Bayes rule allows us to use external knowledge when computing probabilities. This gives us a way to update a prior probability distribution (aka our previous estimate) of a parameter to get the posterior distribution (aka our future prediction) given new data or information about that parameter. In a real world setting, this might involve estimating traffic conditions so that the map app on your phone can provide updated predictions for your commute time. These estimates improve over time as they incorporate new data. Bayes rule provides a principled method of incorporating information, both subjective and objective, into the prior to produce the posterior distribution. It properly modifies your prior beliefs as new data and facts are obtained.
- The Theory That Would not Die by S. B. McGrayne, 2011, Yale Press, New Haven CT
- Optimal Statistical Decisions WCL Edition by M. H. DeGroot, 2004, Wiley, New York
- Statistical Decision Theory and Bayesian Analysis 2nd Ed by J. O. Berger, 1985 Springer, New York
- “An essay towards solving a problem in the doctrine of chances” Philosophical Transactions Royal Society (1783) Vol 53, pp 370-418