Biased-estimations of the Variance and Skewness

Nonlinear combinations of direct observables are often used to estimate quantities of theoretical interest. Without sufficient caution, this could lead to biased estimations. An example of great interest is the skewness $S_3$ of the galaxy distribution, defined as the ratio of the third moment \xibar_3 and the variance squared \xibar_2^2. Suppose one is given unbiased estimators for \xibar_3 and \xibar_2^2 respectively, taking a ratio of the two does not necessarily result in an unbiased estimator of $S_3$. Exactly such an estimation-bias affects most existing measurements of $S_3$. Furthermore, common estimators for \xibar_3 and \xibar_2 suffer also from this kind of estimation-bias themselves: for \xibar_2, it is equivalent to what is commonly known as the integral constraint. We present a unifying treatment allowing all these estimation-biases to be calculated analytically. They are in general negative, and decrease in significance as the survey volume increases, for a given smoothing scale. We present a re-analysis of some existing measurements of the variance and skewness and show that most of the well-known systematic discrepancies between surveys with similar selection criteria, but different sizes, can be attributed to the volume-dependent estimation-biases. This affects the inference of the galaxy-bias(es) from these surveys. Our methodology can be adapted to measurements of analogous quantities in quasar spectra and weak-lensing maps. We suggest methods to reduce the above estimation-biases, and point out other examples in LSS studies which might suffer from the same type of a nonlinear-estimation-bias.Comment: 28 pages of text, 9 ps figures, submitted to Ap

The evolution of the star forming sequence in hierarchical galaxy formation models

It has been argued that the specific star formation rates of star forming galaxies inferred from observational data decline more rapidly below z = 2 than is predicted by hierarchical galaxy formation models. We present a detailed analysis of this problem by comparing predictions from the GALFORM semi-analytic model with an extensive compilation of data on the average star formation rates of star-forming galaxies. We also use this data to infer the form of the stellar mass assembly histories of star forming galaxies. Our analysis reveals that the currently available data favour a scenario where the stellar mass assembly histories of star forming galaxies rise at early times and then fall towards the present day. In contrast, our model predicts stellar mass assembly histories that are almost flat below z = 2 for star forming galaxies, such that the predicted star formation rates can be offset with respect to the observational data by factors of up to 2-3. This disagreement can be explained by the level of coevolution between stellar and halo mass assembly that exists in contemporary galaxy formation models. In turn, this arises because the standard implementations of star formation and supernova feedback used in the models result in the efficiencies of these process remaining approximately constant over the lifetime of a given star forming galaxy. We demonstrate how a modification to the timescale for gas ejected by feedback to be reincorporated into galaxy haloes can help to reconcile the model predictions with the data.Comment: 30 Pages, 16 Figures, MNRAS accepte