Application of spatial auto-beta models in statistical classification

Eglė Zikarienė,Kęstutis Dučinskas

doi:10.15388/lmr.2021.25219

Eglė Zikarienė, Kęstutis Dučinskas

Open Access

https://doi.org/10.15388/lmr.2021.25219

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Abstract

In this paper, spatial data specified by auto-beta models is analysed by considering a supervised classification problem of classifying feature observation into one of two populations. Two classification rules based on conditional Bayes discriminant function (BDF) and linear discriminant function (LDF) are proposed. These classification rules are critically compared by the values of the actual error rates through the simulation study.

Highlights

An approach for spatial classification using Bayes rules was introduced by DuÄinskas [5]
We consider a particular case of spatial auto-beta models for solving classification problem of feature observation by using plug-in discriminant functions
This paper is organized as follows: the problem description and the introduction of spatial auto-beta model are presented in the first section and discriminant functions and error rates are analyzed ; in Section 3 numerical experiments are described and the conclusions are in the last section

Summary

Introduction

An approach for spatial classification using Bayes rules was introduced by DuÄinskas [5]. We consider a particular case of spatial auto-beta models for solving classification problem of feature observation by using plug-in discriminant functions. This paper is organized as follows: the problem description and the introduction of spatial auto-beta model are presented in the first section and discriminant functions and error rates are analyzed ; in Section 3 numerical experiments are described and the conclusions are in the last section. We focus on the spatial auto-beta models (SABE) and supervised classification problem with fixed STL, when feature observation Z0, T = (Z , Y ) are given. L=1 where for l = 1, 2, Pl = Plz((−1)lW (Z0; Ψ ) > 0) = H((−1)lW (z0; Ψ ))f0l(z0)dz0 with H(·) denoted the Heaviside step function: H(ν) := 1ν>0 and probability measure Plz is based on conditional Beta distribution with pdf f0l specified in (1). The actual error rate for the L(Z0; Ψ ) which is denoted by LAR(Ψ ) is defined in (6), when W (Z0; Ψ ) is replaced by L(Z0; Ψ )

Numerical experiments

Discussion and conclusions