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# [Solved]: Difference between Bayesian Networks and Dynamic Bayesian Networks

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Problem Detail:

I'm studying Bayesian networks and want to clarify a couple of things with people who are more knowledgable in the area than me.

As far as I understand it, a Bayesian network (BN) is a directed acyclic graph (DAG) that encodes conditional dependencies between random variables. The graph is drawn in such a way that the the distribution (dictated by a conditional probability table (CPT)) of a random variable conditioned on its parents is independent of all other random variables. I'm assuming that, by definition, both the structure (nodes and edges of the DAG) and the entries of the CPT in a BN assumed to be fixed in time.

Now, I'm wondering about the distinction between BNs and Dynamic BNs (DBNs), specifically, where the dynamic term in a DBN arises from:

Does this mean that the structure AND conditional dependencies between variables are time-varying? If so, is a BN with a fixed structure (DAG) but time-varying probabilities also considered a DBN (does this type of 'DBN' have a name)?

I'm not sure if what I've said is correct. Please let me know if I went wrong anywhere or if there is a better way of thinking about this.

#### Answered By : Nicolas

A DBN means that your model is replicated over each time discrete time step t, called slice. Variables of each slice can be connected together, as well a from previous slice to a latter slice (in this precise direction only). The probability tables and links remain the same in each slice if the model is stationary, which is the default case (otherwise they are a function of t).

In a 2TBN (2-step Timeslice Bayesian Network), there are links only between the previous and current slices.

For more information c.f. section 3.2 of http://journal.frontiersin.org/article/10.3389/fncom.2014.00131/full

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