I recently got my hands on Bayesian Belief Networks to model multi-dimensional decision problems, which include objective and subjective data (“beliefs”) with varying degrees of under uncertainty. To choose a (non)trivial example one can look at the question “Does she/he like me?” after you met this attractive person, randomly picking the same book on machine learning from the shelf in the bookshop, the person smiled at you, chatted for 5 minutes, and gave you his/her phone number. One can construct a conditional probability table for each factor, eg samebookinterest (yes, no) x likesme (yes, no) and derive a probability of “likesme” depending on the various facts. In situations, where one does not have the information eg because you met in the swimming pool and could not exchange any phone numbers, one could use the marginal distribution of people exchanging their phone numbers (conditional on being in a swimming pool) to draw some inferences. In situations, where one has received a strong indicator of “likesme”, other input factors can be “explained away”. For example, if you got a strong indicator of “likesme”, eg kiss on the cheek, then even if the marginal/prior probability of sharing one’s phone number is low, it seems very unlikely that the person’s would not have shared his phone number with you.
This type of thinking can also be applied to a wide-range of business problems, eg estimation of probability of technical success of phase 3 trials in drug development.
Although simplest examples can be calculated with paper and pencil, for realistic models statistical software such as open-source software R (cf packages gRain, Rgraphviz) or the excellent commercial software AgenaRisk (Professional, Lite, and Free versions available) will be necessary.