Statistics 2 Dersi 8. Ünite Sorularla Öğrenelim

What are the steps of decision making?

The first step is to define the decision problem.

Once the problem is clearly defined, the next logical step is to investigate about the alternatives to solve the decision problem.

The next step is to find out about the “states of world”, or “states of nature”.

For each combination of decision alternative and state of nature, a payoff value is calculated.

Once all the payoff values are calculated, a payoff matrix or decision table is created.

The decision maker should calculate all the payoff values.

Once the payoff matrix has been created, the next step is to select a mathematical decision theory model to study the matrix.

Once the model is decided then the last step is to apply the model and find out the best decision alternative suggested by the decision theory model.

For making an effective  decision, explain the first step, which is to define problem.

The first step is to define the decision problem. We need to clearly identify our decision problem and study all the characteristic of the decision problem. We should ensure that when the decision problem is laid out everyone should understand the same think. There should be no debatable points on what the extend of the decision problem is and what is the size of the decision problem etc. An example is “How should I travel to work today?”. In this example, commute to work is the decision problem.

Explain states of nature in decision making process.

In decision making, states of nature are the outcomes on which the decision maker has little or no control. If you make an investment on different assets such as purchasing gold, foreign currency, or bonds for a specific time period, the gain at the end of the period is affected by the state of the economy during your investment period. Different asset’s prices will react differently to the different economic conditions. Therefore, you may define, as an example, two states of nature such as good economic conditions and bad economic conditions in your investment period. Deciding on states of nature is important since these are the conditions that might arise once you commit to your decision. The past data on the decision problem becomes an important issue for choosing the appropriate states of nature. Remember commute to work example, usually the weather conditions will affect the choice of transportation to work, in a snowy day taking a train might be quicker than driving your car. Therefore, weather conditions can be studied as states of nature or states of world in this example.

Explain the payoff values in decision making process.

For each combination of decision alternative and state of nature, a payoff value is calculated. Payoff values might be profits or costs depending on the overall purpose of the decision. If the payoff values are profit based, each payoff value will show you the profit value for the chosen decision alternative and specific state of the nature. In order to find the profit or cost values for each combination of decision alternative, state of nature, you need to seek expert opinions. Calculating the payoff values for each combination requires substantial time and effort.

What is the use of payoff matrix in decision making?

Once all the payoff values are calculated, a payoff matrix or decision table is created. The payoff matrix will show you all the possible decision alternatives of the problem, all the states of nature and the payoff values for each of alternative and states of nature combination.

What are the three main decision environments?

In order to create the mathematical model for the decision theory, we need to study the decision environment. The main question here is that under which conditions the decision should be given. There are three main decision making environments studied in literature as follows:
• Decision making under certainty
• Decision making under uncertainty
• Decision making under risk

Explain decision making under certainty.

The first decision making environment is given as decision making under certainty. In this setting, the decision maker definitely knows, hundred percent sure, what will happen in the decision problem. Naturally, if the decision maker is hundred percent sure that which of the states of nature will be faced with, then choosing the best decision alternative is trivial. The decision with the best payoff value for the known state of nature is chosen and the decision making process is over. For example, a manager wants to build a new factory that cost the same in construction in two different cities, the cost of building the new factory is the same but one of the cities states that if the factory is built in their city they will give this company 5% tax deduction for each product produced and sold from the new factory, whereas the other city offers only 3% tax deduction. In this setting it is easy to see that the best decision alternative is to build the new factory in the first city offering 5% tax deduction on the assumption that all the other factors building a factory in these two different cities are the same.

Explain decision making under uncertainty.

The second decision making environment is decision making under uncertainty. In this environment, the decision maker can list all the states of nature that are possible in the decision problem but cannot assign any probability value to the specific state of nature that might happen. If you want to invest your money to different assets, and if the states of nature are given as “good economic conditions” and “bad economic conditions”, you cannot assign a probability value for facing with good economic conditions or bad economic conditions in decision making under uncertainty environment.

Explain decision making under risk.

The last decision making environment is decision making under risk. In this setting the decision maker is able to assign probabilities to states of nature. In this environment, decision maker assigns a probability to each state of nature, therefore decision maker is able to calculate how much risk is taken if that state of nature happens. In decision making under risk, the payoff matrix shown in Table 8.1 includes the probabilities associated with each state of nature.

Explain optimistic approach in decision making.

As the name implies, in optimistic approach, decision maker thinks that all the good things will happen. Decision maker creates the payoff table based on either profit or cost for each combination of decision alternative and state of nature. Then, the decision maker chooses the maximum or minimum payoff value for each decision alternative, and then decision maker selects the decision alternative that gives the highest or lowest of these payoffs. This method is also known as Plunger’s optimism criterion.

Explain the pessimistic approach in decision making.

This method is also known as Wald’s pessimism criterion. In here, the decision maker follows a pessimistic approach to solve the decision problem. The decision maker tries to minimize the damage since the overall approach is to look for the best among the worst payoff values. Decision maker creates the payoff table table either profit or cost based for each combination of (decision alternative, state of nature). Then, the decision maker chooses the minimum or maximum payoff value for each decision alternative, and then decision maker selects the decision alternative that gives the lowest or highest of these payoffs.

Explain the Hurwicz Criterion in decision making.

In a paper in 1951, Leonard Hurwicz suggested a new method that balances the optimism and pessimism of the decision maker. In this method, the decision maker is allowed to have best and worst possible outcomes considered. In order to achieve this, Hurwicz suggests the use of coefficient of optimism. It is symbolized with ? and it is a decimal number between 0 and 1. If ? = 1, then the decision maker is hundred percent optimistic. If ? = 0, then the decision maker is hundred percent pessimistic. Since ? is the level of optimism we may easily call 1 – ? as the level of pessimism in the decision problem. Therefore, by changing the value of the ?, the decision maker may try to balance the optimism and pessimism. If you remember the weighted arithmetic mean, you may easily identify Hurwicz method of being a weighted average of best and worst possible outcomes.

Explain expected monetary value in decision making.

In decision making under risk environment, it is possible to assign probabilities to the states of nature. If the decision is made under the risk environment, the payoff table shows the probabilities associated with the states of nature. In this setting, it is possible to calculate the expected monetary value or expected of value (mean value) of each decision alternative. Calculating the expected monetary value are easy. For each decision alternative, payoff value and the associated state of the nature’s probability is multiplied and the total of these multiplications for every state of nature for each row of the payoff table gives us the expected monetary value of the decision alternative.

Explain decision tree in decision making under risk.

A graphical representation of a decision problem comes in the form of decision tree. Decision tree is a very useful tool to show all the aspects of the decision problem on one graph. If the payoff matrix is created under the risk environment, decision maker may show all the expected monetary values over the graph. On a decision tree, it will be easier to see which decision alternatives give similar results, and what is the next closest decision alternative to the best decision alternative. The decision tree includes all the scenarios that might happen in the decision process, therefore decision maker can see all the possibilities of the decision problem with their consequences. There are some main components of the decision tree. The decision trees are drawn from left to right starting with the main decision node and ending up payoff values. If you can create a payoff matrix, then you can create the decision tree, therefore the decision trees can be used in both decision making under uncertainty and decision making under risk