Revising opinions in statistics
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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 of a prior distribution for the unknown parameters of the model. So the prior distribution of the unknown mean might be a normal distribution centered at 10 with a standard deviation of 2.
- The data is then observed, and 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.