors (of which Jeffreys prior is a special one) from a differential geometric perspective.

Tentative Workshop Schedule

9:00 – 9:15a.m.	Opening Remarks by Jun Zhang and Richard Golden
9:15 - 10:30 a.m.	Professor Paul Vos On Information Geometry with Application to Inferential Statistics
10:30 - 10:45 a.m.	Coffee Break
10:45 a.m. - noon	Professor Paul Marriott On Preferred Point Geometry and Geometry of Mixture Models
12:00 - 1:30 p.m.	Lunch
1:30 - 2:45 p.m.	Professor Zhongmin Shen On Finsler Geometry with Application to Scaling and Information Geometry
2:45 - 3:00 p.m.	Coffee Break
3:00 - 4:15 p.m.	Professor Hiroshi Matsuzoe On Affine Differential Geometry with Application to Bayesian Inference
4:15 - 5:00 p.m.	General Discussion led by Prof. Shun-ichi Amari