Bayesian Networks and the Imprecise Dirichlet Model Applied to Recognition Problems

In this paper, we present the following contributions: (i) an adaptation of a precise classifier to work on imprecise classification for cost-sensitive problems; (ii) a new measure to check the performance of an imprecise classifier. The imprecise classifier is based on a method to build simple decision trees that we have modified for imprecise classification. It uses the Imprecise Dirichlet Model (IDM) to represent information, with the upper entropy as a tool for splitting. Our new measure to compare imprecise classifiers takes errors into account. Thus far, this has not been considered by other measures for classifiers of this type. This measure penalizes wrong predictions using a cost matrix of the errors, given by an expert; and it quantifies the success of an imprecise classifier based on the cardinal number of the set of non-dominated states returned. To compare the performance of our imprecise classification method and the new measure, we have used a second imprecise classifier known as Naive Credal Classifier (NCC) which is a variation of the classic Naive Bayes using the IDM; and a known measure for imprecise classification.

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An imprecise Dirichlet model for Bayesian analysis of failure data including right-censored observations

Reliability Engineering & System Safety ◽

10.1016/s0951-8320(96)00131-7 ◽

1997 ◽

Vol 56 (1) ◽

pp. 61-68 ◽

Cited By ~ 27

Author(s):

F.P.A. Coolen

Keyword(s):

Bayesian Analysis ◽

Failure Data ◽

Imprecise Dirichlet Model ◽

Dirichlet Model ◽

Censored Observations

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CAUTIOUS ANALYSIS OF PROJECT RISKS BY INTERVAL-VALUED INITIAL DATA

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488506004266 ◽

2006 ◽

Vol 14 (06) ◽

pp. 663-685 ◽

Cited By ~ 3

Author(s):

LEV V. UTKIN

Keyword(s):

Initial Data ◽

Net Present Value ◽

Cash Flows ◽

Random Set ◽

Present Value ◽

Random Set Theory ◽

Imprecise Dirichlet Model ◽

Project Risks ◽

Dirichlet Model ◽

Interval Valued

One of the most common performance measures in selection and management of projects is the Net Present Value (NPV). In the paper, we study a case when initial data about the NPV parameters (cash flows and the discount rate) are represented in the form of intervals supplied by experts. A method for computing the NPV based on using random set theory is proposed and three conditions of independence of the parameters are taken into account. Moreover, the imprecise Dirichlet model for obtaining more cautious bounds for the NPV is considered. Numerical examples illustrate the proposed approach for computing the NPV.

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