Probability can become hard to reason about when many variables interact.

One variable affects another.

Evidence changes belief.

Dependencies start to form a network.

That is where Probabilistic Graphical Models become useful.

Core Idea

A Probabilistic Graphical Model represents uncertainty with a graph.

The nodes are random variables.

The edges represent relationships between them.

Instead of treating probability as a flat list of formulas, a PGM gives it structure.

That structure makes complex uncertainty easier to reason about.

The Key Structure

A simple PGM view looks like this:

Random Variables → Graph Structure → Probability Values → Inference

More compactly:

PGM = graph + probability + inference

The graph shows how variables are connected.

The probability values define how likely different states are.

Inference uses both to answer questions under uncertainty.

Implementation View

At a high level, building a PGM looks like this:

define the random variables

decide which variables…