| Various statistical measures are derived and applied to analyse the large scale structure of the Universe. First, the unique methodological role of statistics in astrophysics is discussed and illustrated through an example of fitting and applying the Tully-Fisher relation to galaxy velocity data. The subtleties of fitting an observed bivariate probability distribution to the relation are discussed as well as the consequences of a lack of knowledge of the source of scatter in the distribution, with regard to systematic bias effects. Next, a general solution to the problem of Malmquist Bias in galaxy velocity fields is presented and applied to elliptical galaxy data. Results indicate that much of the infall signal seen in the Centarus region, the Great Attractor, may be an artifact due to inadequate Malmquist Bias correction. A method using the radial velocity correlation functions of galaxies is derived as a test of whether the large scale mass distribution can be considered a Gaussian random field. This is a prediction of canonical theories of inflation. Present data show consistency with a Gaussian field. A new estimator for the angular correlation function is presented with reduced variance and no bias. Heretofore common estimators are shown to have significantly greater variance than the Poisson variance generally assumed. This estimator is then applied to faint galaxy data as a measure of the angular correlation function of faint galaxies as a function of color. Results show that both the extreme red and blue galaxy subsets have a marked increase in correlation amplitude. This is expected for the red galaxies as they can be identified as the cluster ellipticals. However, the cross correlation of these subsets show that they are uncorrelated with each other. For the faint blue galaxies, this is indicative of a disparate population of galaxies with a tight distribution in redshift space. It is surmized that these galaxies are either a faint population found relatively nearby or tightly clustered such as in sheets. |
