Point process models for astronomy: Quasars, coronal mass ejections, and solar flares

Details Point process models for astronomy: Quasars, coronal mass ejections, and solar flares Point process models for astronomy: Quasars, coronal mass ejections, and solar flares

Aug 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007phdt........18h&link_type=abstract

Proquest Dissertations And Theses 2007. Section 0330, Part 0463 84 pages; [Ph.D. dissertation].United States -- Illinois: The U

Mathematics

Probability

1

Quasar Luminosity Function, Point Process, Quasars, Coronal Mass Ejections, Solar Flares

Scientific paper

This thesis presents a statistical analysis of two interesting astronomical applications that involve point process data.
The first chapter presents an application in solar physics that looks at two types of solar events: solar flares and coronal mass ejections (CMEs). The data are viewed as a marked point process in time, and the analysis seeks to determine whether there is a local temporal correlation between the two event types. A key statistical complication is that the two processes follow an inhomogeneous long term rate function that changes with the solar cycle. Our goal is to evaluate the local temporal correlation, adjusting for the fluctuation in intensity due to changes in the long term solar cycle. We present a novel statistical approach that begins by aggregating the relative onset times for CME events relative to solar flare events in a small local window. Two functional forms are used to model the distribution of the relative time points, and model parameters are estimated by the method of maximum likelihood. Statistical significance of the local temporal correlation and confidence intervals for parameter estimates are attained via a bootstrap approach Our methods point to a statistically significant increase in the probability that a CME will occur in the minutes preceding the onset of a solar flare.
The second chapter involves estimation of the Quasar Luminosity Function. The thrust of the analysis is density estimation, model selection, and the detection of interaction effects in a two-dimensional point process. This paper presents a flexible parametric model of quasars as a non-homogeneous Poisson process over the space of luminosity and redshift. Our contribution to this work is two-fold: first, to allow the introduction of higher-order terms as warranted by the data, and second, to extend the model in order to better detect and describe any interaction effect between luminosity and redshift present in the data. Major complicating factors in this analysis are data truncation and sampling bias.

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