His great contribution to mathematics was Bayes Theorem, seen on the t-shirt to the left. Bayes came up with what is called inverse probability at at time when only forward probability was generally known.
In short, if you know the probability of some event B given some other event A, and if you also know the probabilities of A and B, you can figure out the inverse probability of A given B.
Many people think -incorrectly- that forward and inverse probabilities are the same. That is, if a given test detects, say, 99.9% of people who have used illegal drugs recently, they think anyone who fails that test is 99.9% certain to have used illegal drugs. NOT SO! In some cases, "false positives" can outnumber "true positives" by a factor of two or more.
Here is a great example of how much forward and inverse probabilities may differ. The probability a person is female given that they are pregnant is: P(F;P) = 100%. But probability a person in pregnant given that they are female is: P(P;F) ~ 3%
QUANTIFYING THE RISK OF OIL EXPLORATION
Bayesian probability means, using oil exploration as a practical example, you can figure out the probability you will strike commercially-viable oil if you drill a well at a particular location given that a seismic test was positive. With the value of petroleum going up and down so rapidly in the past few years, this illustrates the fine line between making a big profit and going broke in the oil patch.
MY BAYESIAN AI ADVISOR
Some years ago I created a Bayesian AI ("Artificial Intelligence") Advisor spreadsheet that runs on Excel. I've recently improved the Bayesian AI Advisor and today I published a new Google Knol that explains its use. You are invited to download the Bayesian AI Advisor to your PC.
Of course, Bayesian probability applies to many areas in addition to oil exploration. My Knol looks at targeted marketing (what is the chance a given person will buy my product given that he or she has bought some other product in the past?) and medical testing (what is the chance a person has a particular disease given that he or she tests positive?)QUICK LOOK AT THE RESULTS FOR "DRILL HERE? DRILL NOW?"
The figure shows three cases for oil exploration with three different recomendations. I think this illustrates the risk of oil exploration and that it could be applied to the financial implications of investment in alternative forms of energy.
The user has to input the data in the clear cells, based on known probabilities and financial factors. The leftmost panel shows a case where the Bayesian AI Advisor recommends Test first, If Test is Positive, do the Procedure - in other words, do a seismic test and, if the results are positive, drill.
The middle panel shows the case where all factors are the same except the value of petroleum has gone down by 15% and now the recommendation is Hopeless venture. (Can you reduce expected ROI?) - in other words, do not waste money doing the seismic testing because, even if you get a positive result, it will not pay to do the drilling given the financial assumptions you have entered, unless you are willing to increase the risk to your investors by reducing the expected Return on Investment.
The rightmost panel shows the case where, in a different location in the oil patch, the probabilities of success are much better. Now the recommendation is No Need to Test. Go ahead with the Procedure. - in other words, this area is so good you don't have to waste money doing seismic testing, just go right ahead and drill and you are likely to strike commercially-viable oil and get rich.