Bayesian network
/ BAY-zee-un NET-wurk /
A Bayesian network is a probabilistic graphical model whose connections are arrows — a flowchart of influence. Each dot is a variable, and an arrow from one dot to another says 'this one directly affects that one.' Attached to each dot is a small table giving its odds for every combination of the dots pointing into it. Together, these local tables stitch up into a full picture of how everything in the system behaves.
The arrows often invite a cause-and-effect reading — sprinkler and rain both cause wet grass — and that intuition is part of why these networks are so popular. But here is a critical honesty point: an arrow in a Bayesian network is not, by itself, a proof of causation. The same data can usually be described by networks with arrows pointing the other way. The graph captures patterns of statistical dependence; turning that into genuine causal claims requires extra assumptions or experiments, not just the diagram.
Why they matter: Bayesian networks let you reason in any direction. Knowing the grass is wet, you can ask whether it likely rained; knowing it rained, you can predict wet grass. This 'reasoning backward from effects to causes' is exactly what diagnosis, fault-finding, and risk assessment need, and Bayesian networks powered influential systems in medicine, engineering, and decision support. Their limit is the usual one: building the structure and filling the tables takes real expertise or data, and exact inference can get expensive as the network grows.
The classic 'wet grass' network: Rain and Sprinkler both point to Wet Grass; Rain also points to Sprinkler (it's less likely to run if it's raining). You walk out and the grass is wet. The network lets you compute that rain is now more probable — and, having explained the wet grass, the sprinkler becomes a bit less probable. That subtle 'explaining away' falls out of the math automatically.
'Explaining away': once rain accounts for the wet grass, a competing cause (the sprinkler) becomes less likely.
The most common misconception: arrows in a Bayesian network mean causation. They don't on their own — they encode conditional dependence, and many different arrow directions can fit the same data equally well. Causal interpretation needs assumptions or experiments the graph alone cannot supply.