The relationships between even a small number of random variables can be quite confusing and possibly counter-intuitive. Two variables might be independent before observing the value of a third variable but dependent afterward. The opposite is true as well: two variables may be associated *a priori* but conditionally independent after observing third variable. Sequences of relationships between variables quickly become too complex to manage informally.

Fortunately **Bayesian networks** provide a way to work effectively with interconnected sets of random variables. Bayesian networks let you visualize relationships between variables and guide calculations based on these variables. They are useful in modeling dependencies and carrying out calculations by hand involving a small number of variables. They also **scale up well**, allowing machine learning algorithms to work efficiently with hundreds or thousands of variables.

Bayesian networks are also a useful tool for **causal reasoning**. Here one does not simply passively observe random variables but can also reason about the effects of intervening to set the states modeled by random variables using the so-called “do-calculus.” Causal reasoning also lets you reason rigorously about counterfactuals. Causal inference often makes it possible to carry out calculations that seem at first to be impossible, such as computing probabilities of outcomes in networks that include variables that have not and cannot be observed, such as hypothetical mediating causes.

If you’d like help applying Bayesian networks and causal inference in your business, reach out now to start the discussion.

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