bayes

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The HEASARC and NuSTAR teams are greatly saddened by the sudden passing of Katja Pottschmidt. Most recently Katja was the lead scientist for the NuSTAR Guest Observer Facility (GOF), a role she had supported for many years. During her science career she worked on many other high energy astrophysics missions and played an integral role in advancing our knowledge of the universe. She was a wonderful colleague and friend and will be keenly missed by all who knew her.

bayes

set up for Bayesian inference

Syntax:	bayes	<option>
	bayes	<mod par #> <prior type> [<hyperparameters>]

where <option> ::= [off |on |cons]. If a parameter number is given as the first argument then this command sets up the prior for the specified model parameter but does not turn Bayesian inference on. If the first argument to the bayes command is not a parameter number then one of the options off, on, or cons is used. The first two turn Bayesian inference off or on, while cons turns Bayesian inference on and gives all parameters a constant prior. The options for prior types are as follows:

Prior type	Log(prior)
cons	0
exp	$-p/h_1-\ln{(h_1)}$
jeffreys	$-\ln{(p)}$
gauss	$-0.5\ln{(2\pi h_2)}-0.5(h_1-p)^{2}/h_2^{2}$
lognormal	$-\ln{(p \sqrt{2\pi} h_2)} -0.5(\ln{(p)}-\ln{(h_1)})^{2}/h_2^{2}$
gamma	$h_1\ln{(h_2)} + (h_1-1) \ln{p} - h_2 p - \ln{\Gamma(h_1)}$
cauchy	$-\ln{(1+(p-h_1)^2/h_2^2)} - \ln{\pi} - \ln{h_2}$
beta	$(h_1-1)\ln{x} + (h_2-1)\ln{(1-x)} - \ln{\Gamma(h_1+h_2)} - \ln{\Gamma(h_1)} - \ln{\Gamma(h_2)}$
studentst	$\ln{\Gamma((h_1+1)/2)} - 0.5\ln{(h_1\pi)} - \ln{\Gamma(h_1/2)} - ((h_1+2)/2)\ln{(1+p^2/h_1)}$
halfnormal	$-0.5\ln{(h_1^2\pi/2)} - p^2/(2h_1^2)$
powerlaw	for $h_2 \le p \le h_3$
isotropic	$\ln{(\sin{(p)})}$
shiftedlognormal	$-\ln{((p-h_1) \sqrt{2\pi} h_3)} -0.5(\ln{(p-h_1)}-\ln{(h_2)})^{2}/h_3^{2}$

Where p is the parameter value, h $_{\char93 }$ the hyperparameter values, and for the beta prior x = (p-min)/(max-min) where min and max are the parameter hard limits.

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HEASARC

High Energy Astrophysics Science Archive Research Center

bayes