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**Evsi**

**Evsi**

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The good news is that Bayes’ Theorem can be used to combine the information, and we can use our decision tree to find **EVSI**, the Expected Value of Sample Information. In order to perform these calculations, we first need to know how reliable the potential test may be.

**EVSI** is what is actually gained. E = (**EVSI**/EVPI)100 is the efficiency of sample information. Here we have (1.73/3.2)100 = 54.1%. Should we stop looking for more information about the states of nature? If the efficiency is high there is not much to gain.

Expected Value of Sample Information The expected value of sample information (**EVSI**) is the additional expected profit possible through knowledge of the sample or survey information. Expected Value of Sample Information **EVSI** Calculation Step 1: ...

Expected Value of Sample Information **EVSI** Calculation Step 1: Determine the optimal decision and its expected return for the possible outcomes of the sample using the posterior probabilities for the states of nature. Step 2 ...

A TWO LEVEL MONTE CARLO APPROACH TO CALCULATING EXPECTED VALUE OF SAMPLE INFORMATION (**EVSI**):- HOW TO VALUE A RESEARCH DESIGN. Alan Brennan, , Jim Chilcott, Samer Kharroubi, Tony O’Hagan, University of Sheffield, England.

... **EVSI** For each possible sample result, Ai, find the difference, Vi, between the expected monetary value for the optimal action and that for the action chosen if only the prior probabilities are used.

**EVSI** = EMV with (free) sample information – EMV without information The EVPI is the most one would be willing to pay for the perfect information.

**EVSI** (n) = EVPI * [1 – exp -a*sqrt(n) ] e.g. 1000 * 1000 simulations 0)Decision model, threshold, priors for uncertain parameters 1) Simulate data collection: sample parameter(s) of interest once ~ prior decide on sample size (ni) (1st level) sample ...

**EVSI** = (EMV with free sample information) - (EMV w/o any information) **EVSI** for Thompson Lumber If sample information had been free EMV (with free SI) = 87,961 + 4000 = $91,961 **EVSI** = 91,961 – 86,000 ...

**EVSI** Calculation Step 1: Determine the optimal decision and its expected return for the possible outcomes of the sample using the posterior probabilities for the states of nature. Step 2: Compute the expected value of these optimal returns.

**EVSI** Calculation **EVSI** = .54($17,855) + .46($11,433) - $14,000 = $900.88 Conclusion Because the **EVSI** is less than the cost of the survey, the survey should not be purchased. Bayes’ Theorem can be used to compute branch probabilities for decision trees.

Assuming that perfect information yields an efficiency of 100%, we can calculate: Efficiency = (**EVSI** / EVPI) x 100 Efficiency of Sample Information Efficiency = ...

What is the expected value of the sample information (**EVSI**) obtained from testing chips? What is the expected value of perfect information (EVPI) for this problem? Policies to Consider Rework every batch before sending it Stage 2.

... **EVSI** Sample information are results taken from an actual test 0 < **EVSI** < EVPI Calculations required Obtain probabilities of test results, pk Revise prior probabilities pj for each test result TRk => pjk Calculate best decision Dk* for each test result TRk ...

The **EVSI** using Decision Trees What is the Definition for the **EVSI**? How do you calculate it using decision trees? Bid Project 1 $40,000 -$2,000 Bid Project 2 $100,000 -$10,000 Bid Project 3 $50,000 -$8,000 Bid Project 4 $60,000 -$15,000 Don’t bid on anything 0 0 PAYOFF ...

**EVSI** assumptions Additional data will yield the same mean values as the observed data - if additional data is sampled from prior distribution is there a potential for **EVSI** decreasing with increased sample?

Expected Value of Sample Information The expected value of sample information (**EVSI**) is the additional expected profit possible through knowledge of the sample or survey information. The expected value associated with the market research study is $15.93.

**EVSI** Calculations required Obtain probabilities of each result TRk , pk For each test result TRk Revise prior probabilities pj => pjk Calculate best decision Dk* (Note: this is a k- fold repetition of the original decision problem!!) Calculate EV (after ...

Value of Information Concepts Perfect Information Additional Information Reliability Bayes’ Theorem Imperfect Information Case Studies Value of Information Concepts EVPI **EVSI** Information No Add'l Info Perfect Imperfect EV(no add'l info) EV(Tree including test) EV(advance info) Note: Gross **EVSI** ...

... **EVSI**, and ENGS Expected payoff of sampling: EPS = .646($0) + 0.226($334,061) + 0.128($1,362,500) = $249,898 Expected payoff of no sampling = 0 Expected value of sample information **EVSI** = EPS – EPNS **EVSI** = $249,898 ...

**EVSI** = |EVwSI – EVwoSI| Statistics for Managers Using Microsoft Excel, 4/e © 2004 Prentice Hall, Inc. Statistics for Managers Using Microsoft Excel, 4/e © 2004 Prentice Hall, Inc. Chapter 1 1-* Title: Statistics for Managers Using Microsoft Excel, 4/e Subject:

... **EVSI** = $63,194 - 44,000 = $19,194 The efficiency of sample information is the ratio of the expected value of sample information to the expected value of perfect information: efficiency = **EVSI** /EVPI = $19,194/ 28,000 = .68 Decision Analysis with Additional Information Expected Value of ...

... (**EVSI**) Problem 12.16 Consider the following payoff table (in $$) You have the option of paying $100 to have research done to better predict which state of nature will occur.

**EVSI** calculation Step 1: Determine the optimal decision and its expected profit for the possible outcomes of the sample using the posterior probabilities for the states of nature. Step 2: Compute the expected value of these optimal profits.

