Getting Started with the Bayesian Network
A Bayesian network (belief network) is a probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG). In Bayesian Doctor, you can easily create a Bayesian Network and query the network. You can instantiate a random variable upon observation of a state and the whole network is updated based on the evidence. Intuitive charts are presented to indicate the Root Cause Variables and Ultimate Symptoms variables.
You can watch this video to learn using a Bayesian Network with Bayesian Doctor.
When you start the Bayesian Doctor application, you are given options to choose "Bayesian Network" or "Bayesian Inference". If you have chosen a Bayesian Network, then you will see the following window.
Drawing a Diagram
Bayesian Network tool is easy and simple enough that you can simply drag and drop a new variable node from the toolbar and connect the variables using arrows.
A node as added, you can double click on the node to edit the name of the variable.
You can add a note for the node from the flyover menu.
Once a note is added, it looks like this on the node.
Once the nodes are added, you can connect them to represent probabilistic relationships.
Finally, after connecting the arrows, the diagram will look like this:
Now is the time to set probabilities.
Once you select a Random Variable Node, the probability table shows up as shown here. Click on a cell to edit the probability. When there are just 2 states, the probability of the opposite state is auto calculated. For example, when you change the probability of 'True' state, the probability of 'False' state is calculated as 1 - 'true' state probability.
As the variable "Rain" has no parent Node, the probability table shows only the states of Rain variable. When a node has one or more parent node(s), a Conditional probability table is shown as shown below.
Query the Bayesian Network
Once you have completed the model for a Bayesian Network, you can query the network using the Query window. Click the Query Button from the toolbar and the query window will appear. You can calculate the joint probability, conditional probability or joint with conditional probabilities, in any way you want.
Find Conditional Probability
Say, you want to Query, what is the probability that Rain is true, GIVEN Grass Wet is True?
Find Joint Probability
Say, you want to know, what is the probability that Rain is True AND Grass is Wet is False. You can find that as shown below.
Instantiate a variable upon evidence
When you get an evidence for a variable state, (i.e. you observed the Grass is wet), then you can instantiate the Grass Wet variable with the True state as shown here.
Notice that, when you instantiated the Grass Wet variable to True, the probability of Rain = True is automatically calculated and displayed in the "Rain" node. You can see that the Rain node is showing probability 0.36.
You may ask, how to define what state probability of the Rain variable will be displayed in the Node. You can set that from the Probability table. Notice the Radio button beside the state name. The checked radio button determines which state should be tracked in the node and in the chart.