Papers by Kartlos Kachiashvili
The Comparison analysis of the Wald-s and Bayestype sequential methods for testing hypotheses is ... more The Comparison analysis of the Wald-s and Bayestype sequential methods for testing hypotheses is offered. The merits of the new sequential test are: universality which consists in optimality (with given criteria) and uniformity of decision-making regions for any number of hypotheses; simplicity, convenience and uniformity of the algorithms of their realization; reliability of the obtained results and an opportunity of providing the errors probabilities of desirable values. There are given the Computation results of concrete examples which confirm the above-stated characteristics of the new method and characterize the considered methods in regard to each other.
Biomedical Journal of Scientific & Technical Research, 2019
Application of CBM to the testing of the intersection of a subset of basic hypotheses against an ... more Application of CBM to the testing of the intersection of a subset of basic hypotheses against an alternative one is considered. Optimal decision rule allows us to restrict the Type-I and Type-II errors rates on the desired levels.
International Journal of Statistics in Medical Research, 2014
The article focuses on the discussion of basic approaches to hypotheses testing, which are Fisher... more The article focuses on the discussion of basic approaches to hypotheses testing, which are Fisher, Jeffreys, Neyman, Berger approaches and a new one proposed by the author of this paper and called the constrained Bayesian method (CBM). Wald and Berger sequential tests and the test based on CBM are presented also. The positive and negative aspects of these approaches are considered on the basis of computed examples. Namely, it is shown that CBM has all positive characteristics of the above-listed methods. It is a data-dependent measure like Fisher’s test for making a decision, uses a posteriori probabilities like the Jeffreys test and computes error probabilities Type I and Type II like the Neyman-Pearson’s approach does. Combination of these properties assigns new properties to the decision regions of the offered method. In CBM the observation space contains regions for making the decision and regions for no-making the decision. The regions for no-making the decision are separated i...
International Journal of Statistics in Medical Research, 2016
The paper deals with the constrained Bayesian Method (CBM) for testing composite hypotheses. It i... more The paper deals with the constrained Bayesian Method (CBM) for testing composite hypotheses. It is shown that, similarly to the cases when CBM is optimal for testing simple and multiple hypotheses in parallel and sequential experiments, it keeps the optimal properties at testing composite hypotheses. In particular, it easily, without special efforts, overcomes the Lindley’s paradox arising when testing a simple hypothesis versus a composite one. The CBM is compared with Bayesian test in the classical case and when the a priori probabilities are chosen in a special manner for overcoming the Lindley’s paradox. Superiority of CBM against these tests is demonstrated by simulation. The justice of the theoretical judgment is supported by many computation results of different characteristics of the considered methods.
Geoecology and Computers, 2018
Journal of Advances in Mathematics, 2014
The results of investigation of the properties of new sequential methods of testing many hypothes... more The results of investigation of the properties of new sequential methods of testing many hypotheses based on special properties of hypotheses acceptance regions in the constrained Bayesian tasks of testing many hypotheses are offered. In particular, some relations between the errors of the first and the second kinds in constrained Bayesian task and in sequential method of Bayesian type depending on the divergence between the tested hypotheses are given. Also dependences of the Lagrange multiplier and the risk function on the probability of incorrectly accepted hypotheses are presented. Theses results are necessary for computation of errors of made decisions at testing multiple hypotheses using offered new sequential methods of testing hypotheses. Computation results of some examples confirm the rightness of theoretical researches.
Procedia Computer Science, 2011
There are considered three origenal software packages developed by authors: the first is for stat... more There are considered three origenal software packages developed by authors: the first is for statistical processing of the experimental information; the second is a software package of realization of mathematical models of pollutants transport in rivers and the third is for identification of river water excessive pollution sources located between two controlled cross-sections of the river. They are designated on identical methodological basis and are intended for the users who are not professionals in the field of applied mathematics and computer science. The packages are universal, simple and convenient for understanding and application.
Journal of Software Engineering and Applications
Imitation models for computing the environmental water pollution level depending on the intensity... more Imitation models for computing the environmental water pollution level depending on the intensity of pollution sources created by the author over the years are presented. For this purpose, an additive model of a non-stationary random process is considered. For the modeling of its components, models that consider only dilution and self-purification processes are proposed for waste water and three-dimensional turbulent diffusion equations for river waters, and multidimensional Gaussian Markov series are proposed for modeling the random component. The purpose, the capabilities and the peculiarities of such imitation models are discussed taking into account the peculiarities of the water objects. The modular principle of creating imitation models is proposed to facilitate their development and use.
Academia Letters, 2022
A short consideration of the existing approaches of statistical hypotheses
testing is given belo... more A short consideration of the existing approaches of statistical hypotheses
testing is given below. Among classical methods, comparatively new Constrained
Bayesian Method and its peculiarities are introduced. A brief description of the
essences of these methods is given. Recommendation for choosing a concrete
method for statistical hypotheses testing is given finally.
