Kepler Presearch Data Conditioning II - A Bayesian Approach to Systematic Error Correction

With the unprecedented photometric precision of the Kepler Spacecraft, significant systematic and stochastic errors on transit signal levels are observable in the Kepler photometric data. These errors, which include discontinuities, outliers, systematic trends and other instrumental signatures, obscure astrophysical signals. The Presearch Data Conditioning (PDC) module of the Kepler data analysis pipeline tries to remove these errors while preserving planet transits and other astrophysically interesting signals. The completely new noise and stellar variability regime observed in Kepler data poses a significant problem to standard cotrending methods such as SYSREM and TFA. Variable stars are often of particular astrophysical interest so the preservation of their signals is of significant importance to the astrophysical community. We present a Bayesian Maximum A Posteriori (MAP) approach where a subset of highly correlated and quiet stars is used to generate a cotrending basis vector set which is in turn used to establish a range of "reasonable" robust fit parameters. These robust fit parameters are then used to generate a Bayesian Prior and a Bayesian Posterior Probability Distribution Function (PDF) which when maximized finds the best fit that simultaneously removes systematic effects while reducing the signal distortion and noise injection which commonly afflicts simple least-squares (LS) fitting. A numerical and empirical approach is taken where the Bayesian Prior PDFs are generated from fits to the light curve distributions themselves.Comment: 43 pages, 21 figures, Submitted for publication in PASP. Also see companion paper "Kepler Presearch Data Conditioning I - Architecture and Algorithms for Error Correction in Kepler Light Curves" by Martin C. Stumpe, et a

Pointwise Bounds for Steklov Eigenfunctions

Let (Ω,g) be a compact, real-analytic Riemannian manifold with real-analytic boundary ∂Ω. The harmonic extensions of the boundary Dirichlet-to-Neumann eigenfunctions are called Steklov eigenfunctions. We show that the Steklov eigenfunctions decay exponentially into the interior in terms of the Dirichlet-to-Neumann eigenvalues and give a sharp rate of decay to first order at the boundary. The proof uses the Poisson representation for the Steklov eigenfunctions combined with sharp h-microlocal concentration estimates for the boundary Dirichlet-to-Neumann eigenfunctions near the cosphere bundle S∗∂Ω. These estimates follow from sharp estimates on the concentration of the FBI transforms of solutions to analytic pseudodifferential equations Pu=0 near the characteristic set {σ(P)=0}

Kepler Presearch Data Conditioning I - Architecture and Algorithms for Error Correction in Kepler Light Curves

Kepler provides light curves of 156,000 stars with unprecedented precision. However, the raw data as they come from the spacecraft contain significant systematic and stochastic errors. These errors, which include discontinuities, systematic trends, and outliers, obscure the astrophysical signals in the light curves. To correct these errors is the task of the Presearch Data Conditioning (PDC) module of the Kepler data analysis pipeline. The original version of PDC in Kepler did not meet the extremely high performance requirements for the detection of miniscule planet transits or highly accurate analysis of stellar activity and rotation. One particular deficiency was that astrophysical features were often removed as a side-effect to removal of errors. In this paper we introduce the completely new and significantly improved version of PDC which was implemented in Kepler SOC 8.0. This new PDC version, which utilizes a Bayesian approach for removal of systematics, reliably corrects errors in the light curves while at the same time preserving planet transits and other astrophysically interesting signals. We describe the architecture and the algorithms of this new PDC module, show typical errors encountered in Kepler data, and illustrate the corrections using real light curve examples.Comment: Submitted to PASP. Also see companion paper "Kepler Presearch Data Conditioning II - A Bayesian Approach to Systematic Error Correction" by Jeff C. Smith et a

Assessing the Validity of Several Heart Rate Monitors in Wearable Technology While Mountain Biking

International Journal of Exercise Science 16(7): 1440-1450, 2023. Purpose: This study sought to assess the validity of several heart rate (HR) monitors in wearable technology during mountain biking (MTB), compared to the Polar H7® HR monitor, used as the criterion device. Methods: A total of 20 participants completed two MTB trials while wearing six HR monitors (5 test devices, 1 criterion). HR was recorded on a second-by-second basis for all devices analyzed. After data processing, validity measures were calculated, including 1. error analysis: mean absolute percentage errors (MAPE), mean absolute error (MAE), and mean error (ME), and 2. Correlation analysis: Lin’s concordance correlation coefficient (CCC) and Pearson’s correlation coefficient (r). Thresholds for validity were set at MAPE \u3c 10% and CCC \u3e 0.7. Results: The only device that was found to be valid during mountain biking was the Suunto Spartan Sport watch with accompanying HR monitor, with a MAPE of 0.66% and a CCC of 0.99 for the overall, combined data. Conclusion: If a person would like to track their HR during mountain biking, for pacing, training, or other reasons, the devices best able to produce valid results are chest-based, wireless electrocardiogram (ECG) monitors, secured by elastic straps to minimize the movement of the device, such as the Suunto chest-based HR monitor

Detection of Potential Transit Signals in the First Three Quarters of Kepler Mission Data

We present the results of a search for potential transit signals in the first three quarters of photometry data acquired by the Kepler Mission. The targets of the search include 151,722 stars which were observed over the full interval and an additional 19,132 stars which were observed for only 1 or 2 quarters. From this set of targets we find a total of 5,392 detections which meet the Kepler detection criteria: those criteria are periodicity of the signal, an acceptable signal-to-noise ratio, and a composition test which rejects spurious detections which contain non-physical combinations of events. The detected signals are dominated by events with relatively low signal-to-noise ratio and by events with relatively short periods. The distribution of estimated transit depths appears to peak in the range between 40 and 100 parts per million, with a few detections down to fewer than 10 parts per million. The detected signals are compared to a set of known transit events in the Kepler field of view which were derived by a different method using a longer data interval; the comparison shows that the current search correctly identified 88.1% of the known events. A tabulation of the detected transit signals, examples which illustrate the analysis and detection process, a discussion of future plans and open, potentially fruitful, areas of further research are included

Detection of Potential Transit Signals in Sixteen Quarters of Kepler Mission Data

We present the results of a search for potential transit signals in four years of photometry data acquired by the Kepler Mission. The targets of the search include 111,800 stars which were observed for the entire interval and 85,522 stars which were observed for a subset of the interval. We found that 9,743 targets contained at least one signal consistent with the signature of a transiting or eclipsing object, where the criteria for detection are periodicity of the detected transits, adequate signal-to-noise ratio, and acceptance by a number of tests which reject false positive detections. When targets that had produced a signal were searched repeatedly, an additional 6,542 signals were detected on 3,223 target stars, for a total of 16,285 potential detections. Comparison of the set of detected signals with a set of known and vetted transit events in the Kepler field of view shows that the recovery rate for these signals is 96.9%. The ensemble properties of the detected signals are reviewed.Comment: Accepted by ApJ Supplemen