26 Mar Bayes and Search Theory
What began as a study of belief has turned into a strategy for solving very complex problems. Thomas Bayes (/ˈbeɪz/; 1701–1761) proposed a model in which adding evidence of different types, or from different sources, to a problem will change the calculated probabilities for the outcomes of the “reasoning” process. We’ve forgotten what he looked like, Thomas that is, but we remember what he looked at, out of the windows of the University of Edinburgh 250 years ago.
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Bayes theorem provides a basis for statistical inference in which the addition of evidence can influence the outcome of a predictive exploration. An interesting characteristic of his theory, one I have latched onto, is that the absence of theoretical limits in the number of constraints you can add to the information space for predicting a probability. Naturally there are practical limits. But the problem we most often face in predicting an outcome is lack of enough information about the contributing factors. Consider the case of Air France Flight 447, missing for two years after it crashed into the Atlantic Ocean on June 1, 2009.
Massive search efforts involving very advanced technologies and significant numbers of human searchers were unable to find the sunken wreckage even though parts of the aircraft and 50 bodies had been recovered from the ocean surface not long after the disaster. In July, 2010, after the original search was terminated, Metron, a search consultancy, was hired to develop a probability map to better focus the search. They chose a Bayesian approach, with input constraints including prior probabilities from flight data, local weather and ocean condition reports, and the results from the previous searches.
They chose the “classic” Bayesian search methods, because they had previously been successful in the search for the submarine USS Scorpion. The first model failed to lead the searchers to the correct location because they missed an important assumption: that the black boxes both failed on impact. When they added the new constraint to the model, they found the wreckage on the sea floor very rapidly (See report on NPR).
Using Bayesian probability mathematics, scientists have been able to solve really hard problems.
Back to belief: It is easy from our personal Ivory Tower to pass judgment on the actions others we don’t fully understand. Differences of opinion are often the cause of acrimonious attacks, especially in polarized media outlets. The cacophony of accusations can become noxious very quickly. What often triggers these differences of opinion are gaps in each side’s understanding of the other side’s motivations. Expectations of short-term and long-term outcomes may also differ wildly between stakeholder communities. Another thing often lacking, in most or all communities, is a clear understanding of all the external factors influencing the short- and long-term outcomes.
As an example, I heard a news report on an environmental/energy disaster issue. An explosion at an energy facility in Pennsylvania resulted in one young man’s death and some negative environmental impacts. The company, as a gesture to the local community provided free food vouchers. There was national outrage among observers who felt the gesture was cynical and insulting. They wanted nothing less than for the company to permanently terminate the fracking. But many of the locals were thankful for the gesture, and especially thankful to the company for keeping their community alive through prosperity, in contrast to the destitution they had felt during the gap between the collapse of coal and the rise of natural gas (See article in Newsworks PolicyMic Huffington NPR). Context!
The conflict is more based on future outcomes of fracking than one isolated disaster. Clearly, fracking causes environmental damage. Furthermore, careless and/or excessive use of the power produced contributes unnecessarily to global climate change. The question upon which the sides differ, more than anything else, is whether or not the immediate benefits of prosperity for the residents, power moguls and investors justifies the environmental damage. Until we experience natural disasters of significantly greater proportion than past calamities, events that can be linked to human activities producing excessive greenhouse gasses, the debate will not abate.
The Role of Bayes and Search Theory
If we could do a better job of combining constraints to demonstrate mathematically and provably that:
- human activity is significantly exacerbating global climate change, and
- specific changes in human behavior can change the course of global climate change
then, we may have a good shot at ending the debate and persuading recalcitrant companies and nations to change their policies and behaviors. For me, I plan to use the power of Bayes’ 250 year old theorem to improve the quality of automated language understanding by incorporating more constraints correctly to correctly interpret your intent.
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