Every decision analysis question requires that you setup three components based on the given information: decision variables, states of nature, and the payoff table. I’ll show you how to identify them in the wording, and what to do when you’re presented with revenues and costs instead of profits.

# Chapter 4: Decision Analysis

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## Lessons

## 1 | Setup (Preview)

## 1a | Optimist & Conservative Approach (Preview)

When you don’t have access to the probabilities of the states of nature, a decision must be made based on the goals of the decision maker. An optimist is ruled by greed and will search out the decision with the greatest payoff, while the conservative decision maker is motivated by fear and will seek to avoid the decision that carries the most risk (worst payoff).

## 1a | Minimax Regret Approach (Preview)

Hindsight is 20-20, but what if you want to avoid kicking yourself after you find out how your choice of decision alternates played out? The decision maker using the minimax regret approach will look for the decision with the least regrets (missed opportunities).

## 1b | Expected Value Approach

In between the greedy optimist and the fearful conservative lies the risk-neutral decision maker. Knowing the probabilities of each state of nature makes makes all the difference. See how mathematics alone can select the best decision from the options presented.

## 1c | EVPI

How much would you pay a consultant to help you make a choice? Consultants can make mistakes themselves, so it would help to first know how much a 'perfect' consultant would be worth. This sets an upper limit to your budget, and will allow you to later determine how efficient their input will be.

## 1d | Identifying Given Probabilities

Questions with 'Sample Information' make up the most challenging problems on the test. Learn how to easily identify - based on the given wording - whether or not you are dealing with sample information. This part of the chapter is very similar to the lessons on Probability in Stats 1 (ADMS 2320).

## 1d | EV(without)SI

Good news ... You already know this stuff! Expected-Value-without-Sample-Information (EVwoSI) is just the same as Expected Value (EV) covered in my earlier video. I show you how to solve for EV this time using the decision tree, and how that solution becomes a branch of the tree that will help you later with EV-with-SI.

## 1d | EV(with)SI

Now it's time to put our sample information to use (also known as: Market Research, Consultant, Report, etc...). The key to solving for the Expected-Value-with-Sample-Information is to draw the decision tree, so I'll show you some tricks to make sure you get the tree set up right.

## 1d | EVSI & Optimal Decision Strategy

We can finally solve by comparing the expected value WITH sample information to the cost that the consultants want to charge ($75,000). The final step is then to write out the Optimal Decision Strategy. This is a list of the correct decisions that should be made as we move from the beginning of the decision tree to the end.

## 1e | Efficiency

By comparing the value added by the less-than-perfect market research firm (EVSI) to the value of perfect information (EVPI) that we calculated near the beginning of this video series, we can determine how 'efficient' their input really is.

## 2 | Intro to Posterior Probabilities

This is where Chapter 4 becomes very challenging! The problem occurs when the given probabilities in a question do not match with the format required for using the decision tree to solve the problem. Sometimes you get P(X|s_{i}) when what's needed is P(s_{i}|X). Here's how you identify which version you've been given.

## 2 | Making Posterior Tables

To convert from P(X|s_{i}) to P(s_{i}), you'll need to make one table for each type of report included with the sample information. Your cheat sheet covers the rows and columns on the table, but there are a few important components left out that you'll have to memorize.

## 2 | New Solution

Now that the decision tree can be filled in with the proper probabilities in the format P(s_{i}|X), we can find the solution in the same way that we did in Question 1.

## Multiple Choice

Test your understanding of Chapter 4: Decision Analysis – each question is accompanied by a mini-video lecture showing you how I decided which solution was the correct one.