The AstroStat Slog

BEHR (Bayesian Estimation of Hardness Ratios) is a C program designed to compute hardness ratios – summary statistics of a spectrum for faint X-ray sources – while explicitly modeling the arrival of photons as an inhomogeneous Poisson process and properly accounting for background contamination.

In the previous versions of BEHR, users are allowed to choose only the gamma prior distribution that is parametrized in terms of an index (shape) parameter and a scale parameter. But there was need for using a tabulated prior distribution that does not necessarily look like a gamma distribution. The use of a tabulated prior distribution gives us two advantages:

1. BEHR becomes more flexible in terms of prior specification. Users can use any prior distribution they want as long as it is tabulated.
2. Bayesian updating can be done without inaccurate approximation. When we update a prior distribution to a posterior distribution using previously observed data, we do not have to use an approximate gamma distribution based on the method of moments. Instead, we use a tabulated prior distribution by making a grid for Poisson intensities and evaluating posterior probability at each grid.

Currently, BEHR supports the tabulated prior distribution only under the Gibbs mode, but it will be updated for the quadrature mode.