  This paper presents the non-homogeneous Poisson process (NHPP) for modeling
the rate of fast radio bursts (FRBs) and other infrequently observed
astronomical events. The NHPP, well-known in statistics, can model changes in
the rate as a function of both astronomical features and the details of an
observing campaign. This is particularly helpful for rare events like FRBs
because the NHPP can combine information across surveys, making the most of all
available information. The goal of the paper is two-fold. First, it is intended
to be a tutorial on the use of the NHPP. Second, we build an NHPP model that
incorporates beam patterns and a power law flux distribution for the rate of
FRBs. Using information from 12 surveys including 15 detections, we find an
all-sky FRB rate of 586.88 events per sky per day above a flux of 1 Jy (95\%
CI: 271.86, 923.72) and a flux power-law index of 0.91 (95\% CI: 0.57, 1.25).
Our rate is lower than other published rates, but consistent with the rate
given in Champion et al. 2016.
