Apr 27th, 2009| 05:26 pm | Posted by hlee

To my knowledge, **Richard Feynman** is an iconic figure among physicists and astrophysicists. Although I didn’t read every chapter of his lecture series, from other books like* QED*, *Surely You’re Joking, Mr. Feynman!*, *The Pleasure of Finding Things Out*, and some essays, I became and still am fond of him. The way how this famous physicist put things is straight and simple, blowing out the misconception that physics is full of mathematical equations.

Even though most of my memories about his writings are gone – how many people can beat the time and fading memories! – like other rudimentary astronomy and physics stuffs that I used to know, statistics brought up his name above the surface before it sinks completely to the abyss. Continue reading ‘Feynman and Statistics’ »

Apr 22nd, 2009| 02:02 pm | Posted by hlee

I was reading Lehmann’s memoir on his friends and colleagues who influence a great deal on establishing his career. I’m happy to know that his meeting Landau, Courant, and Evans led him to be a statistician; otherwise, we, including astronomers, would have had very different textbooks and statistical thinking would have been different. On the other hand, I was surprised to know that he chose statistics over physics due to his experience from Cambridge (UK). I thought becoming a physicist is more preferred than becoming a statistician during the first half of the 20th century. At least I felt that way, probably it’s because more general science books in physics and physics related historic events were well exposed so that I became to think that physicists are more cooler than other type scientists. Continue reading ‘[Book] The Physicists’ »

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Apr 20th, 2009| 09:34 pm | Posted by hlee

I asked a couple of astronomers if they heard the term **plug-in estimator** and none of them gave me a positive answer. Continue reading ‘[MADS] plug-in estimator’ »

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Apr 16th, 2009| 07:32 am | Posted by vlk

http://www.tricki.org/

The wikipedia-like repository for mathematical “tricks” has now gone live. Their mission statement:

The main body of the Tricki will be a (large, if all goes according to plan) collection of articles about methods for solving mathematical problems. These will be everything from very general problem-solving tips such as, “If you can’t solve the problem, then try to invent an easier problem that sheds light on it,” to much more specific advice such as, “If you want to solve a linear differential equation, you can convert it into a polynomial equation by taking the Fourier transform.”

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Apr 15th, 2009| 09:51 am | Posted by TomLoredo

The 29th International Workshop on Bayesian and Maximum Entropy Methods in Science and Engineering will be held 5-10 July at the University of Mississippi (“Ole Miss”), in the quaint university town of Oxford, MS. The organizing committee is currently accepting submissions of abstracts for both oral and poster presentations. Visit the MaxEnt 2009 web site for more detailed information.

I’m on the organizing committee and I’m excited about this year’s meeting. It is covering a broad range of areas with some exciting speakers. Topics include straightforward applications of parametric Bayesian methods, nonparametric methods, Bayesian computation (including the nested sampling algorithm currently making an impact in cosmology), experimental design, statistical mechanics, foundations of statistics, and even some talks by leaders in the areas of the foundations of statistical mechanics and the interpretation of quantum mechanics. I’m very much looking forward to this year’s meeting, and I urge any interested AstroStat Slog readers to submit an abstract (the deadline is imminent, but if it takes you a couple days longer to come up with something, do send it).

For those new to Bayesian methods, note that the workshop begins with a full day of tutorial lectures.

Apr 10th, 2009| 03:16 pm | Posted by vlk

Probability density functions are another way of summarizing the consequences of assuming a Gaussian error distribution when the true distribution is Poisson. We can compute the posterior probability of the intensity of a source, when some number of counts are observed in a source region, and the background is estimated using counts observed in a different region. We can then compare it to the equivalent Gaussian.

The figure below (AAS 472.09) compares the pdfs for the Poisson intensity (red curves) and the Gaussian equivalent (black curves) for two cases: when the number of counts in the source region is 50 (top) and 8 (bottom) respectively. In both cases a background of 200 counts collected in an area 40x the source area is used. The hatched region represents the 68% equal-tailed interval for the Poisson case, and the solid horizontal line is the ±1σ width of the equivalent Gaussian.

Clearly, for small counts, the support of the Poisson distribution is bounded below at zero, but that of the Gaussian is not. This introduces a visibly large bias in the interval coverage as well as in the normalization properties. Even at high counts, the Poisson is skewed such that larger values are slightly more likely to occur by chance than in the Gaussian case. This skew can be quite critical for marginal results. Continue reading ‘Poisson vs Gaussian, Part 2’ »

Apr 9th, 2009| 07:01 pm | Posted by vlk

We astronomers are rather fond of approximating our counting statistics with Gaussian error distributions, and a lot of ink has been spilled justifying and/or denigrating this habit. But just how bad is the approximation anyway?

I ran a simple Monte Carlo based test to compute the expected bias between a Poisson sample and the “equivalent” Gaussian sample. The result is shown in the plot below.

The jagged red line is the fractional expected bias relative to the true intensity. The typical recommendation in high-energy astronomy is to bin up events until there are about 25 or so counts per bin. This leads to an average bias of about 2% in the estimate of the true intensity. The bias drops below 1% for counts >50. Continue reading ‘Poisson vs Gaussian’ »

Apr 2nd, 2009| 12:00 pm | Posted by hlee

I cannot remember when I first met **Chernoff face** but it hooked me up instantly. I always hoped for confronting multivariate data from astronomy applicable to this charming EDA method. Then, somewhat such eager faded, without realizing what’s happening. Tragically, this was mainly due to my absent mind. Continue reading ‘[MADS] Chernoff face’ »

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Apr 1st, 2009| 02:55 pm | Posted by TomLoredo

Woncheol Jang pointed me to the following web site describing a proposal opportunity at DOE that may be of interest to readers of this list:

Mathematics for Analysis of Petascale Data

http://www.science.doe.gov/grants/FAPN09-10.html

The Office of Advanced Scientific Computing Research (ASCR) of the Office of Science (SC), U.S. Department of Energy (DOE), hereby announces its interest in receiving grant applications for research addressing the mathematical challenges involved in extracting insights from extremely large datasets (“petascale data”) and investigating fundamental issues in finding key features and understanding the relationships between those features.

…

All applications should address the potential for advances in mathematical methods or numerical algorithms and not just the application of methods and algorithms to a specific science problem, no matter how challenging.

…

This solicitation seeks applications for basic research in mathematical models, methods and tools for the representation, analysis, and understanding of petascale data.

They specifically mention data from physics simulations and observational data from cosmology as examples in the description.

Letters of Intent (required) are due 15 April, proposals are due 29 May. $4M is available for FY09; awards may be for up to 3 yr.