scholarly journals The influence of training sampling size on the expected error rate in spatial classification

2012 ◽  
Vol 53 ◽  
Author(s):  
Lina Dreižienė ◽  
Marta Karaliutė
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Asymptotic Approximation ◽  
Covariance Function ◽  
Spatial Sampling ◽  
Anisotropy Ratio ◽  
Gaussian Data ◽  
Two Populations ◽  
Bayes Discriminant Function

In this paper we use the pluged-in Bayes discriminant function (PBDF) for classification of spatial Gaussian data into one of two populations specified by different parametric mean models and common geometric anisotropic covariance function. The pluged-in Bayes discriminant function is constructed by using ML estimators of unknown mean and anisotropy ratio parameters. We focus on the asymptotic approximation of expected error rate (AER) and our aim is to investigate the effects of two different spatial sampling designs (based on increasing and fixed domain asymptotics) on AER.

scholarly journals Linear discriminant analysis of spatial Gaussian data with estimated anisotropy ratio

2011 ◽  
Vol 52 ◽  
Author(s):  
Lina Dreižienė
Keyword(s):  
Spatial Data ◽  
Asymptotic Approximation ◽  
Covariance Function ◽  
Anisotropy Ratio ◽  
Linear Discriminant ◽  
Gaussian Data ◽  
Unknown Covariance ◽  
Two Populations ◽  
Bayes Discriminant Function

The paper deals with a problem of classification of Gaussian spatial data into one of two populations specified by different parametric mean models and common geometric anisotropic covariance function. In the case of an unknown mean and covariance parameters the Plug-in Bayes discriminant function based on ML estimators is used. The asymptotic approximation of expected error rate (AER) is derived in the case of unknown mean parameters and single unknown covariance parameter i.e., anisotropy ratio.  

scholarly journals Discriminant analysis of the equicorrelated Gaussian observations

2021 ◽  
Vol 47 ◽  
Author(s):  
Kęstutis Dučinskas ◽  
Jurgita Neverdauskaiė
Keyword(s):  
Numerical Analysis ◽  
Discriminant Analysis ◽  
Maximum Likelihood ◽  
Discriminant Function ◽  
Error Rate ◽  
Maximum Likelihood Estimators ◽  
Training Sample ◽  
Common Variance ◽  
Bayes Discriminant Function

In this paper the problem of classification of an observation into one of two Gaussian populations with different means and common variance is considered in the case when equicorrelated training sample is given. Unknown means and common variance are estimated from training sample and these estimators are pluged in the Bayes discriminant function. The maximum likelihood estimators are used. The approximation of the expected error rate associated with Bayes plug-in discriminant function is derived. Numerical analysis of the accuracy of that approximation for various values of correlation is presented.

scholarly journals Error rates in spatial classification of Gaussian data with random labeling

2010 ◽  
Vol 51 ◽  
Author(s):  
Lijana Stabingienė ◽  
Kęstutis Dučinskas
Keyword(s):  
Random Field ◽  
Error Rate ◽  
Field Model ◽  
Gaussian Random Field ◽  
Parametric Uncertainty ◽  
Error Rates ◽  
Spatial Classification ◽  
Random Labeling ◽  
Gaussian Data

In spatial classification it is usually assumed that features observations given labels are independently distributed. We have retracted this assumption by proposing stationary Gaussian random field model for features observations. The label are assumed to follow Disrete Random Field (DRF) model. Formula for exact error rate based on Bayes discriminant function (BDF) is derived. In the case of partial parametric uncertainty (mean parameters and variance are unknown), the approximation of the expected error rate associated with plug-in BDF is also derived. The dependence of considered error rates on the values of range and clustering parameters is investigated numerically for training locations being second-order neighbors to location of observation to be classified.

scholarly journals Statistical Classification of the Observation of Nuggetless Spatial Gaussian Process with Unknown Sill Parameter

2009 ◽  
Vol 14 (2) ◽  
pp. 155-163 ◽  
Author(s):  
K. Dučinskas
Keyword(s):  
Asymptotic Expansion ◽  
Gaussian Process ◽  
Discriminant Function ◽  
Training Sample ◽  
Unknown Parameters ◽  
Process Observation ◽  
Two Populations ◽  
Sample Case ◽  
Accuracy Of Approximation

The problem of classification of spatial Gaussian process observation into one of two populations specified by different regression mean models and common stationary covariance with unknown sill parameter is considered. Unknown parameters are estimated from training sample and these estimators are plugged in the Bayes discriminant function. The asymptotic expansion of the expected error rate associated with Bayes plug-in discriminant function is derived. Numerical analysis of the accuracy of approximation based on derived asymptotic expansion in the small training sample case is carried out. Comparison of two spatial sampling designs based on values of this approximation is done.

scholarly journals Application of spatial auto-beta models in statistical classification

2021 ◽  
Vol 62 ◽  
pp. 36-43
Author(s):  
Eglė Zikarienė ◽  
Kęstutis Dučinskas
Keyword(s):  
Discriminant Function ◽  
Spatial Data ◽  
Supervised Classification ◽  
Classification Problem ◽  
Error Rates ◽  
Classification Rules ◽  
Linear Discriminant ◽  
Actual Error ◽  
Two Populations ◽  
Bayes Discriminant Function

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.

