The AstroStat Slog » Pareto distribution

[ArXiv] 1st week, May 2008

hlee — Mon, 12 May 2008 02:42:54 +0000

I think I have to review spatial statistics in astronomy, focusing on tessellation (void structure), point process (expanding 2 (3) point correlation function), and marked point process (spatial distribution of hardness ratios of X-ray distant sources, different types of galaxies -not only morphological differences but other marks such as absolute magnitudes and existence of particular features). When? Someday…

In addition to Bayesian methodologies, like this week’s astro-ph, studies on characterizing empirical spatial distributions of voids and galaxies frequently appear, which I believe can be enriched further with the ideas from stochastic geometry and spatial statistics. Click for what was appeared in arXiv this week.

[astro-ph:0805.0156]R. D’Abrusco, G. Longo, N. A. Walton
Quasar candidates selection in the Virtual Observatory era
[astro-ph:0805.0201] S. Vegetti& L.V.E. Koopmans
Bayesian Strong Gravitational-Lens Modelling on Adaptive Grids: Objective Detection of Mass Substructure in Galaxies (many like to see this paper: nest sampling implemented, discusses penalty function and tessllation)
[astro-ph:0805.0238] J. A. Carter et al.
Analytic Approximations for Transit Light Curve Observables, Uncertainties, and Covariances
[astro-ph:0805.0269] S.M.Leach et al.
Component separation methods for the Planck mission
[astro-ph:0805.0276] M. Grossi et al.
The mass density field in simulated non-Gaussian scenarios
[astro-ph:0805.0790] Ceccarelli, Padilla, & Lambas
Large-scale modulation of star formation in void walls
[astro-ph:0805.0797] Ceccarelli et al.
Voids in the 2dFGRS and LCDM simulations: spatial and dynamical properties
[astro-ph:0805.0875] S. Basilakos and L. Perivolaropoulos
Testing GRBs as Standard Candles
[astro-ph:0805.0968] A. A. Stanislavsky et al.
Statistical Modeling of Solar Flare Activity from Empirical Time Series of Soft X-ray Solar Emission

[ArXiv] Pareto Distribution

hlee — Thu, 03 Apr 2008 20:55:04 +0000

Astronomy is ruled by Gaussian distribution with a Poisson distribution duchy. From time to time, ranks are awarded to other distributions without their own territories to be governed independently. Among these distributions, Pareto deserves a high rank. There is a preprint of this week on the Pareto distribution:

On the Truncated Pareto Distribution with applications by Zaninetti and Ferraro [astro-ph:0804.0308]

From the abstract:

This note deals with an application of the Pareto distribution to astrophysics and more precisely to the statistical analysis of mass of stars and of diameters of asteroids. In particular a comparison between the usual Pareto distribution and its truncated version is presented.

The paper introduces the pdf, cdf, mean, variance, higher moments, and survival function of the (truncated) Pareto distribution with applications to Star masses from the Hipparcos data^[1] and asteroid sizes, and simulations of primeval nebula^[2]. It concludes that the truncated Pareto works better than the usual Pareto. The Pareto distribution is simple and intuitive.

ps. Not many astronomy papers cite papers from recent statistical publications. I witness that although the most of astronomical papers have no needs for citing papers in statistics, if they do, they tend to have references from four to five decades ago among which books were revised in 90′s or later and articles of modern perspectives are available (exceptions are seminal papers that introduced statistics to the community like EM algorithm). It is quite encouraging to see an article from JASA 2006 was cited in [astro-ph:0804.0308]

Pareto or power law seems not a good model to fit star masses
Mass accretion observes probabilistic model, I guess

[ArXiv] Solar Cycle, June 18, 2007

hlee — Tue, 19 Jun 2007 21:00:23 +0000

From arxiv/astro-ph, arXiv:0706.2590v1 Extreme Value Theory and the Solar Cycle by Ramos, A. This paper might drag a large attention from CHASC members.

The paper points out that the extreme value theory is scarcely applied in astrophysics; however, extreme events are the most interesting ones in astronomy. Their goal is forecasting solar cycles via statistical tools for extreme values. They adopt the generalized Pareto distribution and estimates parameters of the distribution with a maximum likelihood approach. As a consequence of estimating the cumulative distribution of extreme values, return time (waiting time until an event goes beyond a threshold) and return level (typical extreme event to be discovered) were reported to be matching the empirical distribution of solar cycle. Also, a warning on extrapolating on return times has been given due to the short period of observation (250 years).

Note that the tabulated data is publicly available as the International Sunspot Number. Sunspot number has been a standard example for time series studies but still accept challenges from many scholars.

An additional interesting astronomical paper with a bayesian methodology appeared in arxiv/astro-ph on the same date: arXiv:0703417 MCMC analysis of WMAP3 and SDSS data points to broken symmetry inflation potentials and provides a lower bound on the tensor to scalar ratio by Destri et.al.