spatialmht 1.0.0

Code for Spatial Multiple Hypothesis Testing via Local False Discovery Rates with the Spectral Method of Moments

lfdr-sMoM

Spatial Multiple Hypothesis Testing with Local False Discovery Rates (spatialmht)

The spatialmht package provides an implementation of the multiple hypothesis testing methods for spatial data introduced in the references below. This empirical Bayes method estimates the local false discovery rates (lfdr's) with the spectral method of moments (sMoM) and allows to assert the state of a spatial field at the sensors and in between sensors. The method identifies anomalies within the observation area with false positive control (w.r.t. the False Discovery Rate).

Improvements of the base-line method lfdr-sMoM from [Goelz2022TISPN] were proposed in subsequent works [Goelz2022CISS] and [Goelz2022ICASSP]. These are also implemented in this package. The details on the proposed methods are found in the references given below.

Installation

To install the package:

pip install spatialmht

You can also download the repository here and use the directory without_installation to run the code without installing the package locally.

Example

The provided file main.py allows you to recreate the essential plots from the three references given below. By modifying parameters.py, you also have the opportunity to create new spatial fields that similate the propagation of radio waves according to your own desires (with custom number of transmitters, sensors, observations per sensor, propagation environment, sensor densities etc). For such fields, observations and p-values are generated using an energy detector at each sensor. In addition, you can also provide your own p-values generated using your own methods with sensors located at spatial locations that you provide!

If your data does not have any particular spatial structure, or maybe is not even spatial data at all, you can still apply lfdr-sMoM with your custom p-values. However, the spatial interpolation of the lfdrs and spatially varying priors will not be performed in such a case. Please see the comments in main.py to learn about the possible ways you can modify the file to suit your own needs.

References

[Goelz2022TISPN]: Multiple Hypothesis Testing Framework for Spatial Signals. M. Gölz, A.M. Zoubir and V. Koivunen, IEEE Transactions on Signal and Information Processing over networks, July 2022, DOI:10.1109/TSIPN.2022.3190735.

[Goelz2022CISS]: Estimating Test Statistic Distributions for Multiple Hypothesis Testing in Sensor Networks M. Gölz, A.M. Zoubir and V. Koivunen, 2022 56th Annual Conference on Information Sciences and Systems (CISS), Princeton, NJ, February 2022, 10.1109/CISS53076.2022.9751186.

[Goelz2022ICASSP]: Improving Inference for Spatial Signals by Contextual False Discovery Rates. M. Gölz, A.M. Zoubir and V. Koivunen, 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP2022), Singapore, DOI:10.1109/ICASSP43922.2022.9747596.