The tradeoffs between accuracy and computation speed for the mixture distribution approach compare favorably with those for discretization and other approaches in a variety of problems, especially ones that call for extensions of powerful Gaussian models such as the Kalman filter. Influence diagrams, which represent decision and inference problems graphically, are used to represent problems formulated with mixtures, and to solve them efficiently in the case of Gaussian mixtures, exploiting the tractability of the multivariate Gaussian distribution. Product C is essentially a risk-free proposition, from which the company will obtain a net profit of 1 million. Common statistical methods for estimating mixtures, such as the EM algorithm, are adapted for fitting artificial mixtures, and a simple objective that balances accuracy and computational cost is used to select the number of continuous components. EXTRA PROBLEM 2: CONSTRUCTING DECISION TREES & INFLUENCE DIAGAMS The Executives of the general products company (GPC) have to decide which of three products to introduce, A, B, or C. We aim to respond to every message within one working day. Unlike most of the mixture literature, this dissertation emphasizes constructing artificial mixtures in order to approximate arbitrary continuous distributions in a tractable form. We want to help, so if you continue to encounter any sign in problems, email. It generalizes both discrete and Gaussian distributions and can combine advantages of each for analysis. A Gaussian mixture becomes Gaussian when conditioned on the outcome of an unobserved discrete variable. Questions Imagine that you are a DuPont executive charged with making the decision regarding continued production of CFCs. This dissertation develops the use of mixture distributions, especially Gaussian mixtures (normal mixtures), for this purpose. An alternative approximation is to fit tractable continuous probability distributions to the continuous random variables, allowing calculations in closed form. To simplify assessments and computations, practitioners of decision analysis discretize these to a few points. 2 Elements of Decision Problems 3 Structuring Decisions 4 Making Choices. Decision problems often involve continuous random variables and continuous decision variables.
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