# decision analysis in statistics

Decision Analysis: Making Justifiable, Defensible Decisions Decision analysis is the discipline of evaluating complex alternatives in terms of values and uncertainty. Although this text is devoted to discussing statistical ... Bayesian statistics, (2) game theory, and (3) risk-preference analysis. A table showing payoffs for all combinations of decision al- ternatives and states of nature is a payoff table. Suppose management is concerned about the probability assessments when demand for Chardonnay wine is strong. What is Gorman's optimal decision strategy?e. Computerized analysis of data has made the task simpler. What is the recommended decision if Martin does not wait until September? The Chardonnay grapes would be used to produce a dry Chardonnay wine, and the Riesling grapes would be used to produce a semi-dry Riesling wine. I need an expert in decision making skills and optimization for my statistics project . The purpose of Data Analysis is to extract useful information from data and taking the decision based upon the data analysis. The company must first decide whether to undertake the market research study. Time series analysis helps in analyzing the past, which comes in handy to forecast the future. This initial part of the report introduces the basic elements in (statistical) decision theory and reviews some of the basic concepts of both frequentist statistics and Bayesian analysis. In this context, Bayes’s theorem provides a mechanism for combining a prior probability distribution for the states of nature with sample information to provide a revised (posterior) probability distribution about the states of nature. What is the optimal decision strategy?$$\begin{array}{lll}P(E)=.7 & P\left(s_{1} | E\right)=.34 & P\left(s_{1} | V\right)=.20 \\P(V)=.3 & P\left(s_{2} | E\right)=.32 & P\left(s_{2} | V\right)=.26\end{array}$$$$P\left(s_{3} | E\right)=.34 \quad P\left(s_{3} | V\right)=.54$$c. Each branch of the decision tree … Dante Development Corporation is considering bidding on a contract for a new office building complex. In what follows I hope to distill a few of the key ideas in Bayesian decision theory. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following payoff table shows the projected profit (in thousands of dollars).The state-of-nature probabilities are $P\left(s_{1}\right)=.35, P\left(s_{2}\right)=.35,$ and $P\left(s_{3}\right)=.30$a. A consultant developed the following projections of net cash flow (in thousands of dollars) for a five-year planning horizon. Please refer to the appropriate style manual or other sources if you have any questions. Decision analysis is the process of making decisions based on research and systematic modeling of tradeoffs. decision theoretic methods lend themselves to a variety of applications and computational and analytic advances. With two possibilities for each type of wine it was necessary to assess four probabilities. Find the EVPI.c. Decision analysis (DA) is a systematic, quantitative, and visual approach to addressing and evaluating the important choices that businesses sometimes face. Martin's Service Station is considering entering the snowplowing business for the coming winter season. It is used mostly by data scientists. Exploratory Data Analysis (EDA) Exploratory data analysis (EDA) is a complement to inferential statistics. https://www.britannica.com/science/decision-theory-statistics, Stanford Encyclopedia of Philosophy - Decision Theory. Nodes $5,6,$ and 7 are similar in that they are the decision nodes for Dante to either build the office complex or sell the rights in the project to another developer. You might wonder … To save on expenses, Rona and Jerry agreed to form a carpool for traveling to and from work. $\quad$ Construct a decision tree for this problem.b. After you’ve collected the right data to answer your question from Step 1, it’s time for … In this paper, my discussion leans much towards the last of these three, though there are many elements that speak to all three audiences. How many decision alternatives are there? Hudson Corporation is considering three options for managing its data processing operation: continue with its own staff, hire an outside vendor to do the managing (referred to as outsourcing), or use a combination of its own staff and an outside vendor. The mean is useful in determining the overall trend of a data set or providing a rapid snapshot of your data. What is the expected value?c. The end node is the starting point for the calculations required to analyze decision trees DECISIONS BASED ON STATISTICS Decision tree analysis After the decision tree is drawn, it is analyzed from right to left. Values are generally expressed monetarily because this is a major concern for management. It is a highly effective, business-oriented means … What is the expected value of the market research information? mining for insights that are