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DISCOVERY AND VALIDATION OF Kepler-452b: A 1.6 R ⨁ SUPER EARTH EXOPLANET IN THE HABITABLE ZONE OF A G2 STAR
This section describes the most salient validation tests performed inside of the Data Validation component of the SOC pipeline. The DV report resulting from the official SOC 9.2 processing is available at http://exoplanetarchive.ipac.caltech.edu/data/KeplerData/008/008311/008311864/dv/kplr008311864-20141002224145_dvr.pdf.20
4.1. Discriminating Against Background Eclipsing Binaries
Data validation applies several tests for the presence of background eclipsing binaries. The first is the odd/even test: DV fits a limb-darkened transit model to the odd transits and an independent model to the even transits, and then compares the depth fitted to the odd transits to that fitted to the even transits. This results in a test statistic of 
with a corresponding significance of 89.0%.21 In addition, DV examines the ratio of the temporal offsets between the odd and even transits compared to the fitted orbital period, the so-called "epoch" test, giving a result of
and a corresponding significance of 92%. Figure 3 illustrates the odd/even test by plotting the light curve data phase folded separately for the odd and even transits. No other TCEs were generated for this star and no evidence was seen for weak secondary eclipses. Based on these tests, we see no evidence for systematic differences in the odd/even transit depths and durations which often result in the case of background eclipsing binaries, and the transit times are consistent with a strict periodic spacing.
4.2. Statistical Bootstrap Test
In order to better determine the statistical significance of the transit sequence, we examined the bootstrap distribution for the population of null statistics for the out-of-transit data (Jenkins et al. 2002; J. Jenkins & S. Seader 2015, in preparation). This test relaxes the assumption that the observation noise is broadband colored Gaussian noise to establish a robust significance level for the detection statistic of the planet candidate. The Appendix contains a mathematical derivation of the statistical approach and a brief description of its implementation.
The false alarm rate is estimated using a bootstrap statistical analysis of the out-of-transit data for this star. The single event statistics time series, representing the likelihood of a transit of the fitted duration as a function of time, are drawn at random (with replacement) to construct artificial multiple event statistics corresponding to the same number of transits that occurred for the TCE in question. The distribution of all such bootstrap samples provides a means to assess the statistical significance of the maximum multiple event statistic, the maxMES, that resulted in the identification of the TCE in the first place. This methodology relaxes the assumption of perfection on the part of the adaptive, power spectral density estimator in TPS that informs the pre-whitener, allowing for the detection signal-to-noise ratio (S/N) to be evaluated against the distribution of null statistics drawn directly from the observation noise of the light curve. The bootstrap false alarm rate for the transit signature of Kepler-452b is securely established as statistically significant by this test for the
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