For Example, In a office, there is an electric fan that is used often in summer and not in other seasons. Imagine a scenario where you try to switch on the fan, but it does not spin. The fan is plugged into an extension socket or plug, and there is a possibility of a plug failure. How do we figure out what the possible causes are?

The fan has a probability of 0.02 for failure, whereas the plug is very old and has the failure probability 0.2. I also have a mobile phone charger connected to the same plug. I found that the charger works well. What is the probability of the problem caused by a faulty fan?

We can represent this scenario as a simple Bayesian network, shown below. 
In this case, the parents of the random variable Fan are the nodes Faulty Fan and Faulty Plug, whereas the child of Fan is No Spin. The two variables Faulty Fan and Faulty Plug are marginally independent; however, they become conditionally dependent, given Fan.

Due to dependencies and conditional probabilities, a Bayesian Network corresponds to a directed acyclic graph, where no loop or self connection is allowed.

Example of Bayesian Network

A Bayesian network or Belief Model is a probabilistic graphical model for representing knowledge about an uncertain domain where each node corresponds to a random variable and each edge represents the conditional probability for the corresponding random variables.

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Probabilistic models use graphs to show interactions between random variables. A graph is a set of nodes connected by vertices. A probabilistic model represents random variables with nodes and their relationships with vertices between them.

Graph Model Structure

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

Deep Learning

Undirected Models (AKA Markov Random Fields/MRF/Markov Networks) have typical graph structure but the vertices are undirected.

Undirected Models

Separation is used to describe which variables interact indirectly. D-Separation simply refers to separation with a directed graph.

If a path exists between two variables with only unobserved variables, then the variables are separated. Paths like this are considered active, while paths with an observed variable are considered inactive.

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