The ‘system’ behind the Google robotic cars that have driven themselves for hundreds of thousands of miles on the streets of several US states without being involved in an accident, or violating any traffic law, whilst analyzing enormous quantities of data fed to a central onboard computer from radar sensors, cameras and laser-range finders and taking the most optimal, efficient and cost effective route, is built upon the 18th-century math theorem known as Bayes’ rule.

In 1996 Microsoft’s Bill Gates described their competitive advantage as its ‘expertise in Bayesian networks,’ patenting a spam filter in 1998 which relied on Bayes Theorem. Other tech companies quickly followed suit and adapted their systems and programming to include Bayes theorem.

During World War II Alan Turing had used Bayes Theorem to crack the Enigma code, potentially saving millions of lives, and is credited with helping the allied forces victory.

Artificial Intelligence was given a new lease of life when in the early 1980’s Professor Judea Pearl of UCLA’s Computer Science Department and Cognitive System Lab introduced Bayesian networks as a representational device. Pearl’s work showed that Bayesian Networks constitute one of the most influential advances in Artificial Intelligence, with applications in a wide range of domains.

Bayes Theorem is based on the work of Thomas Bayes as a solution to a problem of inverse probability. It was presented in “*An Essay towards solving a Problem in the Doctrine of Chances*” read to the Royal Society in 1763 after Bayes’ death (he died in 1761). Put simply Bayes rule is a mathematical relationship between probabilities, which allows the probabilities to be updated in light of new information.

Before the advent of increased computer power Bayes Theorem was overlooked by most statisticians, scientists and in most industries. Today, thanks to Professor Pearl, Bayes Theorem is used in robotics, artificial intelligence, machine learning, reinforcement learning and big data mining. IBM’s Watson, perhaps the most well known AI system, in all its intricacies, ultimately relies on the deceivingly simple concept of Bayes’ Rule in negotiating the semantic complexities of natural language.

Bayes Theorem is frequently behind the technology development of many of the multi-billion dollar acquisitions we read about, and certainly a core piece of technology behind the billions in profits at leading tech companies, from Google’s search to LinkedIN, Netflix’s and Amazon’s recommendation engines, and will play an even more important role in future developments within automation, robotics and big data.

Professor Pearl, through his work in the Cognitive System Lab, recognized the problems of human psychology in software development and representation. In 1984 he published a book simply called *Heuristics* (Intelligent Search Strategies for Computer Problem Solving).

Pearl’s book relied on research by the founder of Behavioral Economics Daniel Kahneman and Amos Tversky and particularly their work with Paul Slovic: *Judgment under Uncertainty: Heuristics and Biases*. Cambridge University Press, 1982, where they confirmed their own reliance on Bayes Theorem:

Ch.25: Conservatism in human information processing: “Probabilities quantify uncertainty. A probability, according to Bayesians like ourselves; is simply a number between zero and one that represents the extent to which a somewhat idealized person believes a statement to be true…. Since such probabilities describe the person who holds the opinion more than the event the opinion is about, they are called personal probabilities.” (Page 359)

Kahneman (Nobel Prize in Economics) and Tversky showed Bayesian methods more closely reflect how humans perceive their environment, respond to new information, and make decisions. The theorem is a landmark of logical reasoning and the first serious triumph of statistical inference; Bayesian methods interpret probability as the degree of plausibility of a statement.

Kahneman and Tversky especially highlighted the heuristics and biases where Bayes Rule can overcome our irrational decision-making and this is why so many of the tech companies are seeking to train their engineers and programming staff with behavioral economics knowledge. We use the availability heuristic to assess probabilities rather than Bayesian equations. We all know that this gives way to all sorts of judgmental errors: a belief in the law of small numbers and a tendency towards hindsight bias. We know that we anchor around irrelevant information and that we take too much comfort in ever-more information that seems to provide us confirmation of our beliefs.

**The representativeness heuristic**

Heuristics are described as “judgmental shortcuts that generally get us where we need to go – and quickly – but at the cost of occasionally sending us off course.

When people rely on representativeness to make judgments, they are likely to judge wrongly because the fact that something is more representative does not make it more likely. This heuristic is used because it is an easy computation (Think Zipf’s law and human behavior – the principle of least effort). The problem is that people overestimate their ability to accurately predict the likelihood of an event. Thus it can result in neglect of relevant base rates (base rate fallacy) and other cognitive biases, especially confirmation bias.

The base rate fallacy describes how people do not take the base rate of an event into account when solving probability problems and is frequently and error in thinking.

**Confirmation bias**

Confirmation bias is the tendency of people to favor information that confirms their beliefs or hypotheses. Essentially people are prone to misperceive new incoming information as supporting their current beliefs.

It has been found that experts reassess data selectively, depending on their prior hypotheses over time. Bayesian statisticians argue that Bayes’ s theorem is a formally optimal rule about how to revise opinions in the light of evidence. Nevertheless, Bayesian techniques are, so far rarely utilized by management researchers or business practitioners in the wider business world.

Eliezer Yudkowsky of the Machine Intelligence Research Institute has written a detailed introduction of Bayes Theorem using behavioral economics examples and machine learning, which I highly recommend.

**Time to think Bayesian and Behavioral Economics**

As the major tech companies are showing, Bayesian and Behavioral Economics methods are well suited to address the increasingly complex phenomena and problems faced by 21st-century researchers and organizations, where very complex data abound and the validity of knowledge and methods are often seen as contextually driven and constructed.

Bayesian methods that treat probability as a measure of uncertainty may be a more natural approach to some high-impact management decisions, such as strategy formation, portfolio management, and decisions whether or not to enter risky markets.

**If you are not thinking like a Bayesian, perhaps you should be. **

Pretty good synopsis. The only thing I think you should add is a section on models. Bayes is really just a way to test models. In that sense to be used for learning something, you need to have multiple models to test. That means your ability to really apply Bayes wonderful theorem is dictated by a few extra-bayesian processes. How good are the models in the problem space you are in? Are those models well parameterized? Do you need the global best model or will local best-model work well enough? These are the hard parts for humans to get right, Bayes rule is a very simple first step.

Clinical trials have begun to incorporate Bayesian logic, which enables them to become “adaptive” and incorporate information into the trial design as the trial progresses and new information emerges. The result is shorter trials, and the ability to home in on subpopulations of patients for whom the intervention has discretely different results (positive or negative.)

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