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What's the structural difference between a Bayesian net...
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See plansBoth are probabilistic graphical models that factorize a joint distribution over random variables to avoid representing the full joint table explicitly, but they differ in the kind of independence they express and how they factorize. A Bayesian network is a directed acyclic graph where each node’s conditional probability is defined given its parents, so the joint factorizes as a product of these local conditionals — this makes causal or generative structure explicit (an alarm node conditioned on a burglary node) and gives a clean way to sample from the model top-down and encode context-specific independence.
A Markov network (Markov random field) is undirected, and the joint factorizes as a product of potential functions over cliques of the graph, normalized by a partition function — this suits domains with symmetric, non-causal relationships (spatial or relational dependencies like pixel neighborhoods or social ties) where forcing a direction on the edges would be arbitrary or would require awkward extra nodes to avoid cycles. A concrete practical cost: computing that Markov network partition function is generally intractable for anything but small or specially structured graphs, whereas Bayesian networks with the right structure often allow exact inference via message passing. Choose directed when you have genuine causal or generative asymmetry to encode; choose undirected when the dependencies are inherently mutual and you don’t want to force an ordering.