摘要:

One of the most important steps in decision analysis practice is the elicitation of the decision‐maker’s belief about an uncertainty of interest in the form of a representative probability distribution. However, the probability elicitation process is a task that involves many cognitive and motivational biases. Alternatively, the decision‐maker may provide other information about the distribution of interest, such as its moments, and the maximum entropy method can be used to obtain a full distribution subject to the given moment constraints. In practice however, decision makers cannot readily provide moments for the distribution, and are much more comfortable providing information about the fractiles of the distribution of interest or bounds on its cumulative probabilities. In this paper we present a graphical method to determine the maximum entropy distribution between upper and lower probability bounds and provide an interpretation for the shape of the maximum entropy distribution subject to fractile constraints, (FMED). We also discuss the problems with the FMED in that it is discontinuous and flat over each fractile interval. We present a heuristic approximation to a distribution if in addition to its fractiles, we also know it is continuous and work through full examples to illustrate the approach. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570551

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

The requirement of transformation invariance of a probability distribution is employed to derive prior probabilities for the coefficients of the equation describing a hyperplane. In two dimensions, this is a straight line, in three dimensions an ordinary plane etc. We treat the general case ofndimensions and propose a procedure to normalize the resulting distributions in order to make them proper and appropriate for model comparison problems. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570552

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Maximum entropy in the mean provides a very useful tool for solving linear inverse problems with convex constraints. In this note we review some of the basic theoretical issues and present some examples. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570553

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

This paper is a tutorial on a Bayesian estimation approach to multi‐sensor data and image fusion. First a few examples of simple image fusion problems are presented. Then, the simple case of registered image fusion problem is considered to show the basics of the Bayesian estimation approach and its link to classical data fusion methods such as simple mean or median values, Principal Component Analysis (PCA), Factor Analysis (FA) and Independent Component Analysis (ICA). Then, the case of simultaneous registration and fusion of images is considered. Finally, the problem of fusion of really heterogeneous data such as X‐ray radiographic and ultrasound echo‐graphic data for computed tomography image reconstruction of 2D or 3D objects are considered. For each of the mentioned data fusion problems, a basic method is presented and illustrated through some simulation results. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570554

出版商:AIP    

年代:1903

数据来源: AIP