Chi-squared tests using local inhomogeneous mark-weighted K-functions can identify global and local deviations from null hypotheses in marked point patterns, even with subtle structures or small samples.
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Nonparametric Bayesian methods with Gaussian and Besov-Laplace priors achieve minimax-optimal posterior contraction rates for covariate-driven point process intensity estimation under increasing domain asymptotics with ergodic covariates.
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Testing the Structural Properties of Marked Point Processes Using Local Inhomogeneous Mark-Weighted K-Functions
Chi-squared tests using local inhomogeneous mark-weighted K-functions can identify global and local deviations from null hypotheses in marked point patterns, even with subtle structures or small samples.
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Increasing domain asymptotics for covariate-based nonparametric Bayesian intensity estimation with Gaussian and Besov-Laplace priors
Nonparametric Bayesian methods with Gaussian and Besov-Laplace priors achieve minimax-optimal posterior contraction rates for covariate-driven point process intensity estimation under increasing domain asymptotics with ergodic covariates.