Page 139 - DCAP310_INTRODUCTION_TO_ARTIFICIAL_INTELLIGENCE_AND_EXPERT_SYSTEMS

Unit 7: Probabilistic Reasoning

The beliefs originally encoded in the model are known as prior probabilities, because they are Notes
entered before any evidence is known about the situation. The beliefs computed after evidence
is entered are known as posterior probabilities, because they reflect the levels of belief computed
in light of the new evidence.

Parents and Children: Introduction to Diagrams

To recap, every variable in the real world situation is represented by a Bayesian variable. Each
such variable describes a set of states that represent all possible distinct situations for the variable.
Once the set of variables and their states are known, the next step is to define the causal relationships
among them. For any variable, this means asking the questions:

What other variables (if any) directly influence this variable?
What other variables (if any) are directly influenced by this variable?
In a standard Bayesian belief network, each variable is represented by a colored ellipse; this
graphical representation is called a node.
Each causal influence relationship is described by a line (or arc) connecting the influencing
variable to the influenced variable. The influence arc has a terminating arrowhead pointing to
the influenced variable.
The common terminology, then is as follows:

A node is a Bayesian variable.
An arc connects a parent (influencing) node to a child (influenced) node.

Belief Network Creation

To create a belief network, then, the following steps are necessary.
1. Create a set of variables representing the distinct elements of the situation being modeled.
2. For each such variable, define the set of outcomes or states that each can have. This set is
referred to in the mathematical literature as “mutually exclusive and exhaustive,” meaning
that it must cover all possibilities for the variable, and that no important distinctions are
shared between states.
3. Establish the causal dependency relationships between the variables. This involves creating
arcs (lines with arrowheads) leading from the parent variable to the child variable.

4. Assess the prior probabilities. This means supplying the model with numeric probabilities
for each variable in light of the number of parents the variable was given in Step 3.
After the model has been developed, MSBNX allows you to model or mimic real-world situations
by entering or removing evidence on the model. As you do so, there are various methods for
displaying the resulting probabilities.

7.1.5 The Bayesian Belief Network

To keep the formalism simple and general, we develop the notion of features without considering
time explicitly. Constraint satisfaction problems will be described in terms of possible worlds.
When we are not modeling change, there is a direct one-to-one correspondence between features
and variables, and between states and possible worlds. A possible world is a possible way the
world (the real world or some imaginary world) could be. For example, when representing a
crossword puzzle, the possible worlds correspond to the ways the crossword could be filled out.

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