STATISTICAL DECISION THEORY ASSIGNMENT HELP

The business has to operate in an atmosphere of uncertainty and has to select the best course out of several alternative courses of action that may be available to him. In earlier days decisions were made mainly on personal judgment. However, these days judgment is combined with several quantitative techniques and the best action is arrived at in a given situation. Actually Statistics may be considered as the science of decision making in the presence of uncertainty. The theory had tremendous impact on the development of statistics as well as on fields like economic, military science, business, industry and operation research, for in all these fields, we are concerned with decision in the presence of uncertainty.

Decision Environment:

In a given day to day problem whether it is a decision regarding the financial management or factory/company management there are broadly common elements in every environment which are listed below:

• Objective: The objective should be clearly marked.
• Courses of action: To achieve the motive what are the courses of actions?
• Benefit or worth or various alternative: The benefit or worth of various alternatives may be calculable. Then it becomes easy to take the decision. In the present case investor may like to know the after-tax position of the earning of his investment. So that the best decision can be taken.
• Events beyond the control of the decision maker: These uncontrollable events are called outcomes or states of nature.
• Events beyond the control of the decision maker: These uncontrollable events are called outcomes or states of nature.
• Uncertainty about outcome: One cannot predict with confidence the outcome of the decision and uncertainty is actually handled by the use of probabilites.

Expected Profit under uncertainty: Assigning probability values

The probability to each sale level can be obtained by dividing each value by total number of times the all values have appeared.

Utility Theory:

The attitude towards risk was not considered. Although maximum expected profit may be a desirable objective, it may carry more of a risk than the decision maker is willing to take and, thus, the decision maker may choose an action than one giving the maximum expected profit simply because of the lower risk. The present discussion has centered on one’s attitude toward risk. There are a number of factors that could affect this attitude, and financial positions would probability be one of them. It is because some people with significant net worths can afford the loss. On the other hand, people with moderate net worths and heavy family obligation tend to be risk averse and invest only when the expected outcome in positive. The decision criterion of loosing or gaining in the bet will vary person to person. For some person the expected value of profit over small investment may not lure them but are guided by thought of solely of utility. The pain of loosing hard-earned or the pleasure of winning a jackpot situation, the former might be more relevant than you care to experience the joy and prosperity.

Utility Functions:

In the decision to characterize one’s willingness to take certain risks is utility. A graph of utility is obtained from utility function, which is simply a function that provides for a quantification of how much relative value a person places on several alternatives, on a scale from 0 to 1. Thus the willingness of an individual to take risk may be obtained from the utility function for the individual. The value 0 is assigned to utility of the smallest payoff in the payoff matrix, which presumably is the payoff that has the least utility to the decision maker. The greatest utility is assumed to belong to the largest payoff in the payoff matrix; hence, it is given a utility of 1.0.

Assumptions Underlying Utility Theory:

In the nut shell, in order to more adequately measure the desirability or undesirability of various gains or losses to a decision maker, we defined a new measure called utility. This measure is represented by a numerical value associated with each monetary gain and loss in order to indicate the utility of these monetary values to the decision maker. We can also assign these utility to outcomes that have no monetary value. It is important to keep in mind that the type of theory discussed here does not purport to describe the way people actually do behave in the real world, but rather specifies how they should behave if their decisions are to be consistent with their own expressed judgment as to preferences among consequences.