relevant to the business’s primary goals It features visual classification and decision trees to help you present categorical results and more clearly explain analysis to non-technical audiences. The upper branch from node 2 shows that the company has a .8 probability of winning the contract if it submits a bid. Thus, the ideal of decision theory is to make choices rational by reducing them to a kind of routine calculation. The network may decide to reject the series, but it may also decide to purchase the rights to the series for either one or two years. In considering the role of statistics in business decision making, a core question is how will you derive key metrics in the first place. Why or why not? In fact, a few years ago it spawned an entirely new journal that's good to be aware of called Medical Decision Making. What is the optimal decision?b. Decision Scientists frame data analysis in terms of the decision making process. Each outcome is assigned a “utility” value based on the preferences of the decision maker. Extensive use is made of older disciplines…. The arithmetic mean, more commonly known as “the average,” is the sum of a list of numbers divided by the number of items on the list. The decision to build the complex will result in an income of $\$ 5,000,000$if demand is high and$\$3,000,000$ if demand is moderate. Suppose that sample information $I$ is obtained, with $P\left(I | s_{1}\right)=.20$ and $P\left(I | s_{2}\right)=.75$ Find the posterior probabilities $P\left(s_{1} | I\right)$ and $P\left(s_{2} | I\right) .$ Recommend a decision alternative based on these probabilities. Decision tree analysis is an important strategy for project managers to learn and utilize. An optimal decision, following the logic of the theory, is one that maximizes the expected utility. The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.a. The payoff table showing profit is as follows:$$\begin{array}{ccc} & {\text { State of Nature }} \\\text { Decision Alternative } & s_{1} & s_{2} \\d_{1} & 100 & 300 \\d_{2} & 400 & 200\end{array}$$a. At node $1,$ the company must decide whether to bid on the contract. Assume that the probabilities when Chardonnay demand is weak are still .05 and .50e. Should the town elect to lengthen the runway? Using the original probability assessments, determine how this change would affect the optimal decision. The definition of “rationality” is embodied in a set of axioms that, if accepted by the decision maker, should also require acceptance of the procedures and consequent actions. Updates? The decision making process must include collection and analysis of as much data and information as possible in order to arrive at optimal business decisions. Air Express, a major overnight delivery service, is considering establishing a regional distribution center in Potsdam. Management must decide between a full price service using the company's new fleet of jet aircraft and a discount service using smaller capacity commuter planes. within statistics, decision analysis and operational research. Is the agency's information worth the $\$ 5000$fee? a. Verify Dante's profit projections shown at the ending branches of the decision tree by calculating the payoffs of$\$2,650,000$ and $\$ 650,000$for first two outcomes.b. While every effort has been made to follow citation style rules, there may be some discrepancies. Decision curve analysis (DCA) is a method for evaluating the benefits of a diagnostic test across a range of patient preferences for accepting risk of undertreatment and overtreatment to facilitate decisions about test selection and use. Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. A test market study of the potential demand for the product is expected to report either a favorable$(F)$or unfavorable$(U)$condition. If you need to develop complex statistical or engineering analyses, you can save steps and time by using the Analysis ToolPak. Decision Scientists: Data is the Tool to Make Decisions. What is the expected value of this decision strategy? What is the decision to be made, what is the chance event, and what is the consequence?b. Decision Analysis is designed to help when dealing with difficult decisions by offering more structure and guidance (Clemen, 1996: 4). The following table shows the estimated quarterly profits (in thousands of dollars).a. Analyze Data. Real-life decision analysis is a complex exercise, and usually requires the deployment of various mathematical models and statistical techniques. Everybody agreed that the critical factor in choosing the best size is the number of people who will want to use the new facility. The consultant has provided probability assessments of$.10, .60,$and .30 for the worst-case, base-case, and best-case scenarios, respectively. The optimal solution.b, offers, and usually requires the deployment of various mathematical and. 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