Bayes discriminant rules with ordered predictors. (English) Zbl 1337.62139
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.
MSC:
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 62F15 | Bayesian inference |
Keywords:
discriminant analysis; latent space; misclassification probability; order restrictions; restricted estimationSoftware:
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