IEAM Spotlight: Special Series on Bayesian Networks in Environmental & Resource Management
John Toll, Globe EditorinChief
Thomas Bayes
Thomas Bayes was a man 300 years ahead of his time. Bayes, an English Presbyterian minister during the first half of the 18th century, derived a simple and elegant mathematical rule explaining how new evidence should affect existing beliefs. His rule relies only on three simple assumptions that most people find easy to accept:
 All probabilities are ≥ 0.
 The probability that something—anything—is going to happen is 1.
 The probability of any one of a set of disjoint^{1} events happening equals the sum of their probabilities.
Starting with only these three assumptions, Bayes’ rule can be derived in a few simple steps. It tells us how new information should be used to revise our beliefs about the outcomes of uncertain events. Belief in outcomes that are relatively consistent with new information should go up. Belief in outcomes that are relatively inconsistent with new information should go down. Bayes’ rule says that we should use weighting factors to update our beliefs, and it tells us what the weighting factors should be.
Bayes’ rule is a really powerful idea. Why, then, did it take three centuries to catch on? The logic behind Bayes’ rule is simple and elegant, but the arithmetic is not. It uses integral calculus, and the integrals of some of the terms that go into the formulas have not been solved. Until recently, that made using Bayes’ rule impractical. Now, though, we have the computational power to solve the equations numerically, using Monte Carlo techniques. Many practical challenges lie ahead of us, both technological and intellectual. The software has not yet caught up with the raw power of our computers, and we have not yet come to terms with philosophical questions about modeling and uncertainty that our new technical prowess lays bare.
These challenges are surmountable and will be met. The authors and editor of the recent IEAM Special Series on Bayesian Networks in Environmental and Resource Management are on an exciting new frontier that is rife with opportunities for exploration and discovery. The principles and practices that they and others—perhaps you—will develop in the years to come will affect all of us who are working to protect, enhance and manage sustainable environmental quality and ecosystem integrity.
So I urge you to take a look at the IEAM Special Series on Bayesian Networks in Environmental and Resource Management, and listen to the podcast with David Barton, the special series’ guest editor. You may be surprised by the diversity of topics addressed under the Bayesian networks umbrella. Give it some thought, and I suspect that you will see ways that it applies to your work too. Hopefully it will inspire some of you to harness the power of Bayesian inference and Bayesian networks in your own work!
^{1}Events are “disjoint” if the occurrence of one of the events precludes the occurrence of the others.
Author's contact information: johnt@windwardenv.com
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