Inferring probabilistic stellar rotation periods using Gaussian processes

Variability in the light curves of spotted, rotating stars is often non-sinusoidal and quasi-periodic --- spots move on the stellar surface and have finite lifetimes, causing stellar flux variations to slowly shift in phase. A strictly periodic sinusoid therefore cannot accurately model a rotationally modulated stellar light curve. Physical models of stellar surfaces have many drawbacks preventing effective inference, such as highly degenerate or high-dimensional parameter spaces. In this work, we test an appropriate effective model: a Gaussian Process with a quasi-periodic covariance kernel function. This highly flexible model allows sampling of the posterior probability density function of the periodic parameter, marginalising over the other kernel hyperparameters using a Markov Chain Monte Carlo approach. To test the effectiveness of this method, we infer rotation periods from 333 simulated stellar light curves, demonstrating that the Gaussian process method produces periods that are more accurate than both a sine-fitting periodogram and an autocorrelation function method. We also demonstrate that it works well on real data, by inferring rotation periods for 275 Kepler stars with previously measured periods. We provide a table of rotation periods for these 1132 Kepler objects of interest and their posterior probability density function samples. Because this method delivers posterior probability density functions, it will enable hierarchical studies involving stellar rotation, particularly those involving population modelling, such as inferring stellar ages, obliquities in exoplanet systems, or characterising star-planet interactions. The code used to implement this method is available online.Comment: Submitted to MNRAS. Replaced 27/06/2017: corrections made to koi_periods.cs

The Rowley Enigma: How Much Weight is Due to IDEA State Administrative Proceedings in Federal Court?

In this article, I argue that the phrase due weight incorporates a deferential review standard equivalent to the clear error or substantial evidence standard, a conclusion reached by a minority of the circuit courts of appeal. I further argue that, consistent with Rowley, federal courts must afford due weight to administrative officers\u27 substantive or educational conclusions, but no weight to their procedural or non-educational conclusions. Part II offers a general outline of the IDEA, giving special attention to its judicial review provisions. In Part III, I provide a general discussion of judicial review of administrative adjudication. Part IV is devoted to a discussion of Rowley and the First Circuit\u27s seminal opinion in Town of Burlington v. Dep \u27t of Ed. of Com. Of Mass (Burlington II). Part V discusses the majority and minority approaches adopted by the circuit courts of appeal following Rowley. Part VI recommends a deference standard that is consistent with Rowley and employed by a minority of circuit courts. Part VII offers a brief conclusion