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SUMMARY:A Field-test of Basic Empirical Bayes and Bayes Methodologies:  In
 -Season Prediction of Baseball Batting Averages - Lawrence D. Brown (Penns
 ylvania)
DTSTART:20081014T160000Z
DTEND:20081014T170000Z
UID:TALK13753@talks.cam.ac.uk
CONTACT:Helen Innes
DESCRIPTION:Batting average is one of the principle performance measures f
 or an individual baseball player. It has a simple numerical structure as t
 he percentage of successful attempts\, “Hits”\, as a proportion of the
  total number of qualifying attempts\, “At-Bats”. This situation\, wit
 h Hits as a number of successes within a qualifying number of attempts\, m
 akes it natural to statistically model each player’s batting average as 
 a binomial variable outcome\, with a true (but unknown) value of   that re
 presents the i-th player’s latent ability. This is a common data structu
 re in many statistical applications\; and so the methodological study here
  has implications for such a range of applications.\n\nWe will look at bat
 ting records for every Major League player over the course of a single sea
 son (2005). The primary focus is on using only the batting record from an 
 earlier part of the season (e.g.\, the first 3 months) in order to predict
  the batter’s latent ability\,  \, and consequently to predict their bat
 ting-average performance for the remainder of the season. Since we are usi
 ng a season that has already concluded\, we can validate our predictive pe
 rformance by comparing the predicted values to the actual values for the r
 emainder of the season.\n\nThe methodological purpose of this study is to 
 gain experience with a variety of predictive methods applicable to a much 
 wider range of situations. Several of the methods to be investigated deriv
 e from empirical Bayes and hierarchical Bayes interpretations. Although th
 e general ideas behind these techniques have been understood for many deca
 des*\, some of these methods have only been refined relatively recently in
  a manner that promises to more accurately fit data such as that at hand. 
 \n	\nOne feature of all of the statistical methodologies here is the preli
 minary use of a particular form of variance stabilizing transformation in 
 order to transform the binomial data problem into a somewhat more familiar
  structure involving (approximately) Normal random variables with known va
 riances. This transformation technique is also useful in validating the bi
 nomial model assumption that is the conceptual basis for all our analyses.
  If time permits we will also describe how it can be used to test for the 
 presence of “streaky hitters”\, batters whose latent ability appears t
 o significantly change over time.\n\nNo prior knowledge of the sport of ba
 seball is required.\n\n\n* A particularly relevant background reference is
  Efron\, B. and Morris\, C. (1977) Stein’s paradox in statistics” Scie
 ntific American 236 119-127\, and the earlier\, more technical version (19
 75)\, “Data analysis using Stein’s estimator and its generalizations
 ” Jour. Amer. Stat. Assoc. 70 311-319.	\n
LOCATION:Wolfson Room (MR 2) Centre for Mathematical Sciences\, Wilberforc
 e Road\, Cambridge
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