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Available prior families

The full set of priors recognized by the bayes command is listed in the command reference; the table there gives the $\ln p(\theta)$ expression for each. The shapes most often useful for X-ray work fall into three classes:

  • Scale parameters — normalizations, column densities, and other quantities that are bounded below by zero and whose order of magnitude is itself uncertain. Use jeffreys (uniform on $\log\theta$), or lognormal if you have a preferred order of magnitude with a width on $\ln\theta$. Both require strictly positive support; the parameter's hard lower limit must be greater than zero before either is selected.

  • Location parameters — temperatures, line centroids, photon indices, and other quantities defined on a finite linear range. Use gauss (or cauchy if you want heavier tails to avoid undue shrinkage), or cons if the parameter is well-constrained by the data alone over its allowed range.

  • Bounded parameters — covering fractions, abundances normalized to unity, and angles. Use beta on $[0,1]$, isotropic for an angle drawn from a uniform direction on the sphere, or powerlaw for a truncated power-law distribution.
Two further specialized forms are available: shiftedlognormal for quantities bounded below by a non-zero value (useful for black-hole spins displaced from zero), and halfnormal for a mildly informative prior on a positive parameter without committing to a particular scale. exp and gamma are useful when prior knowledge takes the form of a rate parameter or shape-and-rate pair from a previous analysis.

next up previous contents
Next: Practical advice Up: Priors Previous: Why priors matter, and   Contents