Decision and Risk Analysis Influence Diagrams Decision Trees

Decision and Risk Analysis Influence Diagrams, Decision Trees and Probability Reference: Clemen & Reilly. Making Hard Decisions, 2 nd ed. Chapter 3. Duxbury, 2001 NOTE: Some materials for this presentation courtesy of Dr. Dan Maxwell

Decision and Risk Analysis Influence Diagrams • Another way to structure decision problems • Graphical representation • Considers: – Decisions to make – Uncertain events – Value of outcomes } Nodes in network Chance Node Deterministic Node Decision Node Value Node – Relations between nodes

Decision and Risk Analysis Influence Diagrams Chance Relevance Decision Value Probabilistic Relevance Information Arc Chance Deterministic Functional Relevance

Decision and Risk Analysis Representing Influence with Arrows A B The outcome of event A is relevant for assessing the chances associated with event B. C D Decision C is relevant for assessing the chances associated with event D. E F The decision maker has information on the outcome of event E when making decision F. G H Information from Decision G is used to make decision H.

Decision and Risk Analysis Basic Risky Decision Market Activity Investment choice Choices: Stocks Savings Outcomes: Market Up Market Down Payoff Market Choice Outcome Payoff Savings Stocks Up Down 200 500 -400

Decision and Risk Analysis Possible Forecasts Will Hit Miami Won’t Hit Miami Evacuation Decision Forecast Evacuation Decision Choices: Evacuate Stay Note: Decision made after forecast – Forecast is imperfect – Is forecast correct? Hurricane Path Outcomes: Hits Miami Misses Miami Payoff Choice Outcome Payoff Evacuate Stay Hit Miss } Safety High Cost Danger Low cost Safety Low Cost

Decision and Risk Analysis Strategy for Building Influence Diagrams • • No Recipe • • Start with very simple diagram • – Iteratively add detail • – Stop when enough to capture essence of problem • – There is art involved • • Common Mistakes • – Interpret as flowchart • - No sequential nature • - No cycles • – Influence not causation

Decision and Risk Analysis Deterministic Nodes • • Additional nodes to aggregate intermediate results • • Emphasizes and simplifies structure of the ID ex. New Product Introduction (1) Introduce Product Revenue Cost Profit • Very simple representation • Value is the profit – derived from revenue and cost • Might not capture all relevant aspects of problem

Decision and Risk Analysis Deterministic Nodes ex. New Product Introduction Units Sold (2) Fixed Cost Variable Cost Price Introduce Product Profit • More complex – captures more detail • Harder to understand evaluate

Decision and Risk Analysis Deterministic Nodes ex. New Product Introduction Units Sold (3) Fixed Cost Variable Cost Price Introduce Product Revenue Cost • Uses Deterministic Nodes Profit • Sometimes denoted with double circle or as value node • Easier to understand evaluate

Decision and Risk Analysis Deterministic Nodes ex. New Product Introduction Units Sold (3) Fixed Cost Variable Cost Price Introduce Product Revenue Cost • Uses Deterministic Nodes Profit • Sometimes denoted with double circle or as value node • Easier to understand evaluate

Decision and Risk Analysis Multiple Objectives • • Value of outcome depends on tradeoffs of competing objectives • • Can be represented in Influence Diagrams as follows: ex. FAA decision on Bomb Detection System Choice Detection Effectiveness Time to Implement Passenger Acceptance Overall Satisfaction Cost • Build Additive Value Function

Decision and Risk Analysis Multiple Objectives • • Value of outcome depends on tradeoffs of competing objectives • • Can be represented in Influence Diagrams as follows: ex. FAA decision on Bomb Detection System Choice Detection Effectiveness Time to Implement Passenger Acceptance Overall Satisfaction Cost Measure

Decision and Risk Analysis Multiple Objectives • • Value of outcome depends on tradeoffs of competing objectives • • Can be represented in Influence Diagrams as follows: ex. FAA decision on Bomb Detection System Choice Detection Effectiveness Time to Implement Passenger Acceptance Overall Satisfaction Cost Measure Values

Decision and Risk Analysis Sequential Decisions • • Simplest is 2 decision sequence • • No cycles allowed in Influence Diagrams • • Sequential decisions are “strung together” ex. Orchard owner decision to protect trees from bad weather Weather Day 1 Forecast Day 1 Protect? Day 1 Weather Day 2 Forecast Day 2 Payoff Day 1 Protect? Day 2 Total Payoff Weather Day n Forecast Day n Payoff Day 1 Protect? Day n Payoff Day n

Decision and Risk Analysis Sequential Decisions • • Simplest is 2 decision sequence • • No cycles allowed in Influence Diagrams • • Sequential decisions are “strung together” ex. Orchard owner decision to protect trees from bad weather Weather Day 1 Forecast Day 1 Protect? Day 1 Weather Day 2 Forecast Day 2 Payoff Day 1 Protect? Day 2 Total Payoff Weather Day n Forecast Day n Payoff Day 1 Protect? Day n Payoff Day n

Decision and Risk Analysis Strategy for Building Influence Diagrams • • No Recipe • • Start with very simple diagram • – Iteratively add detail • – Stop when enough to capture essence of problem • – There is art involved • • Common Mistakes • – Interpret as flowchart • - No sequential nature • - No cycles • – Influence not causation

Decision and Risk Analysis Solving Influence Diagrams • Step 1: Clean up Influence Diagram – No “Barren Nodes” – Only one Value Node (or one Super Value Node into which all the other value node feed) – No cycles • Step 2: Look for any Chance Nodes that: • Directly precedes the Value Node (only node) • Do not directly precede any other type node – Reduce these nodes by taking expected values – Value node inherits their predecessors

Decision and Risk Analysis Algorithm (continued) • Step 3: Look for Decision node that: • Directly precedes the Value Node, and • Has as predecessors all other direct predecessors of the Value Node – If none, go to Step 5. – Else, reduce the node by choosing the optimum [expected] value. • Step 4: Go to Step 2 and continue until the Influence Diagram is completely solved • Step 5: You are here because you couldn’t reduce any chance nodes. • Reverse the arc between 2 chance nodes using Bayes Theorem and go to Step 2.

Decision and Risk Analysis Solving Influence Diagrams • Influence Diagrams are usually solved using software – Freeware and Commercial software exists – In this class, we will use the Decision Tools software provided with the text – WARNING! Register software < 30 days • For exam, I won’t ask you to solve directly from a influence diagram