Estimation with selected binomial information or do you really believe that dave winfield is batting .471?

George Casella, Roger L. Berger

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Often sports announcers, particularly in baseball, provide the listener with exaggerated information concerning a player’s performance. For example, we may be told that Dave Winfield, a popular baseball player, has hit safely in 8 of his last 17 chances (a batting average of .471). This is biased, or selected information, as the “17” was chosen to maximize the reported percentage. We model this as observing a maximum success rate of a Bernoulli process and show how to construct the likelihood function for a player’s true batting ability. The likelihood function is a high-degree polynomial, but it can be computed exactly. Alternatively, the problem yields to solutions based on either the EM algorithm or Gibbs sampling. Using these techniques, we compute maximum likelihood estimators, Bayes estimators, and associated measures of error. We also show how to approximate the likelihood using a Brownian motion calculation. We find that although constructing good estimators from selected information is difficult, we seem to be able to estimate better than expected, particularly when using prior information. The estimators are illustrated with data from the 1992 Major League Baseball season.

Original languageEnglish (US)
Pages (from-to)1080-1090
Number of pages11
JournalJournal of the American Statistical Association
Volume89
Issue number427
DOIs
StatePublished - 1994
Externally publishedYes

Fingerprint

Likelihood Function
Estimator
Bayes Estimator
Gibbs Sampling
Prior Information
EM Algorithm
Hits
Bernoulli
Maximum Likelihood Estimator
Biased
Brownian motion
Percentage
Likelihood
Maximise
Polynomial
Estimate
Baseball
Model
Sports
Gibbs sampling

Keywords

  • Brownian motion
  • EM algorithm
  • Gibbs sampling
  • Selection bias

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Estimation with selected binomial information or do you really believe that dave winfield is batting .471? / Casella, George; Berger, Roger L.

In: Journal of the American Statistical Association, Vol. 89, No. 427, 1994, p. 1080-1090.

Research output: Contribution to journalArticle

@article{fd439b945b51470fbce4081cb21e4aff,
title = "Estimation with selected binomial information or do you really believe that dave winfield is batting .471?",
abstract = "Often sports announcers, particularly in baseball, provide the listener with exaggerated information concerning a player’s performance. For example, we may be told that Dave Winfield, a popular baseball player, has hit safely in 8 of his last 17 chances (a batting average of .471). This is biased, or selected information, as the “17” was chosen to maximize the reported percentage. We model this as observing a maximum success rate of a Bernoulli process and show how to construct the likelihood function for a player’s true batting ability. The likelihood function is a high-degree polynomial, but it can be computed exactly. Alternatively, the problem yields to solutions based on either the EM algorithm or Gibbs sampling. Using these techniques, we compute maximum likelihood estimators, Bayes estimators, and associated measures of error. We also show how to approximate the likelihood using a Brownian motion calculation. We find that although constructing good estimators from selected information is difficult, we seem to be able to estimate better than expected, particularly when using prior information. The estimators are illustrated with data from the 1992 Major League Baseball season.",
keywords = "Brownian motion, EM algorithm, Gibbs sampling, Selection bias",
author = "George Casella and Berger, {Roger L.}",
year = "1994",
doi = "10.1080/01621459.1994.10476846",
language = "English (US)",
volume = "89",
pages = "1080--1090",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "427",

}

TY - JOUR

T1 - Estimation with selected binomial information or do you really believe that dave winfield is batting .471?

AU - Casella, George

AU - Berger, Roger L.

PY - 1994

Y1 - 1994

N2 - Often sports announcers, particularly in baseball, provide the listener with exaggerated information concerning a player’s performance. For example, we may be told that Dave Winfield, a popular baseball player, has hit safely in 8 of his last 17 chances (a batting average of .471). This is biased, or selected information, as the “17” was chosen to maximize the reported percentage. We model this as observing a maximum success rate of a Bernoulli process and show how to construct the likelihood function for a player’s true batting ability. The likelihood function is a high-degree polynomial, but it can be computed exactly. Alternatively, the problem yields to solutions based on either the EM algorithm or Gibbs sampling. Using these techniques, we compute maximum likelihood estimators, Bayes estimators, and associated measures of error. We also show how to approximate the likelihood using a Brownian motion calculation. We find that although constructing good estimators from selected information is difficult, we seem to be able to estimate better than expected, particularly when using prior information. The estimators are illustrated with data from the 1992 Major League Baseball season.

AB - Often sports announcers, particularly in baseball, provide the listener with exaggerated information concerning a player’s performance. For example, we may be told that Dave Winfield, a popular baseball player, has hit safely in 8 of his last 17 chances (a batting average of .471). This is biased, or selected information, as the “17” was chosen to maximize the reported percentage. We model this as observing a maximum success rate of a Bernoulli process and show how to construct the likelihood function for a player’s true batting ability. The likelihood function is a high-degree polynomial, but it can be computed exactly. Alternatively, the problem yields to solutions based on either the EM algorithm or Gibbs sampling. Using these techniques, we compute maximum likelihood estimators, Bayes estimators, and associated measures of error. We also show how to approximate the likelihood using a Brownian motion calculation. We find that although constructing good estimators from selected information is difficult, we seem to be able to estimate better than expected, particularly when using prior information. The estimators are illustrated with data from the 1992 Major League Baseball season.

KW - Brownian motion

KW - EM algorithm

KW - Gibbs sampling

KW - Selection bias

UR - http://www.scopus.com/inward/record.url?scp=21844513757&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844513757&partnerID=8YFLogxK

U2 - 10.1080/01621459.1994.10476846

DO - 10.1080/01621459.1994.10476846

M3 - Article

AN - SCOPUS:21844513757

VL - 89

SP - 1080

EP - 1090

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 427

ER -