... (**EVSI**) is the difference between the expected value with and without information: For example problem, **EVSI** = $63,194 - 44,000 = $19,194 The efficiency of sample information is the ratio of the expected value of sample information to the expected value of perfect information: ...

It is a number between 0 and 1 given by: Efficiency = **EVSI**/EVPI For the Jones Investment Model: Efficiency = 62.50/141 = .44 Using the Decision Template Bayesian Worksheet Results on Posterior Worksheet Enter Conditional Probabilities Output ...

Expected Value of Sample Information, **EVSI** For each possible sample result, Ai, find the difference, Vi, between the expected monetary value for the optimal action and that for the action chosen if only the prior probabilities are used.

The expected value of sample information (**EVSI**) is the additional expected profit possible through knowledge of the sample or survey information. The expected value associated with the market research study is $15.93.

Expected Value of Sample Information **EVSI** Calculation Step 1: Determine the optimal decision and its expected return for the possible outcomes of the sample using the posterior probabilities for the states of nature. Step 2 ...

... Complex Decision Tree Expected Value of Sample Information Thompson wants to know the actual value of doing the survey **EVSI** = – Expected value with sample information, assuming no cost to gather it Expected value of best decision without sample information = (EV with sample ...

**EVSI** = EV of best decision . with. sample information, assuming no cost to gather it – EV of best decision . without. sample information = EV with sample info. + cost – EV without sample info. DM could pay up to **EVSI** for a survey.

... ranges for decisionmaking Can seek additional information to get a better assessment of likelihoods Can compare **EVSI** to EVPI to determine the efficiency of obtaining additional information Sample Information Once we obtain sample information, ...

... **EVSI** = ($49,200 + $10,000) – $40,000 = $19,200 How sensitive are the decisions to changes in the probabilities? How sensitive is our decision to the probability of a favorable survey result? That is, if the probability of a favorable result ...

... (EVPI/**EVSI**) Obtaining revised Probabilities based on new information (Prior-Probabilities vs. Posterior-Probabilities) Utility function for a company/manager may be hard to define (or non-exist) in real problems. Managers with different backgrounds ...

**EVSI** --- Expected Value of Sample Information More Accurate Test Expected Value of Perfect Information Expected Value of Perfect Info Expected Value of Perfect Information (EVPI) ...

Now the expected value of the test market information, referred to as expected value of sample information (**EVSI**), is defined to be **EVSI** = EVWSI – EVWOI. Expected Value of Perfect Information We can modify the analysis used too determine **EVSI** to find the value of perfect information.

Efficiency = **EVSI** / EVPI = 63 / 141 = 0.45 TOM BROWN – Solution **EVSI** spreadsheet template 6.6 Decision Trees The Payoff Table approach is useful for a non-sequential or single stage. Many real-world decision problems consists of a sequence of dependent decisions.

**EVSI** = expected value of sample information . EVwSI = expected value . with. sample information. about the states of nature. EVwoSI = expected value . without. sample information about the states of nature. where: Expected Value of Sample Information.

Expected Value of Sample Information Sensitivity Analysis **EVSI** = **EVSI** for Thompson Lumber = $59,200 - $40,000 = $19,200 Thompson could pay up to $19,200 and come out ahead. 2,400 $104,000 ($2,400) ($106,400) 1) EMV(node + = ...

... Large Plant Construct Small Plant Do Nothing $200,000 -$180,000 $100,000 -$20,000 0 EMV =$40,000 EMV =$10,000 1 2 **EVSI** = Posterior probabilities Prior probabilities New data Bayes Theorem Market Survey Reliability in Predicting Actual States of Nature Actual States of Nature ...

In general, **EVSI** = - maximum possible expected return with sample information maximum possible expected return without sample information The **EVSI** is an _____of how much one would be willing to pay for this particular sample information. EVPI = 30 (0.45) + 15(0.55) – 12.85 8.90 The ...

In general, the expected value of sample information (**EVSI**) is the additional expected profit possible through knowledge of the sample or survey information. **EVSI** calculation.

Properties of the **EVSI** curve Fitting an Exponential Curve to **EVSI**: Illustrative Model - % response to T0 Fitting an Exponential Curve to **EVSI**: Pharmaco-genetic Test response Unresolved Question Discussion Issues – Phase III trials ...

... (**EVSI**) = expected value with information – expect value without information.: For example problem, **EVSI** = $63,194 - 44,000 = $19,194 How efficiency is this value? From the decision tree From without perfect information (to p45) ...

**EVSI** Calculation **EVSI** = .54($17,855) + .46($11,433) - $14,000 = $900.88 Conclusion Because the **EVSI** is less than the cost of the survey, the survey should not be purchased. Bayes’ Theorem can be used to compute branch probabilities for decision trees.

This value is called the expected value of sample information or **EVSI**. Expected Value of Sample Information -- continued In general we can write the following expression: **EVSI**=EMV with free information - EMV without information For the Acme example the **EVSI** is $3.807 million.

**EVSI** = EVWSI - EVWOI = 4100/3 - 1100 = 800/3. Since **EVSI** > $200, we would ask Ali to draw a coin. 6. The Monty Hall problem . Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats.

Each study will have different **EVSI** as illustrated in the last slide, different costs and therefore difference ENBS and optimal sample sizes. When sample size is very small the posterior mean must be close to the prior mean.

Since perfect information is not obtainable, **EVSI** (expected value of sample information) is usually employed. Thus the netexpected value of information is gained by ‘subtracting’ cost of sampling/procuring information!

Thus, **EVSI** = EMV' - EMV* = $116,516 - $100,000 = $16,516 22.* Expected Value of Sample Information Since the expected value of sample information is greater than the cost of obtaining the information ...