Wavelet-Based Enhanced FDR for Detecting Signals from Complete or Incomplete Spatially Aggregated Data




Enhanced False Discovery Rate (EFDR) is a non-parameteric hypothesting testing procedure used for anomaly detection in noisy spatial signals. The approach, published in Shen et al. (2002), is an extension on standard multiple hypothesis testing approaches (for example those employing the Bonferroni correction, or the standard FDR approach) by reducing the number of tests carried out. A reduced number of tests results in an approach which has more power (a lower Type II error), and hence an increase ability to detect anomalies. EFDR has proven to be vastly superior to the Bonferroni correction and standard FDR: the interested reader is referred to Shen et al. (2002) for a detailed study.

The package EFDR contains the required functions to carry out EFDR in a practical setting. It allows for the possibility of a parallel backend (since the computations are relatively intensive), contains basic interpolation methods to grid data which is spatially irregular, and also contains the more standard methods such as detection using the Bonferroni correction, the standard FDR and the Largest Order Statistic method.


For tutorials on how to use this package, please visit the project index HTML page by typing help(package = "EFDR") after installation.


  • Installation of most dependencies is straightforward. If you are on Linux, for the package gstat you will also need to install libgeos-dev which is widely available in linux repos. In Ubuntu this is available using apt-get install libgeos-dev.
  • To install the latest (development) version please install and load devtools and in an R console type install_github("EFDR","andrewzm").

Open issues

  • regrid() currently accepts data frames in (x,y,z) format. Suggest another function where people can supply images in matrix format with NAs in it. This function will "gather" the rows into xyz format, filter out the NAs and then call regrid.
  • Neighbourhood detection is currently sped up using a parallel backend. This, however, will remain slow on a standard desktop. Suggest implementing in C.
  • Image padding should be integrated, possibly using conditional simulation, see Pavlicov√° et al. (2008).
  • We need to EFDR suitable for non-rectangular domains -- possibly by only using wavelets that are affected by data in the test. This ties in with the padding issue.


Pavlicov√°, M., Santner, T. J., and Cressie, N. "Detecting signals in FMRI data using powerful FDR procedures." Statistics and its interface 1 (2008): 23-32.

Shen, X., Huang, H.-C., and Cressie, N. "Nonparametric hypothesis testing for a spatial signal." Journal of the American Statistical Association 97.460 (2002): 1122-1140.