Expected Bayes Error Rate in Supervised Classification of Spatial Gaussian Data

Informatica ◽  
2011 ◽  
Vol 22 (3) ◽  
pp. 371-381 ◽  
Author(s):  
Kęstutis Dučinskas ◽  
Lijana Stabingienė
Keyword(s):  
Error Rate ◽  
Supervised Classification ◽  
Bayes Error Rate ◽  
Bayes Error ◽  
Gaussian Data

Quadratic Discriminant Analysis of Spatially Correlated Data

2001 ◽  
Vol 6 (2) ◽  
pp. 15-28 ◽  
Author(s):  
K. Dučinskas ◽  
J. Šaltytė
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Gaussian Random Field ◽  
Correlated Data ◽  
Covariance Matrices ◽  
Classification Rule ◽  
Spatial Correlations ◽  
Linear Quadratic ◽  
Spatial Correlation Function ◽  
Spatially Correlated

The problem of classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and different factorised covariance matrices is considered. In such a case optimal classification rule in the sense of minimum probability of misclassification is associated with non-linear (quadratic) discriminant function. Unknown means and the covariance matrices of the feature vector components are estimated from spatially correlated training samples using the maximum likelihood approach and assuming spatial correlations to be known. Explicit formula of Bayes error rate and the first-order asymptotic expansion of the expected error rate associated with quadratic plug-in discriminant function are presented. A set of numerical calculations for the spherical spatial correlation function is performed and two different spatial sampling designs are compared.

Paepalanthus fabianeae (Eriocaulaceae): A New Microendemic Species from a Morphologically Coherent Clade

2020 ◽  
Vol 45 (4) ◽  
pp. 794-801
Author(s):  
Caroline Oliveira Andrino ◽  
Marcelo Fragomeni Simon ◽  
Jair Eustáquio Quintino Faria ◽  
André Luiz da Costa Moreira ◽  
Paulo Takeo Sano
Keyword(s):  
New Species ◽  
Iucn Red List ◽  
Phylogenetic Position ◽  
Similar Species ◽  
Infrageneric Classification ◽  
Espinhaço Range ◽  
Nuclear Its ◽  
Two Populations

Abstract—We describe and illustrate Paepalanthus fabianeae, a new species of Eriocaulaceae from the central portion of the Espinhaço Range in Minas Gerais, Brazil. Previous phylogenetic evidence based on analyses of nuclear (ITS and ETS) and plastid (trnL-trnF and psba-trnH) sequences revealed P. fabianeae as belonging to a strongly supported and morphologically coherent clade containing five other species, all of them microendemic, restricted to the Espinhaço range. Due to the infrageneric classification of Paepalanthus being highly artificial, we preferred not assigning P. fabianeae to any infrageneric group. Paepalanthus fabianeae is known from two populations growing in campos rupestres (highland rocky fields) in the meridional Espinhaço Range. The species is characterized by pseudodichotomously branched stems, small, linear, recurved, and reflexed leaves, urceolate capitula, and bifid stigmas. Illustrations, photos, the phylogenetic position, and a detailed description, as well as comments on habitat, morphology, and affinities with similar species are provided. The restricted area of occurrence allied with threats to the quality of the habitat, mainly due to quartzite mining, justifies the preliminary classification of the new species in the Critically Endangered (CR) category using the guidelines and criteria of the IUCN Red List.

Validity and Clinical Scale Comparisons between the MMPI and MMPI-2 with Psychiatric Inpatients

1992 ◽  
Vol 70 (1) ◽  
pp. 323-332 ◽  
Author(s):  
Dudley David Blake ◽  
Phillip M. Kleespies ◽  
Walter E. Penk ◽  
Suellen S. Walsh ◽  
DeAnna L. Mori ◽  
...  
Keyword(s):  
Discriminant Function ◽  
Relative Stability ◽  
Patient Population ◽  
Psychiatric Patients ◽  
Special Populations ◽  
Clinical Scale ◽  
Acute Psychiatry ◽  
Highly Correlated ◽  
Discriminant Function Analyses

This study was designed to investigate the comparability of the original MMPI (1950) and the MMPI-2 (1989) with a psychiatric patient population. 34 male and 3 female patients, shortly after admission to one of two acute psychiatry units, completed the old and revised versions of the MMPI. Paired t tests indicated but scant differences for raw scores, while many more differences were found among T scores for validity, clinical, and supplemental scales. Analyses, however, showed all scales on the two forms to be highly correlated. Analysis of the high-point and two-point codes across the two administrations also showed relative stability, although the proportion of Scales 2 (Depression) and 8 (Schizophrenia) decreased, while those for Scales 6 (Paranoia) and 7 (Psychasthenia) increased markedly in the MMPI-2 protocols. Examination of each version's discriminability among mood- and thought-disordered subsamples suggested that the MMPI provides slightly better delineation between diagnostic classes. Discriminant function analyses showed that there were essentially no differences between the two forms in the accurate classification of clinical and nonclinical groups. The findings reported here provide support for the MMPI-2; despite modification, the newer form retains the advantages of the original MMPI. Differences found here may be unique to psychiatric patients and their patterns of MMPI/MMPI-2 equivalence and may not generalize to other special populations.

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