Quant test 3
Computing Branch Probabilities
- Bayes' Theorem - prior probabilities - sample info - posterior probabilities
Decision analysis with sample information
- prior probabilities - Sample information - posterior probabilities
Problem Formulation
- state the problem - identify decision alternatives - identify chance events - identify the payoffs
EVwPI =
Weighted average of the best payoffs for each state of nature
Expected value
Weighted average of the payoffs
Weighted average of the payoffs
Weights are the probabilities for the states of nature
EVPI calculation
= |EVwPI - EVwoPI|
Utility
A measure of the total worth of a particular decision maker's attitude towards a collection of factors
Utilities
Are used when the decision criteria must be based on more than just expected monetary values
How is E measured?
As a percentage %%%%%%%%%%
Optimistic decision making approach
Assume best possibility Determine the best payoff for each decision alternative Choose the decision alternative that would provide the best payoff "Best of the best"
Conservative (pessimistic) decision making approach
Assume worst possibility Determine the worst payoff for each decision alternative Choose the decision alternative that provides the best payoff "Best of the worst"
Decision strategy approach
Backward pass Chance nodes Decision nodes
Expected value approach
Calculate the expected value for each decision alternative
For EV approach,
Choose the decision with the best expected value
EVwoPI =
EV of best decision
Efficiency of Sample Information
EVSI/EVPI*(100%)
Decision making approaches with probabilities
Expected value approach
Decision analysis with sample information decision strategy
Identify the sequence of decisions and chance outcomes
Utility analysis
Is particularly appropriate in cases where payoffs can assume extremely high or extremely low values.
Minimax Regret approach
Make a decision based off of regret Calculate regret Compare payoffs for a specific state of nature Determine the maximum regret for each decision alternative Choose the decision alternative with the minimum regret
States of nature
Mutually exclusive, collectively exhaustive
CHOOSE A DECISION
NOT A PAYOFF
Decision making approaches without probability
Optimistic, Conservative (pessimistic), Minimax Regret approach
Identify decision alternatives
Options available to the decision maker
Shown by branches on a decision tree
Payoffs
Types of payoffs
Profit, cost, time
Factors of utilities include
Profit, loss, or risk
Posterior Probabilities
Revised probabilities for your states of nature
Tabular approach
See table on pg. 135
Nodes on a decision tree
Square for decisions Circle for chance events
Sensitivity Analysis best alternative table
Table with all probs from 0-1 represented as points or intervals on the left, and which decision to pick on the right.
Sensitivity Analysis graphical approach
USED WITH ONLY TWO STATES OF NATURE Calculate the EV of each decision alt. using p as the prob. for state of nature one. Find where p = 0 and p = 1 Graph the lines accordingly Calculate where the EV's are equal, using only the top values
Identify chance events
Uncertain events that will affect the outcomes of a decision
Sensitivity Analysis
Used to determine how changes in probabilities for the states of nature affect the recommended decision alternative
Decision trees
Visual representation of the decision making process
EVSI =
|EVwSI - EVwoSI|
EVPI provides
an upper bound on the expected value of any sample or survey information
Identify the payoffs
measure the outcome of the decision
Sample information
new or additional information gained such as through a survey
Expected value of Sample Information (EVSI)
the additional expected profit possible through knowledge of the sample or survey information
Expected Value of Perfect Information (EVPI)
the increase in the expected profit that would result if one knew with certainty which state of nature would occur