Dark Matter in Dwarf Spheroidals I: Models

This paper introduces a new two-parameter family of dwarf spheroidal (dSph) galaxy models. The density distribution has a Plummer profile and falls like the inverse fourth power of distance in projection, in agreement with the star-count data. The first free parameter controls the velocity anisotropy, the second controls the dark matter content. The dark matter distribution can be varied from one extreme of mass-follows-light through a near-isothermal halo with flat rotation curve to the other extreme of an extended dark halo with harmonic core. This family of models is explored analytically in some detail -- the distribution functions, the intrinsic moments and the projected moments are all calculated. For the nearby Galactic dSphs, samples of hundreds of discrete radial velocities are becoming available. A technique is developed to extract the anisotropy and dark matter content from such data sets by maximising the likelihood function of the sample of radial velocities. This is constructed from the distribution function and corrected for observational errors and the effects of binaries. Tests on simulated data sets show that samples of 1000 discrete radial velocities are ample to break the degeneracy between mass and anisotropy in the nearby dSphs. Interesting constraints can already be placed on the distribution of the dark matter with samples of 160 radial velocities (the size of the present-day data set for Draco).Comment: 16 pages, version in press at MNRA

A Tutorial on Fisher Information

In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different statistical paradigms. First, in the frequentist paradigm, Fisher information is used to construct hypothesis tests and confidence intervals using maximum likelihood estimators; second, in the Bayesian paradigm, Fisher information is used to define a default prior; lastly, in the minimum description length paradigm, Fisher information is used to measure model complexity

Non-Gaussian Geostatistical Modeling using (skew) t Processes

We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with $t$ marginals obtained through scale mixing of a Gaussian process with an inverse square root process with Gamma marginals. We then generalize this construction by considering a skew-Gaussian process, thus obtaining a process with skew-t marginal distributions. For the proposed (skew) $t$ process we study the second-order and geometrical properties and in the $t$ case, we provide analytic expressions for the bivariate distribution. In an extensive simulation study, we investigate the use of the weighted pairwise likelihood as a method of estimation for the $t$ process. Moreover we compare the performance of the optimal linear predictor of the $t$ process versus the optimal Gaussian predictor. Finally, the effectiveness of our methodology is illustrated by analyzing a georeferenced dataset on maximum temperatures in Australi