View source for 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 of a [[prior probability|prior]] distribution for the unknown [[parameter]]s 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 probability|posterior]] distribution.  

==See also==

*[[statistical theory]]
*[[applied statistics]]

[[Category:Statistics]]