1 / 14

If you give a man a fish he will eat for a day. If you teach a man to fish he will eat for a lifetime.

POISSON TALES. FISH TALES. If you give a man Cash he will analyze for a day. If you teach a man Poisson, he will analyze for a lifetime. . If you give a man a fish he will eat for a day. If you teach a man to fish he will eat for a lifetime. . It is all about Probabilities!.

oria
Download Presentation

If you give a man a fish he will eat for a day. If you teach a man to fish he will eat for a lifetime.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. POISSON TALES FISH TALES If you give a man Cash he will analyze for a day. If you teach a man Poisson, he will analyze for a lifetime. If you give a man a fish he will eat for a day. If you teach a man to fish he will eat for a lifetime.

  2. It is all about Probabilities! • The Poisson Likelihood • Probability Calculus – Bayes’ Theorem • Priors – the gamma distribution • Source intensity and background marginalization • Hardness Ratios (BEHR)

  3. 0 1 N,t®¥ Deriving the Poisson Likelihood

  4. marginalization :: p(a|D) = p(ab|D) db Probability Calculus A or B :: p(A+B) = p(A) + p(B) - p(AB) A and B :: p(AB) = p(A|B) p(B) = p(B|A) p(A) Bayes’ Theorem :: p(B|A) = p(A|B) p(B) / p(A) p(Model |Data) = p(Model) p(Data|Model) / p(Data) prior distribution posterior distribution likelihood normalization

  5. Priors

  6. Priors • Incorporate known information • Forced acknowledgement of bias • Non-informative priors • – flat • – range • – least informative (Jeffrey’s) • – gamma

  7. Priors the gamma distribution

  8. Panning for Gold: Source and Background

  9. Hardness Ratios Simple, robust, intuitive summary Proxy for spectral fitting Useful for large samples Most needed for low counts

  10. BEHR http://hea-www.harvard.edu/AstroStat/BEHR/

More Related