The Benefits of the Bayesian Approach V.S. the Frequentist Approach When Dealing with Low Data Samples.
Foussier, P.
3F

Everything starts with the data ... (there is no substitute). The traditional way for building a CER from these existing data (the "regression analysis" you generally use) is often called the "frequentist approach" because it is only based on the occurrences of costs among your data. This is fine (although not fully satisfactory as I previously mentioned it) when you have nothing more than your data.

However we know that experienced cost analysts very often have some idea(s) of what the CER should be - about - and the question is then : how can I add these ideas to the data when I prepare a CER ? The "bayesian approach" is the answer to this question.

This bayesian approach - of which theory is now very well established - is very different from the frequentist approach : - in the frequentist approach the coefficients of the CER are defined as fix values ; the purpose of the approach is to determine these values, with the lowest level of uncertainty (presented as the confidence interval). - in the bayesian approach the coefficients of the CER are defined as random values. This may sound strange, but, when you think about it, this definition is much closer to reality than the hypothesis of the frequentist approach ; after all there is no theoretical reason for the coefficients of a CER to keep the same value for all the products of the data base. We can expect these coefficients to slightly change from one product to another one (this is a characteristic of human activities).

How are the "ideas" mentioned earlier communicated to the CER building process ? Very simply : the cost analyst expresses his ideas by a probability distribution of the coefficients. In order not to make the computations too complex, this "a priori" distribution is generally Gaussian (if the cost analyst has no opinion, a flat distribution is used) : in other words the cost analyst says "from my experience I expect such a coefficient to follow a Gaussian distribution with this average value and this variance".

The purpose of the bayesian approach is then to compute (computations are rather complex but a computer can easily do it !) an "a posteriori distribution", of the coefficient, using the data of the base.

Several examples will show the interest of this approach. Of course, as you may expect, the interest is especially valuable when the number of data is limited and when they are scattered : in such a case the frequentist approach may give anything and the result cannot really be used.