Analytic Approximations for Transit Light Curve Observables, Uncertainties, and Covariances

The light curve of an exoplanetary transit can be used to estimate the planetary radius and other parameters of interest. Because accurate parameter estimation is a non-analytic and computationally intensive problem, it is often useful to have analytic approximations for the parameters as well as their uncertainties and covariances. Here we give such formulas, for the case of an exoplanet transiting a star with a uniform brightness distribution. We also assess the advantages of some relatively uncorrelated parameter sets for fitting actual data. When limb darkening is significant, our parameter sets are still useful, although our analytic formulas underpredict the covariances and uncertainties.Comment: 33 pages, 14 figure

Exact Bayesian curve fitting and signal segmentation.

We consider regression models where the underlying functional relationship between the response and the explanatory variable is modeled as independent linear regressions on disjoint segments. We present an algorithm for perfect simulation from the posterior distribution of such a model, even allowing for an unknown number of segments and an unknown model order for the linear regressions within each segment. The algorithm is simple, can scale well to large data sets, and avoids the problem of diagnosing convergence that is present with Monte Carlo Markov Chain (MCMC) approaches to this problem. We demonstrate our algorithm on standard denoising problems, on a piecewise constant AR model, and on a speech segmentation problem