A Bayesian classifier

Authors:
B. A. Zalessky and P. V. Lukashevich

Translated by:
N. Semenov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **78** (2008).

Journal:
Theor. Probability and Math. Statist. **78** (2009), 23-35

MSC (2000):
Primary 62C10; Secondary 90Bxx

DOI:
https://doi.org/10.1090/S0094-9000-09-00759-5

Published electronically:
August 4, 2009

MathSciNet review:
2446846

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a new Bayesian classifier for the classification of multidimensional observations of if the learning sample is known. We assume that the data are generated by two disjoint bounded sets and each vector of the sample is a result of the observation after one of the sets , , with a random error. In other words, we assume that a priori the Bayesian probability is given on the set and that every vector of observations has the density

The maximum a posteriori probability estimators , , for the sets , , are constructed with the help of the learning sample. Under natural assumptions imposed on and , we show that the estimators converge to some sets (possibly different from and ). If the mean frequencies of observations of the classes are equal to , , then the estimators are consistent in the sense that , . We also discuss some results of numerical experiments showing the applicability of our classifier for solving the problems of the statistical classification.

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Additional Information

**B. A. Zalessky**

Affiliation:
United Institute of Informatics Problems, National Academy of Sciences, Surganova Street 6, Minsk, 220012, Belarus’

Email:
zalesky@newman.bas-net.by

**P. V. Lukashevich**

Affiliation:
United Institute of Informatics Problems, National Academy of Sciences, Surganova Street 6, Minsk, 220012, Belarus’

DOI:
https://doi.org/10.1090/S0094-9000-09-00759-5

Received by editor(s):
October 23, 2006

Published electronically:
August 4, 2009

Additional Notes:
The first author was supported by the INTAS grant 04-77-7036

Article copyright:
© Copyright 2009
American Mathematical Society