Bayesian confidence intervals for count rates (pwkit.kbn_conf)¶
pwkit.kbn_conf - calculate Poisson-like confidence intervals assuming a background
This module implements the Bayesian confidence intervals for Poisson processes in a background using the approach described in Kraft, Burrows, & Nousek (1991). That paper provides tables of values; this module can calculate intervals for arbitrary inputs. Requires scipy.
This implementation almost directly transcribes the equations. We do, however, work in log-gamma space to try to avoid overflows with large values of N or B.
Functions:
kbn_conf - Compute a single confidence limit. vec_kbn_conf - Vectorized version of kbn_conf.
TODO: tests!
- pwkit.kbn_conf.kbn_conf(N, B, CL)[source]¶
Given a (integer) number of observed Poisson events N and a (real) expected number of background events B and a confidence limit CL (between 0 and 1), return the confidence interval on the source event rate.
Returns: (Smin, Smax)
This interval is calculated using the Bayesian formalism of Kraft, Burrows, & Nousek (1991), which assumes no uncertainty in B and returns the smallest possible interval that satisfies the above properties.
Example: in a certain time interval, 3 events were recorded. Based on external knowledge, it is expected that on average 0.5 background events will be recorded in the same interval. The 95% confidence interval on the source event rate is
>>> kbn_conf.kbn_conf (3, 0.5, 0.95) <<< (0.22156, 7.40188)
which agrees with the entry in Table 2 of KBN91.
Reference info: 1991ApJ…374..344K, doi:10.1086/170124