Gaussian Processes time series modelling with focus on period detection on irregularly-sampled stochastically-varying astronomical time series

The method effectively combines Gaussian Process modelling with the likelihood ratio test outline in Protassov et al. 2002. At present, the code uses the celerite kernels proposed by Foreman-Mackey et al. 2017

Installation

To install the repository, first clone to your compute: git clone https://github.com/andresgur/mind_the_gaps then enter the mind_the_gaps main directory and pip install it by running: pip install .

Warning

Users are welcome to use/test the code and provide feedback but beware, the code is still in alpha phase, so expect bugs, errors and crashes! If you are intending to use the code, my recommendation would be to get in touch first!

Usage

The code can be used as a standalone to generate lightcurves or as it is desineg for, to test for a periodicity in a lightcurve. At a minimum your lightcurve should have timestamps, rates, uncertainties and exposures, and it can also contain background rates and uncertainties on the background.

Usually the first task is to identify the null hypothesis (a stochastic-only model) and the alternative model, which contains the periodic component (stochastic model + periodic component). To see how to go about model selection, see the notebook in tutorials. Once you've established these two (note you can also have several sets of null hypothesis and alternative model) we follow the method outlined by Protassov et al. 2002

1. Fit the observed data using the two null and alternative models
2. Generate lightcurves from the posteriors of the stochastic model
3. Fit the generated lightcurves using both models
4. Build a histogram of the fit-improvements (LRT) found for the simulated lightcurves and check where the value observed in the data falls in the histogram. An outlier (say p<0.05) suggest the fit-improvement observed in the data is highly unlikely. High p-values indicate the fit-improvement is simply due to noise.

Another notebook in tutorials shows how to implement this process using functions and objects from the package.

Tests

Tests are included in the tests/ directory and can be run as:

python setup.py test

Warning: Tests currently are not passing. Please check the issues on the respository to see the current status.

Citation

You can cite the paper or the code as given below:

@article{10.1093/mnras/staf196,
    author = {Gúrpide, Andrés and Middleton, Matthew},
    title = {Mind the gaps: improved methods for the detection of periodicities in unevenly-sampled data},
    journal = {Monthly Notices of the Royal Astronomical Society},
    pages = {staf196},
    year = {2025},
    month = {01},
    abstract = {The detection of periodic signals in irregularly-sampled time series is a problem commonly encountered in astronomy. Traditional tools used for periodic searches, such as the periodogram, have poorly defined statistical properties under irregular sampling, which complicate inferring the underlying aperiodic variability used for hypothesis testing. The problem is exacerbated in the presence of stochastic variability, which can be easily mistaken by genuine periodic behaviour, particularly in the case of poorly sampled lightcurves. Here we present a method based on Gaussian Processes (GPs) modelling for period searches and characterization, specifically developed to overcome these problems. We argue that in cases of irregularly-sampled time series, GPs offer an appealing alternative to traditional periodograms, because the known distribution of the data (correlated Gaussian) allows a well-defined likelihood to be constructed. We exploit this property and draw from existing statistical methods to perform traditional likelihood ratio tests for an additional, (quasi-)periodic component, using the aperiodic variability inferred from the data as the null hypothesis. Inferring the noise from the data allows the method to be fully generalizable, with the only condition that the data can be described as a Gaussian process. We demonstrate the method by applying it to a variety of objects showing varying levels of noise and data quality. Limitations of the method are discussed and a package implementing the proposed methodology is made publicly available.},
    issn = {0035-8711},
    doi = {10.1093/mnras/staf196},
    url = {https://doi.org/10.1093/mnras/staf196},
    eprint = {https://academic.oup.com/mnras/advance-article-pdf/doi/10.1093/mnras/staf196/61722589/staf196.pdf},
}

@software{andres_gurpide_lasheras_2024_14253754,
  author       = {Andrés Gúrpide Lasheras and
                  Sam Mangham},
  title        = {{andresgur/mind\_the\_gaps: Release for paper}},
  month        = jan,
  year         = 2025,
  publisher    = {Zenodo},
  version      = {v1.2.0-beta},
  doi          = {10.5281/zenodo.14600069},
  url          = {https://doi.org/10.5281/zenodo.14600069}
}