Bayes’ Theorem in Action: Ongoing Applications
If you are not familiar with it, Bayes’ Theorem can be summarized in a simple, qualitative formula: “Initial Beliefs + Recent Objective Data = A New and Improved Belief.” An article in Scientific American talks about how the idea has been used in the past and how it is influencing many parts of our world today. This is a brief excerpt:
“A modern form comes from French mathematician Pierre-Simon Laplace, who, by recalculating the equation each time he got new data, could distinguish highly probable hypotheses from less valid ones … Many theoretical statisticians over the years have assailed Bayesian methods as subjective. Yet decision makers insist that they bring clarity when information is scarce and outcomes uncertain. During the 1970s John Nicholson, the U.S. submarine fleet commander in the Mediterranean, used Bayesian computer analysis to figure out the most probable paths of Soviet nuclear subs. Today Bayesian math helps sort spam from e-mail, assess medical and homeland security risks and decode DNA, among other things.”
The Theorem enjoys widespread use in science and engineering, but we find that it has interesting applications for investing. Although there is a qualitative aspect to investing that cannot be effectively reduced to math (or logic), the idea that an investor must effectively synthesize new information is essential to making good investment decisions. Processing this information in a disciplined way is especially critical to the decision-making process, and an investor must do his best to eliminate psychological tendencies that impair objectivity:
- As we have written about before, commitment bias is the tendency to misprocess subsequent data in support of an original decision. In other words, people typically twist new data to confirm a hypothesis rather than rejecting it and forming a new hypothesis incorporating these data. In the Bayes’ Theorem framework, the impact of this bias is that people never get to a “new and improved belief” because they do not incorporate information objectively. To combat this bias and to ensure we are consistently assessing and improving our rationale for investment decisions, we have a conscious practice of always asking ourselves how new information proves that previous conclusions and related assumptions are wrong (and, in fact, we do the same with previously gathered information). Our ideas have a chance to be effective investments if they are able to survive this ongoing assault to their credibility.
- On the other hand, an investor must exercise good judgment about how important and relevant new information actually is. There is a tendency among market participants, particularly for speculators, to frequently overreact to new facts. For example, a company missing its latest quarter’s earnings by a penny may cause it to trade off when in fact the miss is not relevant for an investor. Being unaware of this tendency and lacking the emotional or intellectual discipline to prevent “freaking out” can have a significant negative effect on results.