94 research outputs found
A Bayesian marked spatial point processes model for basketball shot chart
The success rate of a basketball shot may be higher at locations where a
player makes more shots. For a marked spatial point process, this means that
the mark and the intensity are associated. We propose a Bayesian joint model
for the mark and the intensity of marked point processes, where the intensity
is incorporated in the mark model as a covariate. Inferences are done with a
Markov chain Monte Carlo algorithm. Two Bayesian model comparison criteria, the
Deviance Information Criterion and the Logarithm of the Pseudo-Marginal
Likelihood, were used to assess the model. The performances of the proposed
methods were examined in extensive simulation studies. The proposed methods
were applied to the shot charts of four players (Curry, Harden, Durant, and
James) in the 2017--2018 regular season of the National Basketball Association
to analyze their shot intensity in the field and the field goal percentage in
detail. Application to the top 50 most frequent shooters in the season suggests
that the field goal percentage and the shot intensity are positively associated
for a majority of the players. The fitted parameters were used as inputs in a
secondary analysis to cluster the players into different groups
Heterogeneity Pursuit for Spatial Point Pattern with Application to Tree Locations: A Bayesian Semiparametric Recourse
Spatial point pattern data are routinely encountered. A flexible regression
model for the underlying intensity is essential to characterizing the spatial
point pattern and understanding the impacts of potential risk factors on such
pattern. We propose a Bayesian semiparametric regression model where the
observed spatial points follow a spatial Poisson process with an intensity
function which adjusts a nonparametric baseline intensity with multiplicative
covariate effects. The baseline intensity is piecewise constant, approached
with a powered Chinese restaurant process prior which prevents an unnecessarily
large number of pieces. The parametric regression part allows for variable
selection through the spike-slab prior on the regression coefficients. An
efficient Markov chain Monte Carlo (MCMC) algorithm is developed for the
proposed methods. The performance of the methods is validated in an extensive
simulation study. In application to the locations of Beilschmiedia pendula
trees in the Barro Colorado Island forest dynamics research plot in central
Panama, the spatial heterogeneity is attributed to a subset of soil
measurements in addition to geographic measurements with a spatially varying
baseline intensity.Comment: 21 pages, 7 figure
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