In the process of making a decision given a logical set of relationships between events, it is useful to first make real-time observations of the entire system. Knowledge that an event is more or less likely to occur than previously thought will influence the final decision. For example, if your lawn is wet, you may wonder whether it rained or your sprinklers have gone off. You may know that the sky is usually cloudy after it rains and that your sprinklers are set to go off every Monday night. Before making your decision, you would look at the sky and check the day on a calendar. Both of these observations would then influence your decision.
A Bayesian network is a directed acyclic graphical model that can be used to solve such decision-making problems. Each node in the graph describes an event, such as the grass being wet or the sprinklers going off, and an arc from one node to another expresses that the first event causes the second. Each node defines a function that describes the conditional probability distribution for the event at that node. These networks are most useful in the context of making decisions given a large set of statistical data that describes the relationship between multiple events. Once a Bayesian network has been created, mathematical tools such as the sum-product algorithm can be used to adjust the network to reflect more recent observations.
This paper first explores the sum-product algorithm as a method of solving a Bayesian network. The sum-product algorithm is then broken down into the fundamental computations that it performs, and their implementation as analog subthreshold CMOS circuits is discussed. With these circuits, a simple Bayesian network is built and its performance and feasibility is analyzed.