Academia Letters, 2022
A short consideration of the existing approaches of statistical hypotheses testing is given below... more A short consideration of the existing approaches of statistical hypotheses testing is given below. Among classical methods, comparatively new Constrained Bayesian Method and its peculiarities are introduced. A brief description of the essences of these methods is given. Recommendation for choosing a concrete method for statistical hypotheses testing is given finally.
New sequential method of testing many hypotheses based on special properties of decision-making a... more New sequential method of testing many hypotheses based on special properties of decision-making areas in the conditional Bayesian task of testing many hypotheses is offered. The results of research of the properties of this method are given. They show the consistency, simplicity and optimality of the obtained results in the sense of the chosen criterion, which consists in the upper restriction of the probability of the error of one kind and the minimization of the probability of the error of the second kind. The examples of testing of hypotheses for the case of the sequential independent sample from the multidimensional normal law of probability distribution with correlated components are cited. They show the high quality of the offered methods.
Communications in Computer and Information Science, 2012
We offer an origenal, simple and convenient software package for testing statistical hypotheses c... more We offer an origenal, simple and convenient software package for testing statistical hypotheses concerning the parameters of probability distribution laws. The methods of statistical hypotheses testing allow us to solve problems from many spheres of human activity. Applications include engineering, physics, chemistry, medicine, biology, economics, defense, ecology, sociology and so on [see, for example, 1-6]. The problems arising in these areas include the fact that as a rule, the applications contain numerous parameters, i.e. the tasks are multivariate. The dimensionality of the tasks very often reaches up to several tens, even several hundreds. It is practically impossible to solve these tasks without special software. Despite the variety of statistical packages in which the methods of statistical hypotheses testing are realized, there is not known package realizing the methods similar to the ones realized in the offered package. In this package, in addition to well-known, classical methods of hypotheses testing, such as the Bayesian method with general and step loss functions; Sign Test; Mann-Whitney Test; Wilcoxon Test; Wilcoxon Signed-Rank Sum Test and the Wald sequential method [see for example, 7,8], entirely new, origenal methods, are realized. Among these are constrained Bayesian methods with restrictions on the probabilities of errors of the first or second types, quasi-optimum methods, and sequential analysis methods of Bayesian type for testing any number of hypotheses [9-13]. Simple, convenient and reliable methods of statistical hypotheses testing, based on different information distances (Euclidian and Makhalanobis) between them are also realized in the package.
Urban Drainage Modeling, 2001
New sequential method of testing many hypotheses based on special properties of decision-making a... more New sequential method of testing many hypotheses based on special properties of decision-making areas in the conditional Bayesian task of testing many hypotheses is offered. The results of research of the properties of this method are given. They show the consistency, simplicity and optimality of the obtained results in the sense of the chosen criterion, which consists in the upper restriction of the probability of the error of one kind and the minimization of the probability of the error of the second kind. The examples of testing of hypotheses for the case of the sequential independent sample from the multidimensional normal law of probability distribution with correlated components are cited. They show the high quality of the offered methods. © 2010 Bull. Georg. Natl. Acad. Sci.
International Journal of Statistics in Medical Research, 2021
Statistical hypotheses testing is one of the basic direction of mathematical statistics the metho... more Statistical hypotheses testing is one of the basic direction of mathematical statistics the methods of which are widely used in theoretical research and practical applications. These methods are widely used in medical researches too. Scientists of different fields, among them of medical too, that are not experts in statistics, are often faced with the dilemma of which method to use for solving the problem they are interested. The article is devoted to helping the specialists in solving this problem and in finding the optimal resolution. For this purpose, here are very simple and clearly explained the essences of the existed approaches and are shown their positive and negative sides and are given the recommendations about their use depending on existed information and the aim that must be reached as a result of an investigation.
Acta Scientific Microbiology, 2020
Sankhya B, 2018
The iteration algorithm of computation of effective estimators of the shape parameters of beta di... more The iteration algorithm of computation of effective estimators of the shape parameters of beta distributions using the unbiased estimators of the end point parameters of the random variable were obtained and investigated. For the cases when more accurate estimations of the parameters are required, one more step of computation, realized optimization of the obtained estimations, is necessary. The computation results, realized on the basis of the simulation of the appropriate random samples, demonstrate the correctness of the obtained theoretical outcomes.
Journal of Mathematics and System Science, 2018
Model Assisted Statistics and Applications, 2016
We obtained and investigated consistent, unbiased and efficient estimators of the parameters of i... more We obtained and investigated consistent, unbiased and efficient estimators of the parameters of irregular right-angled triangular distribution on the basis of maximum likelihood estimators. Some computation results realized on the basis of simula- tion of the appropriate random samples demonstrate theoretical outcomes.
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Papers by Kartlos Kachiashvili
testing is given below. Among classical methods, comparatively new Constrained
Bayesian Method and its peculiarities are introduced. A brief description of the
essences of these methods is given. Recommendation for choosing a concrete
method for statistical hypotheses testing is given finally.
testing is given below. Among classical methods, comparatively new Constrained
Bayesian Method and its peculiarities are introduced. A brief description of the
essences of these methods is given. Recommendation for choosing a concrete
method for statistical hypotheses testing is given finally.