This paper introduces a new model and methodology for estimating the ability
of NBA players. The main idea is to directly measure how good a player is by
comparing how their team performs when they are on the court as opposed to when
they are off it. This is achieved in a such a way as to control for the
changing abilities of the other players on court at different times during a
match.
Sequential Monte Carlo (SMC) methods are not only a popular tool in the
analysis of state{space models, but o?er an alternative to MCMC in situations
where Bayesian inference must proceed via simulation. This paper introduces a
new SMC method that uses adaptive MCMC kernels for particle dynamics. The
proposed algorithm features an online stochastic optimization procedure to
select the best MCMC kernel and simultaneously learn optimal tuning parameters.
Theoretical results are presented that justify the approach and give guidance
on how it should be implemented.