I recently completed a series on Bayesian Statistics and BI, with the good fortune of a capstone interview with venerable statistician Brad Efron. The more I get into Bayesian thinking, the more I realize Efron is correct: To be a Bayesian, an analyst must always think like one. The current ascendance of Bayesian analysis in the statistical world is, I believe, a boon for BI.
In its simplest form, Bayes Law can be explained as follows: If E is an event or hypothesis of interest and D is data or evidence, we are concerned about P(E|D), the probability of hypothesis E given or conditioned on evidence D. P(E|D) is calculated as:
P(E)*(P(D|E)/(P(D|E)*P(E) + P(D|~E)*P(~E)), where ~E means not event E . Note the "(" before the first P(D|E).
The holy grail P(E|D) is often called the posterior probability, while P(E) is known as the prior, P(D|E) is the likelihood function, and the ugly right-side denominator is a normalizing factor. So we have the posterior probability = prior probability*likelihood function/normalizing factor. What makes this mumbo-jumbo pertinent is that it provides a powerful way of helping BI realize its charter of facilitating sequential and adaptive organizational learning. We can assess the posterior probability of an important business outcome given a shift in company strategy or operations by establishing the known prior probabilities and wrestling through a likelihood function. The calculated posterior probabilities from step one then become the priors for step two, and the posteriors ~= priors*likelihood cycle repeats, promoting adaptive learning.
Steve Miller's blog can also be found at miller.openbi.com.
Sorry for the confusion.