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A master once told his student, "Decisions are only hard when there is little difference between the choices." The master was Professor Lofti Zadeh, the father of fuzzy logic. The student was Bruce D'Ambrosio, later a Professor of Artificial Intelligence at Oregon State University and co-developer with David Ullman of Bayesian Team Support (BTS), the decision methodology used in Accord. Similar to fuzzy logic, Bayesian decision theory can deal effectively with elements of uncertainty that are often a part of making a decision. However, Bayesian fits team decision making in ways that fuzzy logic cannot. Read on to learn how Bayesian methods can now be easily applied to improve decisions we make on a daily basis.

Bayesian decision theory roots date back to an obscure eighteenth century cleric, Reverend Bayes, who worried about how to combine evidence in legal matters. Its modern form traces to the work of John Von Neumann, mathematician and computer pioneer, in the 1940s, and J. Savage in the 1950s. Bayesian methods rely on measuring and managing the degree to which a person believes a proposition. The basic equations Bayes developed are used as the basis for updating beliefs in the light of new information; such updating is known as Bayesian inference.

BTS is based on Bayesian decision theory. It offers a well-founded computational theory for applying general knowledge to individual situations that are characterized by varying degrees of uncertainty and risk.

As classical statistics revolutionized the discovery of knowledge in the early 20th century, Bayesian decision theory is revolutionizing the application of knowledge in the 21st. This revolution is already underway:

  • Most major spam tools are based on Bayesian methods; As a classic example involving uncertainty, it gives the software the ability to learn which mail is spam and which isn't.
  • All speech recognition tools are Bayesian
  • Medical diagnosis is increasingly relying on Bayesian methods
  • Counter terrorism is using Bayesian method to determine who are the bad guys
  • Robotics and navigation use Bayesian method to navigate their environment.

Before we continue, it is important to compare and contrast Bayesian probabilities to what we learned in school. Bayesian probabilities look at the world differently from traditional probabilities (called Frequentist probabilities to differentiate it from Bayesian). Frequentists see probability as the long-run expected frequency of occurrence. P(A) = n/N, where n is the number of times event A occurs in N opportunities. Thus, Frequentists worry about measuring what has already happened to estimate the probabilities of future events. However, the Bayesian view of probability is related to degree of belief. It begins with a hypothesis about reality (often called a "prior") and updates this as more information is learned. It is a measure of the probability of an event given incomplete knowledge.

The difference between Bayesian and Frequentist approaches can be summarized in the table below.

Bayesian vs. Frequentist Approaches

Title Frequentist Bayesian
View Based on measurements of past events Based on estimates of future events provided by decision stakeholders
Evidence Measures past results Uncertain estimates of the world provided by decision stakeholders
Statistical results Based on data description Based on the chance of parameters meeting targets
Rigidity Must follow a set design Updated as new information becomes available
Use in making decisions Can only give evidence from past experience for decisions Tailored for decisions and leverages all levels of knowledge and uncertainty

Here's a simple example:
I am planning a picnic at noon tomorrow. I need to make a decision by 9 a.m. tomorrow morning whether or not to cancel it, which I will if it is going to rain. From my Frequentist perspective, I have data that tells the probability of it raining tomorrow based on the barometer and other data about today. All of this is based on past measurements that results in statistics such as "it rains 70% of the time on September 5." The only results I can get from this data are what have been designed into the reduction of the past data (i.e., I can't say anything about the probability of mice falling from the sky if that type of precipitation was not measured and modeled). This Frequentist view helps me make a decision only by providing me with evidence for a future event, but this is not enough.

The morning of the picnic I look outside. I am armed with the Frequentist prediction of 70% chance of rain. I look at the sky, the barometer, and my Ouija Board, and update the 70% (i.e. the prior) with new information: a Bayesian view. I would like a clear day (my target), but there are some clouds which make this possibility uncertain. Based on my best estimates I believe that the chance of rain is 60% and this is almost low enough for me not to cancel the picnic. The phone rings and it is my friend who lives thirty miles west of me. It is clearing over his house and the weather always comes from his direction. Based on this new information, I update my 60% "prior" to a 40% chance of rain and decide to have the picnic. I am truly a Bayesian.

Bayesian Team Support (BTS), the method in RDI's Accord, assists teams making a decision as they collect evidence to support or refute alternative courses of action. BTS assumes that the information collected is incomplete, uncertain, conflicting and evolving. As evidence accumulates across all stakeholders in the decision process, a single degree of belief in one of the alternatives will emerge as the best choice. To help bring this process to closure, Accord provides graphical and textual feedback to the team that includes satisfaction, risk, probability of being best and what to do next analyses to guide deliberation.

This material is derived from Making Robust Decisions by David G. Ullman, 2006 Book.

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