Published On:Sunday 27 November 2011
Posted by Muhammad Atif Saeed
UNCERTAINTY AND USE OF PROBABILITIES
UNCERTAINTY AND USE OF PROBABILITIES
Risk
Risk involves situations or events which may or may not occur, but whose probability of occurrence can be calculated statistically and the frequency of their occurrence predicted from past record
Uncertain events are those whose outcome cannot be predicted with statistical confidence.
Risk seeker
A decision maker who is interested in the best outcomes no matter how small the chance that may occur.
Decision maker
A risk neutral if he is concerned with what will be the most likely outcome.
Risk averse
A decision maker acts on the assumption that the worst outcome might occur.
Maxi min/mini max decision
The play it safe basis for decision making is referred to as the maxi min i.e. “Maximise the minimum achievable profit”. It might called “MiniMax” which is short for “minimise the maximum potential loss”
Maximax /minimin cost
A basis for making decisions by looking for the best outcome is known as the maximax basis ”maximise the maximum achievable profit”. It can also be called the minimin cost rule- minimise the minimum cost/rule.
Decision Tree
A decision tree is a pictorial method of showing a sequence of interrelated decisions and their expected outcomes. Decision trees can incorporate both the probabilities of, and value of, expected outcomes, and are used in decision-making.
Perfect information
Perfect information removes all doubts and uncertainity from a decision, and enables managers to make decisions with complete confidence that they have selected the optimum course of action. Market research can be used to determine with a reasonable degree of accuracy what the demand for a new product will be. How ever market research cost money and it has to decide whether it worth paying for the research or not.
Value of perfect information
The value of perfect information is the difference between the EV of profit with perfect information and the EV of profit without perfect information.
Frequently information is available which can improve the probability estimates for the states of nature.
The expected value of perfect information (EVPI) is the increase in the expected profit that would result if one knew with certainty which state of nature would occur.
The EVPI provides an upper bound on the expected value of any sample or survey information.
EVPI Calculation
• Step 1:
Determine the optimal return corresponding to each state of nature.
• Step 2:
Compute the expected value of these optimal returns.
• Step 3:
Subtract the EV of the optimal decision from the amount determined in step (2).
Bayes’ Theorem and Posterior Probabilities
Knowledge of sample or survey information can be used to revise the probability estimates for the states of nature.
Prior to obtaining this information, the probability estimates for the states of nature are called prior probabilities.
`With knowledge of conditional probabilities for the outcomes or indicators of the sample or survey information, these prior probabilities can be revised by employing
Bayes' Theorem.
The outcomes of this analysis are called posterior probabilities or branch probabilities for decision trees
