A Decision Tree is a graphical tool used to map complex decision-making processes, showcasing different paths and their outcomes. It’s useful for handling uncertainty, risk analysis, and sequential decisions, but can be complicated or misleading if not used properly.

## Definition

A Decision Tree is a flowchart-like structure that visualizes the course of action or a statistical probability algorithm. It displays an algorithm that only contains conditional control statements.

## Nodes

Decision Trees are composed of decision nodes, represented by squares; chance nodes, represented by circles, accounting for uncertainty and depicting potential outcomes; and end nodes or leaf nodes, represented by triangles, illustrating the final outcome of a decision path.

## Branches

Branches in a Decision Tree symbolize the potential choices available at each decision point, or the potential outcomes in the case of a chance event.

## Root Node

The initial decision that instigates the tree structure is known as the root node. It represents the ultimate question or decision that is being explored.

## Decision Analysis

This is the practice of making decisions using Decision Trees. It can involve many branches of mathematics, including statistics, probability, and game theory.

## Sequential Decision Making

Decision Trees often represent decisions that must be made sequentially. Each decision impacts subsequent decisions and, therefore, the final outcome.

## Expected Value Calculation

One common approach to deciding the best decision within a Decision Tree is through the calculation of expected values at each decision node.

## Risk Analysis

Decision Trees can be used to understand and quantify risk. This is done by assigning probabilities to chance nodes and using these to calculate expected values and variances.

## Sensitivity Analysis

This process involves adjusting the probabilities or payoffs in a Decision Tree to see how sensitive the final outcome is to changes in these inputs.

## Utility Theory

In some complex decisions, where outcomes have different levels of satisfaction or utility, Decision Trees may incorporate utility functions to better capture the decision maker’s preferences.

## Pruning

This refers to the removal of decision branches in a Decision Tree that don’t affect the final decision, simplifying the tree.