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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENT SEMINAR}
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\centerline{ Sequoia Hall, Room 200}
\centerline{4:15 p.m., Thursday, August 15, 2002}


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\centerline{\sl Minggao Gu}
\centerline{\sl The Chinese University of Hong Kong}
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\centerline{\bf Probit Models for Handicapped Horse Racing}

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In their seminal work on horse racing, Bolton and Chapman (1986)
proposed a model for estimating individual horse win probabilities from
fundamental data. Because of limitations in the computing facilities and
methods available at that time, the authors chose the multinomial logit
model, which arises from the theoretically sub-optimal assumption that
the errors in estimated horse performance follow the negative
double-exponential distribution. In this talk, we consider models that
are based on the more natural assumption that those errors follow the
normal distribution. We call such models probit models. We overcome the
computational difficulties associated with the probit model by applying
the Markov chain Monte Carlo stochastic approximation algorithm
developed in Gu and Zhu (2001). A likelihood ratio procedure for testing
parameters is also devised. We apply both logit and probit methodologies
to a data set composed of 1000 races from Hong Kong Jockey Club during
the 1998 to 2000 seasons. Hold-out simulation betting shows a
significant improvement for the probit model over the logit model.

Based on Joint work with Dr Changquan Huang and William Benter

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