Revising opinions in statistics
Researchers who use personal probability can proceed as follows:
- A statistical model for the data generating process is assumed. The model might specify that the data follows a normal distribution with an unknown mean.
- The researcher describes his opinion about the unknown mean as having a normal distribution centered at 10 with a standard deviation of 2. This would be called the researcher's prior distribution for the mean.
- With the likelihood function of the observed data and the probabilistic description of his opinion, the researcher can calculate (using Bayes' theorem) the appropriate opinion consistent with both sources of information. This is called the posterior distribution.