wotan 1.0

Detrending algorithms

Wōtan...

...offers free and open source algorithms to automagically remove stellar trends from light curves for exoplanet transit detection.

In Germanic mythology, Odin (/ˈoːðinː/ Old High German: Wōtan) is a widely revered god. He gave one of his eyes to Mimir in return for wisdom. Thus, in order to achieve a goal, one sometimes has to turn a blind eye. In Richard Wagner's "Der Ring des Nibelungen", Wotan is the King of the Gods (god of light, air, and wind) and a bass-baritone. According to Wagner, he is the "pinnacle of intelligence".

Example usage

from wotan import flatten
flatten_lc, trend_lc = flatten(time, flux, window_length=0.5, method='biweight')

For more details, have a look at the interactive playground, the documentation and tutorials.

Available detrending algorithms

• Time-windowed sliders with robust location estimates:
  • biweight Tukey's biweight
  • andrewsinewave Andrew's sine wave
  • hodges Hodges-Lehmann-Sen
  • welsch Welsch-Leclerc
  • huber Huber's M-estimator (1981)
  • median the most robust (but least efficient)
  • medfilt a cadence-based median filter (not time-windowed) for comparison
  • mean the least robust (but most efficient for white noise)
  • trim_mean trimmed mean with adjustable caps
  • winsorize outliers are winsorized to a specified percentile
• Splines:
  • untrendy Spline with iterative sigma-clipping (based on the "untrendy" package)
  • hspline Spline with a robust Huber estimator (Huber 1981)
  • pspline Penalized spline to automatically select the knot distance (Eilers 1996), with iteratively sigma-clipping
• Polynomials and others:
  • lowess Locally weighted scatterplot smoothing (Cleveland 1979)
  • cofiam Cosine Filtering with Autocorrelation Minimization (Kipping et al. 2013)
  • savgol sliding segments are fit with polynomials (Savitzky & Golay 1964), cadence-based
  • supersmoother Friedman's (1984) Super-Smoother, a local linear regression with adaptive bandwidth
• gp Gaussian Processes offering:
  • squared_exp Squared-exponential kernel
  • matern Matern 3/2 kernel
  • periodic Periodic kernel informed by a user-specified period
  • periodic_auto Periodic kernel informed by a Lomb-Scargle periodogram pre-search

Available features

• window_length The length of the filter window in units of time (usually days).
• break_tolerance If there are large gaps in time, especially with corresponding flux level offsets, the detrending is much improved when splitting the data into several sub-lightcurves and applying the filter to each individually. Comes with an empirical default and is fully adjustable.
• edge_cutoff Trends near edges are less robust. Depending on the data, it may be beneficial to remove edges.
• cval Tuning parameter for the robust estimators (see documentation)
• return_trend If True, the method will return a tuple of two elements (flattened_flux, trend_flux) where trend_flux is the removed trend. Otherwise, it will only return flattened_flux.

Installation

To install the released version, type

$ pip install wotan

which automatically installs numpy, numba and scipy if not present. Depending on the algorithm, additional dependencies exist:

• lowess and huber depend on statsmodels
• hspline and gp depend on `sklearn
• pspline depends on pygam
• supersmoother depends on supersmoother
• untrendy depends on untrendy

To install all additional dependencies, type $ pip install statsmodels sklearn supersmoother untrendy pygam.

Attribution

Please cite Hippke et al. (2019, XXX) if you find this code useful in your research. The BibTeX entry for the paper is:

@ARTICLE{XXX,
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

Originality

As all scientific work, wōtan is standing on the shoulders of giants. Particularly, many detrending methods are wrapped from existing packages. Original contributions include:

• A time-windowed detrending master module with edge treatments and segmentation options
• Robust location estimates using Newton-Raphson iteration to a precision threshold for Tukey's biweight, Andrew's sine wave, and the Welsch-Leclerc. This is probably a "first", which reduces jitter in the location estimate by ~10 ppm
• Robustified penalized splines for automatic knot distance determination and outlier resistance
• Bringing together many methods in one place in a common interface, with sensible defaults
• Providing documentation, tutorials, and a paper which compares and benchmarks the methods