It is all about Probabilities!

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It is all about Probabilities!

• The Poisson Likelihood
• Probability Calculus Bayes Theorem
• Priors the gamma distribution
• Source intensity and background marginalization
• Hardness Ratios (BEHR)

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Deriving the Poisson Likelihood
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Probability Calculus
A or B p(AB) p(A) p(B) - p(AB) A and B
p(AB) p(AB) p(B) p(BA) p(A) Bayes Theorem
p(BA) p(AB) p(B) / p(A) p(Model Data)
p(Model) p(DataModel) / p(Data)
prior distribution
posterior distribution
likelihood
normalization
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Priors
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Priors

• Incorporate known information
• Forced acknowledgement of bias
• Non-informative priors
• flat
• range
• least informative (Jeffreys)
• gamma

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Priors
the gamma distribution
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Panning for Gold Source and Background
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Hardness Ratios
Simple, robust, intuitive summary Proxy for
spectral fitting Useful for large samples Most
needed for low counts
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BEHR
http//hea-www.harvard.edu/AstroStat/BEHR/
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