DQ1 Week 6 Please respond to this discussion question by Thursday Day 3 What are the elements of a decision How does statistical decision theory differ in conditions of certainty and uncertainty When making a decision can doing nothing be a valid alternative Why Please remember to cite your sources First of all decision theory is in statistics a set of quantitative methods for reaching optimal decisions A solvable decision problem must be capable of being tightly formulated in terms of initial conditions and choices or courses of action with their consequences In general such consequences are not known with certainty but are expressed as a set of probabilistic outcomes Each outcome is assigned a utility value based on the preferences of the decision maker An optimal decision following the logic of the theory is one that maximizes the expected utility Thus the ideal of decision theory is to make choices rational by reducing them to a kind of routine calculation Brittanica com 2012 http www britannica com EBchecked topic 155155 decision theory What are the elements of a decision There are 4 basic elements in decision theory acts events outcomes and payoffs Acts are the actions being considered by the agent Occurrences taking place outside the control of the agent Outcomes are the result of the occurrence or lack of it of acts and events Payoffs are the values the decision maker is placing on the occurrences Sieu edu 2012 http www siue edu evailat decision htm How does statistical decision theory differ in conditions of certainty and uncertainty Decision theory can apply to conditions of certainty risk or uncertainty Decision under certainty means that each alternative leads to one and only one consequence and a choice among alternatives is equivalent to a choice among consequences In decision under risk each alternative will have one of several possible consequences and the probability of occurrence for each consequence is known Therefore each alternative is associated with a probability distribution and a choice among probability distributions When the probability distributions are unknown one speaks about decision under uncertainty Decision theory for risk conditions is based on the concept of utility The decision maker s preferences for the mutually exclusive consequences of an alternative are described by a utility function that permits calculation of the expected utility for each alternative The alternative with the highest expected utility is considered the most preferable For the case of uncertainty decision theory offers two main approaches The first exploits criteria of choice developed in a broader context by game theory as for example the maxmin rule where we choose the alternative such that the worst possible consequence of the chosen alternative is better than or equal to the best possible consequence of any other alternative The second approach is to reduce the uncertainty case to the case of risk by using subjective probabilities based on expert assessments or on analysis of previous decisions made in similar circumstances Professor Hossein Arsham 1994 2012 http homogenated stat stat data DsAppendix htm When making a decision can doing nothing be a valid alternative according to way2wellness com Decide on an alternative 1 After the data has been gathered and the analysis is complete those responsible for making the final decision should consider the opinions of others who will be affected by the decision 2 Even a senior manager who must decide on the future direction of his or her unit or organization should consult the staff involved before making a final choice 3 By getting other people s opinions at this critical stage the manager increases the chances of successful implementation of the ultimate decision 4 Remember that making a decision to do nothing constitutes a valid alternative 5 Be sure to consider this opinion actively and avoid slipping into this alternative through indecision http www myway2wellness com w2w w2w Content subContent Ways Way2 Self actualization R2FEWL2 I4T1 asp Why with regard to the decision theory model electing to do nothing is a valid option as an available alternative Research can lead to evidence suggesting a change in inputs could adversely affect the outcomes If an event influenced a certain outcome but is not probable to occur again doing nothing is a viable option in the decision making process 3 Develop alternatives Make a list of all the possible choices you have including the choice of doing nothing Not choosing one of the candidates or one of the building sites is in itself a decision Often a non decision is harmful as we mentioned above not choosing to turn either right or left is to choose to drive into the bridge But sometimes the decision to do nothing is useful or at least better than the alternatives so it should always be consciously included in the decision making process Robert Harris 2009