The AstroStat Slog » spectral analysis 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 worse than the Drake eq. http://hea-www.harvard.edu/AstroStat/slog/2009/worse-than-the-drake-eq/ http://hea-www.harvard.edu/AstroStat/slog/2009/worse-than-the-drake-eq/#comments Sat, 04 Jul 2009 05:59:45 +0000 hlee http://hea-www.harvard.edu/AstroStat/slog/?p=3080 I was reading the June 2009 IMS bulletin on my way to Korea for the 1st IMS-APRM meeting. Then, I was in half shock and in half sadness. Something unlike than the Drake equation had happened.

The Drake eq. is used as an indicator that the chance of finding an organic society equivalent to the human society. As you guess, such chance is extremely low. What would be a chance that two obituaries of eminent statisticians who influenced many can appear in the same bulletin. Personal thought led that the obituary section of the bulletin is further extreme than the Drake equation.

If you are an astronomer who are interested in spectral analysis and looked for statistical or data analysis literature, you cannot miss I.J.Good’s bump hunting paper.

Density Estimation and Bump-Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data
by I.J.Good and R.A. Gaskins in JASA, Vol.75, No. 369, pp. 42-56

The penalized likelihood approach for density estimation and bump hunting and its Bayesian interpretation has popularized statistical application to spectrum type natural science data.

Not by the popularity but by my personal interest in computational geometry and its statistical expansion, Worlsey’s publications became my reading list. Computational geometry pertains the goodness of nonparametric statistics for multivariate data which are not well explored compared to nonparametric methods for univariate data. His introductory paper about computational geometry like

Keith Worsley (1996)
The Geometry of Random images (zipped postscript), Chance, 9(1), pp.27-40

can be informative and useful to some astronomers.

Speaking of the Drake equation, it was the first thing that gave me a notion of probability, it describes how one would simply formulate and compute the chance of finding life beyond the earth. The equation is a process of constructing a likelihood function. In fact, I didn’t think this equation to be a likelihood function at that time but its unique creativity carved my memory. The way this equation describes how to compute the chance of the existence of extraterrestrial intelligence is a good example of chain rule in modifying likelihood functions.

I have never met those scholars face to face but through their writings, their works shaped my way of thinking. This personal experience made me hard to believe obituaries of two respectful statisticians. It was like getting estimates of the chance of meeting ETs which I found very small when I played with the equation. Although their chances are extremely low, things can happen. Finding life outside of the earth and finding a sad news of two eminent scientists’ death are alike.

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[ArXiv] Spectroscopic Survey, June 29, 2007 http://hea-www.harvard.edu/AstroStat/slog/2007/arxiv-spectroscopic-survey-june-29-2007/ http://hea-www.harvard.edu/AstroStat/slog/2007/arxiv-spectroscopic-survey-june-29-2007/#comments Mon, 02 Jul 2007 22:07:39 +0000 hlee http://hea-www.harvard.edu/AstroStat/slog/2007/arxiv-spectroscopic-survey-june-29-2007/ From arXiv/astro-ph:0706.4484

Spectroscopic Surveys: Present by Yip. C. overviews recent spectroscopic sky surveys and spectral analysis techniques toward Virtual Observatories (VO). In addition that spectroscopic redshift measures increase like Moore’s law, the surveys tend to go deeper and aim completeness. Mainly elliptical galaxy formation has been studied due to more abundance compared to spirals and the galactic bimodality in color-color or color-magnitude diagrams is the result of the gas-rich mergers by blue mergers forming the red sequence. Principal component analysis has incorporated ratios of emission line-strengths for classifying Type-II AGN and star forming galaxies. Lyα identifies high z quasars and other spectral patterns over z reveal the history of the early universe and the characteristics of quasars. Also, the recent discovery of 10 satellites to the Milky Way is mentioned.

Spectral analyses take two approaches: one is the model based approach taking theoretical templates, known for its flaws but straightforward extractions of physical parameters, and the other is the empirical approach, useful for making discoveries but difficult in the analysis interpretation. Neither of them has substantial advantage to the other. When it comes to fitting, Chi-square minimization has been dominant but new methodologies are under developing. For spectral classification problems, principal component analysis (Karlhunen-Loeve transformation), artificial neural network, and other machine learning techniques have been applied.

In the end, the author reports statistical and astrophysical challenges in massive spectroscopic data of present days: 1. modeling galaxies, 2. parameterizing star formation history, 3. modeling quasars, 4. multi-catalog based calibration (separating systematic and statistics errors), 5. estimating parameters, which would be beneficial to VO, of which objective is the unification of data access.

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