"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.
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 one of 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)."
Wikipedia: Credibility Theory
"Credibility theory is the art of combining different collections of data to obtain an accurate overall estimate. It provides actuaries with techniques to determine insurance premiums for contracts that belong to a (more or less) heterogeneous portfolio, where is limited or irregular claim experience for each contract but ample claim experience for the portfolio. Credibility theory can be seen as one of quantitative tools that allows the insurers to perform experience rating, that is, to adjust future premiums based on past experiences. In many cases, a compromise estimator is derived from a convex combination of prior mean and the mean of the current observations. Credibility theory began with papers by Mowbray (1914) and Whitney (1918)."
Source: Payandeh Najafabadi, Amir T. (2010). A new approach to the credibility formula. Munich Personal RePEc Archive.
Department of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
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