The AstroStat Slog » poisson point process http://hea-www.harvard.edu/AstroStat/slog Weaving together Astronomy+Statistics+Computer Science+Engineering+Intrumentation, far beyond the growing borders Fri, 09 Sep 2011 17:05:33 +0000 en-US hourly 1 http://wordpress.org/?v=3.4 [ArXiv] 2nd week, May 2008 http://hea-www.harvard.edu/AstroStat/slog/2008/arxiv-2nd-week-may-2008/ http://hea-www.harvard.edu/AstroStat/slog/2008/arxiv-2nd-week-may-2008/#comments Mon, 19 May 2008 14:42:56 +0000 hlee http://hea-www.harvard.edu/AstroStat/slog/?p=306 There’s no particular opening remark this week. Only I have profound curiosity about jackknife tests in [astro-ph:0805.1994]. Including this paper, a few deserve separate discussions from a statistical point of view that shall be posted.

  • [astro-ph:0805.1290]R. Barnard, L. Shaw Greening, U. Kolb
    A multi-coloured survey of NGC 253 with XMM-Newton: testing the methods used for creating luminosity functions from low-count data

  • [astro-ph:0805.1469] Philip J. Marshall et al.
    Automated detection of galaxy-scale gravitational lenses in high resolution imaging data

  • [astro-ph:0805.1470] E. P. Kontar, E. Dickson, J. Kasparova
    Low-energy cutoffs and in electron spectra of solar flares: statistical survey (It is not statistically rigorous but the topic can be connected to dip tests or gap tests in statistics)

  • [astro-ph:0805.1936] J. Yee & B. Gaudi
    Characterizing Long-Period Transiting Planets Observed by Kepler (discusses uncertainty in light curves and Fisher matrix)

  • [astro-ph:0805.1994] the QUad collaboration: C. Pryke et al.
    Second and third season QUaD CMB temperature and polarization power spectra (What is jackknife tests? A brief scan of the paper does not register with my understanding of jackknifing. It looks more close to cross validation. Another slog topic shall come: bootstrap, cross validation, jackknife, and resampling.)

  • [astro-ph:0805.2121] N. Cole et al.
    Maximum Likelihood Fitting of Tidal Streams With Application to the Sagittarius Dwarf Tidal Tails

  • [astro-ph:0805.2155] J Yoo & M Zaldarriaga
    Improved estimation of cluster mass profiles from the cosmic microwave background

  • [astro-ph:0805.2207] A.Vikhlinin et al.
    Chandra Cluster Cosmology Project II: Samples and X-ray Data Reduction (it mentions calibration uncertainty and background, can it be a reference to stacking, coadding, source detection, etc?)

  • [astro-ph:0805.2325] J.M. Loh
    A valid and fast spatial bootstrap for correlation functions

  • [astro-ph:0805.2326] T. Wickramasinghe, M. Struble, J. Nieusma
    Observed Bimodality of the Einstein Crossing Times of Galactic Microlensing Events
]]> http://hea-www.harvard.edu/AstroStat/slog/2008/arxiv-2nd-week-may-2008/feed/ 0 [ArXiv] Spatial Correlation in the Scan Statistic http://hea-www.harvard.edu/AstroStat/slog/2007/arxiv-spatial-correlation-in-the-scan-statistic/ http://hea-www.harvard.edu/AstroStat/slog/2007/arxiv-spatial-correlation-in-the-scan-statistic/#comments Wed, 12 Dec 2007 05:50:13 +0000 hlee http://hea-www.harvard.edu/AstroStat/slog/2007/arxiv-spatial-correlation-in-the-scan-statistic/ Accounting for Spatial Correlation in the Scan Statistic by Loh &Zhu [stat.AP:0712.1458] provides a picture that helps us to understand excessive false alarms in source detection when the image data set is based on the Poisson point process. Without any experience in source detection analysis, empirically I cannot state the detection statistics nor the p-values of detection methods. However, with acknowledging the over-dispersed Poisson count data and the unknown spatial correlation prior to detecting analysis, we could guess that the false discovery of sources occurs more often than what we expect.

To incorporate overdispersion and spatial correlation in detecting clusters from the spatial Poisson point process, the authors proposed the null model that includes spatial correlation, which is referred as the spatial generalized linear mixed model (SGLMM), or generalized spatial linear model (GSLM). They show theoretically this over-dispersion and spatial correlation leads to the increase of false positives, which is verified through a simulation study as well. Their simulation study also illustrates that their modified scan statistic substantially reduces the false alarm.

Due to the complexity of the models and theories, the authors rely on simulation study heavily. Nonetheless, the figures that illustrates the posterior distributions of the scan statistic are difficult to read (due to the low resolution scanned images). Please, keep this in your mind while you are reading it.

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