  Giant impacts by comets and asteroids have probably had an important
influence on terrestrial biological evolution. We know of around 180 high
velocity impact craters on the Earth with ages up to 2400Myr and diameters up
to 300km. Some studies have identified a periodicity in their age distribution,
with periods ranging from 13 to 50Myr. It has further been claimed that such
periods may be causally linked to a periodic motion of the solar system through
the Galactic plane. However, many of these studies suffer from methodological
problems, for example misinterpretation of p-values, overestimation of
significance in the periodogram or a failure to consider plausible alternative
models. Here I develop a Bayesian method for this problem in which impacts are
treated as a stochastic phenomenon. Models for the time variation of the impact
probability are defined and the evidence for them in the geological record is
compared using Bayes factors. This probabilistic approach obviates the need for
ad hoc statistics, and also makes explicit use of the age uncertainties. I find
strong evidence for a monotonic decrease in the recorded impact rate going back
in time over the past 250Myr for craters larger than 5km. The same is found for
the past 150Myr when craters with upper age limits are included. This is
consistent with a crater preservation/discovery bias modulating an otherwise
constant impact rate. The set of craters larger than 35km (so less affected by
erosion and infilling) and younger than 400Myr are best explained by a constant
impact probability model. A periodic variation in the cratering rate is
strongly disfavoured in all data sets. There is also no evidence for a
periodicity superimposed on a constant rate or trend, although this more
complex signal would be harder to distinguish.
