Matched filtering with non-Gaussian noise for planet transit detections

Abstract

We develop a method for planet detection in transit data, which is based on the matched filter technique, combined with the Gaussianization of the noise outliers. The method is based on Fourier transforms and is as fast as the existing methods for planet searches. The Gaussianized matched filter (GMF) method significantly outperforms the standard baseline methods in terms of the false positive rate, enabling planet detections at up to 30 per cent lower transit amplitudes. Moreover, the method extracts all the main planet transit parameters, amplitude, period, phase, and duration. By comparison to the state-of-the-art Gaussian process methods on both simulations and real data, we show that all the transit parameters are determined with an optimal accuracy (no bias and minimum variance), meaning that the GMF method can be used for both the initial planet detection and the follow-up planet parameter analysis.

Statistical Significance Testing for Mixed Priors: A Combined Bayesian and Frequentist Analysis

“…In the absence of a transiting planet, the data are described by a stationary correlated Gaussian noise modeling the stellar variability. Note that the long-term trends in the Kepler data are removed by the preprocessing module [ 22 ] and outliers can be efficiently Gaussianized without affecting the planet transits [ 23 ]. Here, we ignore other defects in the data, such as binary stars, sudden pixel-sensitivity dropouts, etc.…”

“…The amplitude’s MAP value at fixed is by Equation ( A3 ) where we have restored a model normalization factor. This is the matched filtering expression for the signal-to-noise ratio [ 23 ] and can be computed efficiently using Fourier transforms [ 23 ] for all phases on a fine grid at once. Our strategy for finding the highest MAP solutions is therefore to first find a maximum likelihood estimator (MLE) by scanning over the entire parameter space (for details, see [ 23 ]) and then use it as an initial guess in a nonlinear MAP optimization.…”

“…We take a realistic power spectrum extracted from Kepler’s data for the star Kepler 90. The power spectrum and example realizations are shown in Figures 2 and 4 of [ 23 ]. A realization is a uniformly distributed choice of the phases of the Fourier components and normally distributed amplitudes of the Fourier components with a zero mean and variance, given by the power spectrum.…”

fBLS -- a fast-folding BLS algorithm

“…Robnik & Seljak (2020) recently demonstrated that correlated noise induced by stellar variability becomes significant for frequencies 0.25 d -1 , therefore expected to affect the detection of long-duration transit signals. In a follow-up study, Robnik & Seljak (2021) also pointed out that the noise properties may vary significantly between different Kepler stars. We are expanding the capabilities of the algorithm, in terms of its matched-filtering statistic, to account for correlated noise (Ivashenko et al, in preparation; also see Appendix B).…”