Bayesian Networks Bring Order to Complex Relationships
They not only capture random variables but also their effects on each other
I stood in my basement staring at the crack in my foundation that I had sealed last summer, as torrential rains descended. The incoming brown liquid mocked my efforts at foundation repair. So, I braved the 90-degree weather and crawled under my deck, armed with my short-handled shovel and heavy-duty power drill. For several hours I labored through solid, concrete-like clay to dig a deep-enough hole to access the exterior of the foundation in order to seal the culprit.
Because I am an engineer, my mind turned to probabilities. What was the probability that this crack would have leaked again? What was the probability that it would have rained this much? What was the probability that the local weather forecaster was ever right?
Making sense of chaos
The forecasters have to predict the weather while trying to factor in temperature, humidity, precipitation, cloud cover, wind speed, wind direction, jet streams, cold fronts, warm fronts, and more. These seemingly random factors combine to cause weather (and my leaky basement).
Many years ago, one of my systems engineering professors discussed chaos theory, describing how systems, like the weather, are sensitive to and dependent on initial conditions, i.e., what happens first. He told us about the “butterfly effect,” in which a small change in the state of a system can result in differences in a later state.
For example, the flapping of the wings of a butterfly in China can affect the weather thousands of miles away in New York a few weeks later. Really? What’s the probability that a butterfly flapping its wings could influence weather thousands of miles away?
Bayesian networks to the rescue
The good news is that there is an engineering concept for that! Thomas Bayes was an English statistician, philosopher, and Presbyterian minister who lived in the early 1700s and is known for formulating the theorem that bears his name. A Bayesian network is a model representing a set of random variables, like those that affect the weather. Not only does it capture a set of random variables, but it also describes their conditional dependencies on one another.
For example, given the conditions that there is complete cloud cover and the humidity is 100 percent, what is the probability that it will precipitate? This probability is based on conditions and called conditional probability. Bayes translated a set of complex relationships or dependencies into an intuitive, mathematic model.
Bayesian network models incorporate uncertainty, and they work in the face of missing or inconsistent data. Sounds like a weather forecaster’s dream to me! Not only do forecasters use Bayesian networks, but SAIC uses them, too. Our robust systems engineering is underpinned by mathematical methods. Recently I was part of a team that developed a method to probabilistically determine integration readiness in complex systems using a Bayesian network model.
Our method may not save me a call to the handyman, but chances are my next engineering job will have a lot less risk.
FURTHER READING: More from our systems engineering expert Don York.
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