Lecture 7 (End of Chapter Questions)

Question 1

What does Bayes’ Theorem say? Why is it important?

Answer 1

• Bayes’ Theorem reverses the conditional probability
• It is used for revising a probability value (prior p(y)) based on additional information that is later obtained (signal s) -> this information is used to construct he posterior distribution p(y|s)
• By using Bayes’ Theorem we can reverse an event tree

Question 2

How do you flip an event tree?

Answer 2

• By using Bayes’ Theorem we can reverse an event tree

Question 3

How do you calculate the value of imperfect information?

Answer 3

Value of imperfect information = EV with imperfect information - EV without

Question 4

What is the advantage of Monte Carlo Simulation?

Answer 4

• Monte Carlo Simulation is used if there are many uncertain factors that affect the decision or if the uncertain variables can have many possible values
• It is used to describe or predict how a system will operate and to determine values for the controllable inputs
• Results show what could happen and how likely it is

Question 5

How do you determine the number of simulation runs?

Answer 5

We calculate N using the formula:

N = [(z_1 - alpha/2 * sigma) / ε]^2

• > ensures that p(|θ_n − θ| ≤ ε) = 1 − α
• > We have to determine sigma by doing a pilot simulation with a small number of runs (>50)