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CATEGORIES:Kuwait Foundation Lectures
SUMMARY:A Field-test of Basic Empirical Bayes and Bayes Me
thodologies: In-Season Prediction of Baseball Bat
ting Averages - Lawrence D. Brown (Pennsylvania)
DTSTART;TZID=Europe/London:20081014T170000
DTEND;TZID=Europe/London:20081014T180000
UID:TALK13753AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/13753
DESCRIPTION:Batting average is one of the principle performanc
e measures for an individual baseball player. It h
as a simple numerical structure as the percentage
of successful attempts\, “Hits”\, as a proportion
of the total number of qualifying attempts\, “At-B
ats”. This situation\, with Hits as a number of su
ccesses 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 repres
ents the i-th player’s latent ability. This is a c
ommon data structure in many statistical applicati
ons\; and so the methodological study here has imp
lications for such a range of applications.\n\nWe
will look at batting records for every Major Leagu
e player over the course of a single season (2005)
. The primary focus is on using only the batting r
ecord from an earlier part of the season (e.g.\, t
he first 3 months) in order to predict the batter’
s latent ability\, \, and consequently to predict
their batting-average performance for the remaind
er of the season. Since we are using a season that
has already concluded\, we can validate our predi
ctive performance by comparing the predicted value
s to the actual values for the remainder of the se
ason.\n\nThe methodological purpose of this study
is to gain experience with a variety of predictive
methods applicable to a much wider range of situa
tions. Several of the methods to be investigated d
erive from empirical Bayes and hierarchical Bayes
interpretations. Although the general ideas behind
these techniques have been understood for many de
cades*\, some of these methods have only been refi
ned 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 methodo
logies here is the preliminary use of a particular
form of variance stabilizing transformation in or
der to transform the binomial data problem into a
somewhat more familiar structure involving (approx
imately) Normal random variables with known varian
ces. This transformation technique is also useful
in validating the binomial model assumption that i
s the conceptual basis for all our analyses. If ti
me permits we will also describe how it can be use
d to test for the presence of “streaky hitters”\,
batters whose latent ability appears to significan
tly change over time.\n\nNo prior knowledge of the
sport of baseball is required.\n\n\n* A particula
rly relevant background reference is Efron\, B. an
d Morris\, C. (1977) Stein’s paradox in statistics
” Scientific American 236 119-127\, and the earlie
r\, more technical version (1975)\, “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 Scienc
es\, Wilberforce Road\, Cambridge
CONTACT:Helen Innes
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