Can Bayesian statistics help pinpoint dating?

The crux of Bayesian statistics is Bayes’ theorem. This (deceptively) simple mathematical expression relates the probability of two things co-occurring, one of which is directly measurable and the other not. What Bayes’ theorem allows us to do is use the former to draw conclusions about the latter. A simple example might involve rainfall measurements at a weather station. If records exist of daily rainfall at the station for several years, and then a record of 100 mm is found without a date, can anything be said about which day of the year it is most likely to have come from? Bayes theorem tells us that our best estimate (the posterior) will be achieved by combining the probability of getting that particular measurement in the first place (the likelihood) with any other information we might have about the possible day it was made (the prior). In this case, the likelihood is the chance of getting 100 mm of rain on any given day of the year. We can work this out using the records we have of past measurements. It might turn out, for example, that 100 mm is extremely unlikely at some times of the year. In terms of relevant prior information, we might know that the station was never occupied during the winter months. On the basis of these two things, we can begin to hone in on which days of the year the observation was most likely to have been made.