Belief Function Approach to Evidential Reasoning in Causal Maps

2005 ◽  
pp. 109-141
Author(s):  
Rajendra P. Srivastava ◽  
Mari W. Buche ◽  
Tom L. Roberts
Keyword(s):  
Job Satisfaction ◽  
Information Technology ◽  
Belief Function ◽  
Evidential Reasoning ◽  
Belief Functions ◽  
Causal Maps ◽  
Dempster Shafer Theory ◽  
Evidential Reasoning Approach ◽  
Theory Of Belief Functions ◽  
Shafer Theory

The purpose of this chapter is to demonstrate the use of the evidential reasoning approach under the Dempster-Shafer (D-S) theory of belief functions to analyze revealed causal maps (RCM). The participants from information technology (IT) organizations provided the concepts to describe the target phenomenon of Job Satisfaction. They also identified the associations between the concepts. This chapter discusses the steps necessary to transform a causal map into an evidential diagram. The evidential diagram can then be analyzed using belief functions technique with survey data, thereby extending the research from a discovery and explanation stage to testing and prediction. An example is provided to demonstrate these steps. This chapter also provides the basics of Dempster-Shafer theory of belief functions and a step-by-step description of the propagation process of beliefs in tree-like evidential diagrams.

scholarly journals Plato's Cave in the Dempster-Shafer land--the Link between Pignistic and Plausibility Transformations

2017 ◽  
Author(s):  
Chunlai Zhou ◽  
Biao Qin ◽  
Xiaoyong Du
Keyword(s):  
Statistical Inference ◽  
Belief Function ◽  
Belief Functions ◽  
Reasoning Under Uncertainty ◽  
Function Model ◽  
Probability Functions ◽  
Degree Of Belief ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Theory Of Evidence

In reasoning under uncertainty in AI, there are (at least) two useful and different ways of understanding beliefs: the first is as absolute belief or degree of belief in propositions and the second is as belief update or measure of change in belief. Pignistic and plausibility transformations are two well-known probability transformations that map belief functions to probability functions in the Dempster-Shafer theory of evidence. In this paper, we establish the link between pignistic and plausibility transformations by devising a belief-update framework for belief functions where plausibility transformation works on belief update while pignistic transformation operates on absolute belief. In this framework, we define a new belief-update operator connecting the two transformations, and interpret the framework in a belief-function model of parametric statistical inference. As a metaphor, these two transformations projecting the belief-update framework for belief functions to that for probabilities are likened to the fire projecting reality into shadows on the wall in Plato's cave.

Risk and Reliability Formulas for Systems Security under Dempster-Shafer Theory of Belief Functions

2008 ◽  
Vol 5 (1) ◽  
pp. 189-219 ◽  
Author(s):  
Rajendra P. Srivastava ◽  
Chan Li
Keyword(s):  
Network Model ◽  
Analytical Formula ◽  
Sensitivity Analyses ◽  
Belief Functions ◽  
Security Risk ◽  
Tree Model ◽  
Dempster Shafer Theory ◽  
Systems Security ◽  
Theory Of Belief Functions ◽  
Shafer Theory

ABSTRACT: This paper develops comprehensive formulas for assessing the risk and reliability of “Systems Security” under the Dempster-Shafer theory of belief functions, using the Trust Services framework as proposed by the American Institute of Certified Public Accountants (AICPA) and Canadian Institute of Chartered Accountants (CICA). In addition, we discuss how these formulas can be used for planning and evaluation of “Systems Security” risk under the SysTrust services. The analytical formulas are derived for a tree-structured evidential diagram which is constructed by converting the exact network-structured evidential diagram. The use of an analytical formula eliminates the computational complexities of propagating beliefs in a network and allows the assurance provider to use a simple spreadsheet to combine evidence. We provide theoretical justification and perform sensitivity analyses to show that the analytical formula based on a tree-type evidential diagram is a good approximation of the exact network model under realistic situations. However, as shown theoretically and also through the sensitivity analysis, the analytical formula provides significantly different results when input beliefs are significantly negative. It should be noted that the analytical formula based on the tree model provides a more conservative assessment of information systems risk than the exact network model.

Using Dempster-Shafer Theory in Data Mining

2011 ◽  
pp. 1166-1170
Author(s):  
Malcolm J. Beynon
Keyword(s):  
Data Mining ◽  
Mathematical Theory ◽  
Evidential Reasoning ◽  
Belief Functions ◽  
Partial Knowledge ◽  
Dempster Shafer Theory ◽  
Upper And Lower Probabilities ◽  
Shafer Theory ◽  
Theory Of Evidence

The origins of Dempster-Shafer theory (DST) go back to the work by Dempster (1967) who developed a system of upper and lower probabilities. Following this, his student Shafer (1976), in his book “A Mathematical Theory of Evidence” added to Dempster’s work, including a more thorough explanation of belief functions. In summary, it is a methodology for evidential reasoning, manipulating uncertainty and capable of representing partial knowledge (Haenni & Lehmann, 2002; Kulasekere, Premaratne, Dewasurendra, Shyu, & Bauer, 2004; Scotney & McClean, 2003).

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