Why we should base our decisions on probabilistic networks

We know from behavioral economics that humans are inherently biased in their decisions.
Basically "the expectations we have in our intuitive system are different than in our reasoning system" (D. Kahneman).
Constructing a probability network enables us to use our reasoning system with the qualitative structure of the influences in our decisions, while leaving the actual inference to the conceptual framework of Bayesian statistics. Because this is were usually our intuitive system kicks in and biases us towards wrong decisions. Because we are build to survive in nature, not to reason about the risk of complex derivative finance products.
Having a probabilistic network documents our decisions and allows a Shewart-cycle of improvements.
We would be able to peer review our decision networks and building up a pattern language of optimal decisions. As Steven Wolfram tried for the natural sciences by collecting algorithmic particles describing nature, we could try to make a executable Wiki of fundamental decision patterns describing recurring decision problems.

Influence Diagrams

A Bayesian network is a probabilistic network for reasoning under uncertainty, whereas an influence diagram is a probabilistic network for reasoning about decision making under uncertainty. - Kjaerulff, Uffe; Madsen, Anders

An Influence Diagram consists of observations, decisions, utility functions and a precedence ordering. It extends the Bayesian Network by a sequence of decisions in time, their utility and their costs.

For example the Influence Diagram above shows the utility of treating apple trees under the observation that they lose leaf. This can be because of drought or sickness. If the phenomenon persist until later when the harvesting time gets nearer, we might lose income.
If we want to maximize income, a cure is barly recommended by the Bayesian inference. It will cost us € 80 and give us a gross income of € 176.  We earn € 96 over the € 84 gross for net without treat.
Download a version of the apple tree problem without barren variables leaf' and dry'.
Download GeNie

Understanding Bayesian Theorem

Eliezer S. Yudkowsky says:

Maybe you see the theorem, and you understand the theorem, and you can use the theorem, but you can't understand why your friends and/or research colleagues seem to think it's the secret of the universe. Maybe your friends are all wearing Bayes' Theorem T-shirts, and you're feeling left out. [...] What matters is that Bayes is cool, and if you don't know Bayes, you aren't cool.

His first example in a nutshell (by M. H. Herman):

Here's a story problem about a situation that doctors often encounter: 1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?

Only around 15% of doctors get it right (Casscells, Schoenberger, and Grayboys 1978; Eddy 1982; Gigerenzer and Hoffrage 1995; and many other studies.)…On the story problem above, most doctors estimate the probability to be between 70% and 80%, which is wildly incorrect…The correct answer is 7.8%, obtained as follows: Out of 10,000 women, 100 have breast cancer; 80 of those 100 have positive mammographies. From the same 10,000 women, 9,900 will not have breast cancer and of those 9,900 women, 950 will also get positive mammographies. This makes the total number of women with positive mammographies 950+80 or 1,030. Of those 1,030 women with positive mammographies, 80 will have cancer. Expressed as a proportion, this is 80/1,030 or 0.07767 or 7.8%”

I modeled this as BN with GeNie and came to the right result:
yes = 7.8% genie displays it rounded to 8%
I learned hereby:

• I don't understand Bayes well yet
• I don't need to understand Bayes to model a Bayesian Network successfully