All your bias are belong to us

Leccardi & Molendi (2007) have a paper in A&A (astro-ph/0705.4199) discussing the biases in parameter estimation when spectral fitting is confronted with low counts data. Not surprisingly, they find that the bias is higher for lower counts, for standard chisq compared to C-stat, for grouped data compared to ungrouped. Peter Freeman talked about something like this at the 2003 X-ray Astronomy School at Wallops Island (pdf1, pdf2), and no doubt part of the problem also has to do with the (un)reliability of the fitting process when the chisq surface gets complicated.

Anyway, they propose an empirical method to reduce the bias by computing the probability distribution functions (pdfs) for various simulations, and then averaging the pdfs in groups of 3. Seems to work, for reasons that escape me completely.

[Update: links to Peter's slides corrected]

One Comment
  1. hlee:

    1. All Chi-sq methods I’ve seen from astronomy literature (only a few, though) assume central Chi-sq dist’n. I wonder if there are works using non-central Chi-sq dist’n (considering your best fit minimizes variance but it’s biased).

    2. Above question leads these questions: how do I estimate bias? or make it asymptotically unbiased? or as you mentioned, average properly (model averaging is studied in statistics by both frequentists and bayesians)? or is non-central Chi-sq suitable?

    3. I don’t have any answers. People of different paradigms have various answers and opinions, and I like to learn.

    06-05-2007, 11:28 am
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