Posts tagged ‘PDF’

Poisson vs Gaussian, Part 2

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’ »

my first AAS. VI. Normalization

One realization of mine during the meeting was related to a cultural difference; therefore, there is no relation to any presentations during the 212th AAS in this post. Please, correct me if you find wrong statements. I cannot cover all perspectives from both disciplines but I think there are two distinct fashions in practicing normalization. Continue reading ‘my first AAS. VI. Normalization’ »

[ArXiv] 4th week, Nov. 2007

A piece of thought during my stay in Korea: As not many statisticians are interested in modern astronomy while they look for data driven problems, not many astronomers are learning up to date statistics while they borrow statistics in their data analysis. The frequency is quite low in astronomers citing statistical journals as little as statisticians introducing astronomical data driven problems. I wonder how other fields lowered such barriers decades ago.

No matter what, there are preprints from this week that may help to shrink the chasm. Continue reading ‘[ArXiv] 4th week, Nov. 2007’ »

[ArXiv] 1st week, Nov. 2007

To be exact, the title of this posting should contain 5th week, Oct, which seems to be the week of EGRET. In addition to astro-ph papers, although they are not directly related to astrostatistics, I include a few statistics papers which may be profitable for astronomical data analysis. Continue reading ‘[ArXiv] 1st week, Nov. 2007’ »