Bayes Discriminant Rules with Ordered Predictors

We propose and discuss improved Bayes rules to discriminate between two populations using ordered predictors. To address the problem we propose an alternative formulation using a latent space that allows to introduce the information about the order in the theoretical rules. The rules are first defin...

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Bibliographic Details
Published in:Journal of classification 2009-08, Vol.26 (2), p.201-225
Main Authors: Rueda, Cristina, Fernández, Miguel A., Salvador, Bonifacio
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Automatic classification
Automatic text analysis
Bioinformatics
Classification
Computer science
control theory
systems
Discriminant analysis
Exact sciences and technology
Marketing
Mathematical analysis
Mathematics
Mathematics and Statistics
Methods of scientific computing (including symbolic computation, algebraic computation)
Multivariate analysis
Numerical analysis. Scientific computation
Pattern Recognition
Probability and statistics
Psychometrics
Sciences and techniques of general use
Signal,Image and Speech Processing
Statistical methods
Statistical Theory and Methods
Statistics
Studies
Theoretical computing
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Summary:We propose and discuss improved Bayes rules to discriminate between two populations using ordered predictors. To address the problem we propose an alternative formulation using a latent space that allows to introduce the information about the order in the theoretical rules. The rules are first defined when the marginal densities are fully known and then under normality when the parameters are unknown and training samples are available. Several numerical examples and simulations in the paper illustrate the methodology and show that the new rules handle the information appropriately. We compare the new rules with the classical Bayes and Fisher rules in these examples and we show that the misclassification probability is smaller for the new rules. The method is also applied to data from a diabetes study where we again show that the new rules improve over the usual Fisher rule.
ISSN:0176-4268
1432-1343
DOI:10.1007/s00357-009-9034-z