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Credibility theory
Credibility theory is a branch of actuarial science used to quantify how unique a particular outcome will be compared to an outcome deemed as typical. It was developed originally as a method to calculate the risk premium by combining the individual risk experience with the class risk experience. Credibility can be calculated using two popular approaches, Bayesian and Buhlmann.
==Types of Credibility==
In Bayesian credibility, we separate each class (B) and assign them a probability (Probability of B). Then we find how likely our experience (A) is within each class (Probability of A given B). Next, we find how likely our experience was over all classes (Probability of A). Finally, we can find the probability of our class given our experience. So going back to each class, we weight each statistic with the probability of the particular class given the experience.
Buhlmann credibility works by looking at the Variance across the population. More specifically, it looks to see how much of the Total Variance is attributed to the Variance of the Expect Values of each class (Variance of the Hypothetical Mean), and how much is attributed to the Expected Variance over all classes (Expected Value of the Process Variance). Say we have a basketball team with a high number of points per game. Sometimes they get 128 and other times they get 130 but always in between the two. Compared to all basketball teams this is a relatively low variance, meaning that they will contribute very little to the Expect Value of the Process Variance. Also, their unusually high point totals greatly increases the variance of the population, meaning that if the league booted them out, they'd have a much more predictable point total for each team (lower variance). So, this team is definitely unique (they contribute greatly to the Variance of the Hypothetical Mean). So we can rate this team's experience with a fairly high credibility. They often/always score a lot (low Expected Value of Process Variance) and not many teams score as much as them (high Variance of Hypothetical Mean).
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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