The optical light curves of many quasars show variations of tenths of a magnitude or more on time scales of months to years. This variation often cannot be described well by a simple deterministic model. We perform a Bayesian comparison of over 20 de
terministic and stochastic models on 6304 QSO light curves in SDSS Stripe 82. We include the damped random walk (or Ornstein-Uhlenbeck [OU] process), a particular type of stochastic model which recent studies have focused on. Further models we consider are single and double sinusoids, multiple OU processes, higher order continuous autoregressive processes, and composite models. We find that only 29 out of 6304 QSO lightcurves are described significantly better by a deterministic model than a stochastic one. The OU process is an adequate description of the vast majority of cases (6023). Indeed, the OU process is the best single model for 3462 light curves, with the composite OU process/sinusoid model being the best in 1706 cases. The latter model is the dominant one for brighter/bluer QSOs. Furthermore, a non-negligible fraction of QSO lightcurves show evidence that not only the mean is stochastic but the variance is stochastic, too. Our results confirm earlier work that QSO light curves can be described with a stochastic model, but place this on a firmer footing, and further show that the OU process is preferred over several other stochastic and deterministic models. Of course, there may well exist yet better (deterministic or stochastic) models which have not been considered here.
Testing theories of angular-momentum acquisition of rotationally supported disc galaxies is the key to understand the formation of this type of galaxies. The tidal-torque theory tries to explain this acquisition process in a cosmological framework an
d predicts positive autocorrelations of angular-momentum orientation and spiral-arm handedness on distances of 1Mpc/h. This disc alignment can also cause systematic effects in weak-lensing measurements. Previous observations claimed discovering such correlations but did not account for errors in redshift, ellipticity and morphological classifications. We explain how to rigorously propagate all important errors. Analysing disc galaxies in the SDSS database, we find that positive autocorrelations of spiral-arm handedness and angular-momentum orientations on distances of 1Mpc/h are plausible but not statistically significant. This result agrees with a simple hypothesis test in the Local Group, where we find no evidence for disc alignment. Moreover, we demonstrate that ellipticity estimates based on second moments are strongly biased by galactic bulges, thereby corrupting correlation estimates and overestimating the impact of disc alignment on weak-lensing studies. Finally, we discuss the potential of future sky surveys. We argue that photometric redshifts have too large errors, i.e., PanSTARRS and LSST cannot be used. We also discuss potentials and problems of front-edge classifications of galaxy discs in order to improve estimates of angular-momentum orientation.
Reduced chi-squared is a very popular method for model assessment, model comparison, convergence diagnostic, and error estimation in astronomy. In this manuscript, we discuss the pitfalls involved in using reduced chi-squared. There are two independe
nt problems: (a) The number of degrees of freedom can only be estimated for linear models. Concerning nonlinear models, the number of degrees of freedom is unknown, i.e., it is not possible to compute the value of reduced chi-squared. (b) Due to random noise in the data, also the value of reduced chi-squared itself is subject to noise, i.e., the value is uncertain. This uncertainty impairs the usefulness of reduced chi-squared for differentiating between models or assessing convergence of a minimisation procedure. The impact of noise on the value of reduced chi-squared is surprisingly large, in particular for small data sets, which are very common in astrophysical problems. We conclude that reduced chi-squared can only be used with due caution for linear models, whereas it must not be used for nonlinear models at all. Finally, we recommend more sophisticated and reliable methods, which are also applicable to nonlinear models.
