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
  

Advertisment as a game of chance

Let there be no doubt: Ads are a gamble. Their purpose is to increase the chance someone buys your product. I realized this only when i red Seth Godin's thought: "If your ads work throw all the money on them." I think he failed to understand that there can be no determinism between ads and turnover, since an ad is never (1) forcing someone to buy or (2) informing that there is a product fulfilling a desperate need. In both cases: p(ads)=1

What we see is: there is a correlation between ads and turnover. Especially you don't know if the campaign works until you try it, a.k.a. subjective probability. Therefore we should model advertisement as a probabilistic game. Therefore the Kelly Criterion is highly relevant.

Thank you for listening

How should I call it?

Did you know that german is the only language that preferrs notebook over laptop?

Monty Hall Problem

The Monthy Hall Problem shows how little intuition humans bear to solve probabilistic enigmas.

Tree doors, one hides a price. The candidate chooses one and then the show master opens another one bearing no price. Would the candidate increase his probability in choosing the leftover door, giving up his first choose?

The astonishing answer: the two doors left (the first-chosen and the remaining-closed) are not of the same probability the price-doors. But the remaining-closed now has a probability of 2/3 in comparison with the first-chosen 1/3.

The trick: the show-master opened a door, given the candidates first choice. in 2/3 of the cases he had to avoid the price-hiding door, indicating that the other bears the price. only if the candidates original try was right, the show-master could open any other door.

I modeled this as BN with GeNie:

The candidate chose State0, the quiz-master showed State1 and the price probability resulted in p(Door0)= 1/3 and p(Door3)= 2/3.

Download the original Genie Ziege.xdsl.

Belief Nets

Based on the Bayesian Theorem we are able to model a network of evidences and influences to conduce a prediction: a Bayesian Network or Belief Net (BN). Somebody found out, such BNs beat other techniques in predicting certain sportsbets.

BNs allow an expert to map his expertise as causal dependencies leading to a certain prediction.

While Humans have shown skills in doing so, there is evidence that they fail in computing the overall estimate well.

While the domain expert and data available to us build up the nodes and their node probability table (NPT), the reasoning is left to Bayesian Theorem. Machine Prediction with a human designer.

A second benefit is the documentation of the evidences and influences leading to prediction and decisions. The state of the art is in combining Decision Analysis and Belief Nets in the model.

With University of Pittsburgs GeNie modeling tool, the world of Belief Nets opens for experimenting also to the interested layman.

Lets share some experiments!