False discovery control in large-scale
spatial multiple testing.
Wenguang Sun, Brian Reich, Tony Cai, Michele Guindani,
and Armin Schwartzman
Summary. This article develops a unified
theoretical and computational framework for false discovery control in multiple
testing of spatial signals. We consider both point-wise and cluster-wise
spatial analyses, and derive oracle procedures that optimally control the false
discovery rate, false discovery exceedance and false
cluster rate, respectively. A data-driven finite approximation strategy is
developed to mimic the oracle procedures on a continuous spatial domain. Our
multiple testing procedures are asymptotically valid and can be effectively
implemented using Bayesian computational algorithms for analysis of large spatial
data sets. Numerical results show that the proposed procedures lead to more
accurate error control and better power performance than conventional methods.
We demonstrate our methods for analyzing the time trends in tropospheric ozone
in eastern US.
The paper and web appendix can be
code for the MCMC
Here are a description
of the code and an example.