1. Decision Tree Analysis
Dr. T. T. Kachwala

2. What is a Decision Tree?
Decision Tree is a pictorial representation of the decision process.
It represents the State of nature with the associated probability and strategies with the associated payoff.

3. How to draw a Decision Tree?
Slide 3
How to draw a Decision Tree?
Decision Tree comprises of two basic elements
Nodes
Branches.
Nodes: There are two types of nodes:
The Decision node is represented by a square
The Chance node is represented by a circle D C

4. How to draw a Decision Tree?
Slide 4
How to draw a Decision Tree?
The decision node represents a point on the decision tree where a decision maker takes a decision.
The chance node represents a point on the decision tree where a decision maker evaluates the outcome of his decision. D C

5. How to draw a Decision Tree?
Slide 5
How to draw a Decision Tree?
Branches: are lines or segments that connect the nodes.
There are three types of branches:
Decision branch
signifies the branch that commences from the decision node. It signifies the strategy the decision maker selects at that point. D C
Decision Branch D

6. How to draw a Decision Tree?
Slide 6
How to draw a Decision Tree?
(ii) Chance branch
signifies the branch that commences from the chance node. It signifies the state of nature that occurs at that point.
(iii) Terminal branch signifies the last branch of the decision tree. It is not followed by either decision or chance node. The terminal branches are mutually exclusive & collectively exhaustive at that point.
Chance Branch C

7. Diagram of a representative Decision Tree
Chance Branch
Terminal Branch
Decision Branch
Terminal Branch
Terminal Branch

8. Objective of drawing a Decision Tree
Slide 8
Objective of drawing a Decision Tree
The objective of drawing a decision tree is multiple stage decision analysis.
The calculation starts with the terminal branch. Starting from the terminal branch we calculate the position value progressively at each node & roll back to the earlier node till we reach the initial node.

9. Decision Tree - Roll back Technique
Slide 9
Decision Tree - Roll back Technique
The position value at the chance node is the EMV at that point. The position value at the decision node is the maximum payoff amongst the branches at that point.
In the process of rolling back to the initial node, we identify a series or sequence of optimum strategies that maximizes the payoff at the initial node.

10. Decision Tree - Roll back Technique
max payoff
EMV
EMV
max payoff
EMV
EMV
max payoff

11. Use of TreePlan (Excel Add-Ins)

12. Bayesian Approach to Decision Making
Bayesian Approach is an amalgamation of two theoretical disciplines – Bayes Theorem & Decision Tree Analysis
The so called ‘Bayesian’ approach to the problem addresses itself to the question of determining the probability of some event Ai given that another event B has been observed, i.e. determining the value of P(Ai/B).

13. Bayes Theorem - Introduction
One of the most interesting applications of the results of the probability theory involves estimating unknown probabilities and making decisions on the basis of new (sample) information.
Decision theory is another field of study, which is based on Bayes theorem. This theorem consists of a method of calculating conditional probabilities.
Thomas Bayes developed a simple rule for calculating Posterior or Revised Probability given the Prior Probabilities & Conditional Probabilities popularly referred as Bayes Theorem

14. Bayes Theorem – Given Data
Let A1 and A2 be a set of events which are mutually exclusive and collectively exhaustive as indicated in the Venn diagram (i)
Let B be a simple event such that it intersects with both A1 and A2 as indicated in the Venn diagram (ii)

15. Bayes Theorem - Calculation of Posterior (Revised) probability P(Ai/B)
P(A1) and P(A2) are the prior probabilities (simple probabilities prior to occurrence of event B).
P(B/A1) is the conditional probability of B given that A1 has occurred.
P(B/A2) is the conditional probability of B given that A2 has occurred.
Given the values of P(A1), P(A2), P(B/A1) and P(B/A2) the following table on the next slide explains the calculations of P(Ai / B) using Bayes Theorem.

16. Bayes Theorem - Calculation of Posterior (Revised) probability P(Ai/B)
Event
Prior Probability
Conditional Probability
Joint Probability
Posterior Probability
(1)
(2)
(3)
(4) = (2) x (3)
(5) = (4)  P (B) A1
P (A1)
P (B/A1)
P (A1B)
P (A1/B) A2
P (A2)
P (B/A2)
P(A2B)
P(A2/B) 1
P (B)