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Using Model/Data Simulations to Detect Streakiness

Summary: Using Model/Data Simulations to Detect
Jim Albert
Bowling Green State University, Bowling Green, OH
Patricia Williamson
Virginia Commonwealth University, Richmond, VA, USA
June 1999
A simulation­based approach is proposed for approximating a Bayesian analysis.
Parameters and data are simulated from a Bayesian model and inference about a pa­
rameter is performed by exploring the set of simulated parameter values conditional on
a set of values of a simulated statistic. The approach is used to learn about parameters
of a streaky model on the basis of a statistic used to measure streakiness. The method
is illustrated to detect streakiness in baseball hitting data and basketball shooting data.
1 Introduction
There has been much recent interest in the detection of streakiness or the ``hot hand'' in the
performance of athletes in baseball, basketball, and other sports. Gilovich et al (1985) and
Tversky and Gilovich (1989) discuss the existence of the hot hand in basketball data and
conclude that any observed streakiness in data is simply one's misperception of the patterns
inherent in random sequences. Larkey et al (1989), in their analysis of basketball shooting


Source: Albert, James H. - Department of Mathematics and Statistics, Bowling Green State University


Collections: Mathematics