In this paper we present results from the weak lensing shape measurement GRavitational lEnsing Accuracy Testing 2010 (GREAT10) Galaxy Challenge. This marks an order of magnitude step change in the level of scrutiny employed in weak lensing shape meas
urement analysis. We provide descriptions of each method tested and include 10 evaluation metrics over 24 simulation branches. GREAT10 was the first shape measurement challenge to include variable fields; both the shear field and the Point Spread Function (PSF) vary across the images in a realistic manner. The variable fields enable a variety of metrics that are inaccessible to constant shear simulations including a direct measure of the impact of shape measurement inaccuracies, and the impact of PSF size and ellipticity, on the shear power spectrum. To assess the impact of shape measurement bias for cosmic shear we present a general pseudo-Cl formalism, that propagates spatially varying systematics in cosmic shear through to power spectrum estimates. We also show how one-point estimators of bias can be extracted from variable shear simulations. The GREAT10 Galaxy Challenge received 95 submissions and saw a factor of 3 improvement in the accuracy achieved by shape measurement methods. The best methods achieve sub-percent average biases. We find a strong dependence in accuracy as a function of signal-to-noise, and indications of a weak dependence on galaxy type and size. Some requirements for the most ambitious cosmic shear experiments are met above a signal-to-noise ratio of 20. These results have the caveat that the simulated PSF was a ground-based PSF. Our results are a snapshot of the accuracy of current shape measurement methods and are a benchmark upon which improvement can continue. This provides a foundation for a better understanding of the strengths and limitations of shape measurement methods.
We present results of a Bayesian analysis of radial velocity (RV) data for the star HIP 5158, confirming the presence of two companions and also constraining their orbital parameters. Assuming Keplerian orbits, the two-companion model is found to be
e^{48} times more probable than the one-planet model, although the orbital parameters of the second companion are only weakly constrained. The derived orbital periods are 345.6 +/- 2.0 d and 9017.8 +/- 3180.7 d respectively, and the corresponding eccentricities are 0.54 +/- 0.04 and 0.14 +/- 0.10. The limits on planetary mass (m sin i) and semimajor axis are (1.44 +/- 0.14 M_{J}, 0.89 +/- 0.01 AU) and (15.04 +/- 10.55 M_{J}, 7.70 +/- 1.88 AU) respectively. Owing to large uncertainty on the mass of the second companion, we are unable to determine whether it is a planet or a brown dwarf. The remaining `noise (stellar jitter) unaccounted for by the model is 2.28 +/- 0.31 m/s. We also analysed a three-companion model, but found it to be e^{8} times less probable than the two-companion model.
Stellar radial velocity (RV) measurements have proven to be a very successful method for detecting extrasolar planets. Analysing RV data to determine the parameters of the extrasolar planets is a significant statistical challenge owing to the presenc
e of multiple planets and various degeneracies between orbital parameters. Determining the number of planets favoured by the observed data is an even more difficult task. Bayesian model selection provides a mathematically rigorous solution to this problem by calculating marginal posterior probabilities of models with different number of planets, but the use of this method in extrasolar planetary searches has been hampered by the computational cost of the evaluating Bayesian evidence. Nonetheless, Bayesian model selection has the potential to improve the interpretation of existing observational data and possibly detect yet undiscovered planets. We present a new and efficient Bayesian method for determining the number of extrasolar planets, as well as for inferring their orbital parameters, without having to calculate directly the Bayesian evidence for models containing a large number of planets. Instead, we work iteratively and at each iteration obtain a conservative lower limit on the odds ratio for the inclusion of an additional planet into the model. We apply this method to simulated data-sets containing one and two planets and successfully recover the correct number of planets and reliable constraints on the orbital parameters. We also apply our method to RV measurements of HD 37124, 47 Ursae Majoris and HD 10180. For HD 37124, we confirm that the current data strongly favour a three-planet system. We find strong evidence for the presence of a fourth planet in 47 Ursae Majoris, but its orbital period is suspiciously close to one year, casting doubt on its validity. For HD 10180 we find strong evidence for a six-planet system.
