Welcome! What is a Bayesian Network?

How Can a Bayesian Network Support Critical Infrastructure?
May 11, 2019

Welcome to our Bayesian network blog! What is a Bayesian network (BN), you ask? It is essentially a tool that uses probabilities to help us make better decisions. The networks can involve machine learning and/or expert knowledge; they can be geared toward predicting one particular event or helping us to understand a system. There are lots of complicating nuances, but regardless of how they are developed or why, there are two features that I think make BNs incredibly powerful tools.

The first reason Bayesian networks are so great is that they don’t force us to use binary logic. For example, if you build a forecast model in Excel, you can explore lots of “what ifs”, but not how likely they are. Your model may tell you that based on the variables you have chosen, you can expect a profit of $10M. However, what if that was only 30% likely. If you knew that would you make different decisions? Wouldn’t you want to not only maximize the profit but also maximize the likelihood of it occurring? The standard Excel-based models most commonly used do not consider probability of one event, let alone the probability of one event occurring given that another event did or did not occur.

The second reason Bayesian networks are immensely helpful is that they allow us to reason in two directions. Consider the following in Excel.

Pretty straight forward: I know the two inputs, and that gives me the outcome. However, what if I know the outcome is 0? It won’t tell me anything about what the inputs were. It only tells me what is on the left side of the equals sign in an Excel-based formula, not anything about the right.

Clearly when adding 1 and 0, this isn’t a critical challenge, but what if we change the headings?

What if we have a bunch of children showing up to the hospital with measles? Perhaps we will want to know the likelihood that they were vaccinated, given that they have the disease. A simple Bayesian network allows us to identify the probability of a child having been vaccinated, given that they do, in fact, have the measles. An Excel-based model won’t allow this kind of “backward” analysis.

             

The arrows in the network can be read as “causes me to update my beliefs about”. So knowledge about whether someone has been exposed to measles or not will cause me to update my beliefs about whether she acquired the disease or not. Note there is no arrow between “Vaccinated” and “Exposed to Measles” as those two are independent of each other; you are no more likely to be exposed to measles whether you have been vaccinated or not. The probabilities are assigned based on personal estimates and not any objective data (strictly illustrative). When we know for certain that the subject has the measles, the probability of “Acquired Measles” is no longer 3.05%, but rather 100%. Because of the interconnectedness of the variables, we can see that the probabilities of the subject being exposed as well as their likelihood of being vaccinated are updated.

The ability to embrace the complexity of problems and avoid binary logic as well as omni-directional inference are what I believe to be the two most powerful attributes of Bayesian networks. Over this blog series, we will aim to explore other features, some practical applications, as well as some interesting musings as we work with different groups on different challenges. We hope you enjoy!