Prediction is very hard. We have no choice but to use the past events to make a prediction about the future events. If you can detect a trend or cycle then the job gets easier but sometimes there is neither a trend nor a cycle. Even when there is a trend or cycle it may be impossible to detect it using a short look-back period. In these situations Bayesian statistics can be more useful.
The reason Bayesian statistics/probability is so controversial is that it allows beliefs to enter into the equations.
Recently, there was an article about Bayesian statistics in NYT by F.D. Flam
The best review I have seen on the subject of Bayesian statistics and probability is
Notes on Bayesian Confirmation Theory by Michael Strevens
Other tutorials worth mentioning (I will add to this list as I discover more)
- Bayesian probability article at Wikipedia
- Statistics portal at Wikipedia
- Bayesian statistic article at Scholarpedia
- Introduction to Bayesian Learning by Aaron Hertzmann
- An Introduction to Bayesian Statistics Without Using Equations by Tomoharu Eguchi