In this paper the consistent criteria for testing Hypothesis for the Sharle statistical structure are defined. It is shown that the necessary and sufficient conditions for the existence of these critical are considered. Also the necessary... more
In this paper the consistent criteria for testing Hypothesis for the Sharle statistical structure are defined. It is shown that the necessary and sufficient conditions for the existence of these critical are considered. Also the necessary and sufficient conditions for the existence of such criteria for the Sharle strongly statistical structure.
The river Vere is a typical mountain river with its gorge of more than 40 km length, range of heights up to 1500 m. This river is considered to be one of the most dangerous rivers in the east Georgia due to its frequent catastrophic... more
The river Vere is a typical mountain river with its gorge of more than 40 km length, range of heights up to 1500 m. This river is considered to be one of the most dangerous rivers in the east Georgia due to its frequent catastrophic overflows. One of the aims of this paper was to estimate the approximate volume of the temporary water reservoir, formed between the Tamarashvili Highway and Gabashvili Street during the catastrophic flood in the Vere River Valley on June 15, 2015. The paper estimates that the temporary water reservoir has a strategic load to manage the catastrophic flood and its consequences, considering the maximum water consumption of the tunnel leading from Svanidze Street and the maximum water permeability of the second tunnel and also taking into account the water flowing from the slopes of temporary water reservoir.
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In the paper there are discussed Gaussian fields Statistical Structures in Banach Space of measures, we prove necessary and sufficient conditions for existence of such criterion in Banach space of measures.
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A certain modified version of Kolmogorov’s strong law of large numbers is used for an extension of the result of C. Baxa and J. Schoi\(\beta \)engeier (2002) to a maximal set of uniformly distributed sequences in (0, 1) that strictly... more
A certain modified version of Kolmogorov’s strong law of large numbers is used for an extension of the result of C. Baxa and J. Schoi\(\beta \)engeier (2002) to a maximal set of uniformly distributed sequences in (0, 1) that strictly contains the set of all sequences having the form \((\{\alpha n\})_{n \in \mathbf{N}}\) for some irrational number \(\alpha \) and having the full \(\ell _1^{\infty }\)-measure, where \(\ell _1^{\infty }\) denotes the infinite power of the linear Lebesgue measure \(\ell _1\) in (0, 1).
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In this paper, we define Sharle statistical Structure such that the probability of any kind of error is zero for given criterion. The necessary and sufficient conditions for the existence of such criteria are given.
In 20th century, more than 10 strong earthquakes (EQs) of magnitudes 6,7 hit South Caucasus, causing thousands of casualties and gross economic losses. Thus, strong-EQ forecast is an actual problem for the region. In this direction, we... more
In 20th century, more than 10 strong earthquakes (EQs) of magnitudes 6,7 hit South Caucasus, causing thousands of casualties and gross economic losses. Thus, strong-EQ forecast is an actual problem for the region. In this direction, we developed a physical percolation model of fracture, which considers the final failure of solid as a termination of the prolonged process of destruction: generation and clustering of micro-cracks, till appearance-at some critical concentration-of the infinite cluster, marking the final failure. Percolation provides a model of preparation of an individual strong event (slip or EQ). The natural seismic process contains many such events: the appropriate model is a non-linear stick-slip model, which is a particular case of the general theory of the integrate-and-fire process. Non-linearity of the seismic process is in contradiction with a memoryless Poissonian approach to seismic hazard. The complexity theory offers a chance to improve strong EQs' forecast using analysis of hidden (non-linear) patterns in seismic time series, such as attractors in the phase space plot. For a regional forecast, we applied the Bayesian approach to assess the conditional probability expected in the next 5 years of strong EQs of magnitudes five and more. Later on, in addition to Bayesian probability assessment, we applied to seismic time series the pattern recognition technique, based on the assessment of the empirical risk function [generalized portrait (GP) method]: nowadays, this approach is known as the support vector machine (SVM) technique. The preliminary analysis shows that application of the GP technique allows predicting retrospectively 80% of M5 events in Caucasus. Besides long-and middle-term forecast studies, intensive work is under way on the short-term (next-day) EQ prediction also. Here, we present the results of multiparametrical (hydrodynamic and magnetic) monitoring carried out on the territory of Georgia. In order to assess the reliability of the precursors, we used the machine learning approach, namely, the algorithm of deep learning ADAM, which optimizes target function by a combination of optimization algorithm designed for neural networks and a method of stochastic gradient descent with momentum. Finally, we used the method of receiver operating characteristics (ROC) to assess the forecast quality of this binary classifier system. We show that the true positive rate statistical measure is preferable for the EQ forecast.
By using the notion of a Haar ambivalent set introduced by Balka, Buczolich and Elekes (2012), essentially new classes of statistical structures having objective and strong objective estimates of unknown parameters are introduced in a... more
By using the notion of a Haar ambivalent set introduced by Balka, Buczolich and Elekes (2012), essentially new classes of statistical structures having objective and strong objective estimates of unknown parameters are introduced in a Polish non-locally-compact group admitting an invariant metric and relations between them are studied in this paper. An example of such a weakly separated statistical structure is constructed for which a question asking " whether there exists a consistent estimate of an unknown parameter" is not solvable within the theory (ZF) & (DC). A question asking " whether there exists an objective consistent estimate of an unknown parameter for any statistical structure in a non-locally compact Polish group with an invariant metric when subjective one exists" is answered positively when there exists at least one such a parameter the pre-image of which under this subjective estimate is a prevalent. These results extend recent results of author...
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This chapter contains a brief description of Yamasaki’s remarkable investigation (1980) of the relationship between Moore–Yamasaki–Kharazishvili type measures and infinite powers of Borel diffused probability measures on \(\mathbf{R}\).... more
This chapter contains a brief description of Yamasaki’s remarkable investigation (1980) of the relationship between Moore–Yamasaki–Kharazishvili type measures and infinite powers of Borel diffused probability measures on \(\mathbf{R}\). More precisely, there is given Yamasaki’s proof that no infinite power of the Borel probability measure with a strictly positive density function on R has an equivalent Moore–Yamasaki–Kharazishvili type measure . A certain modification of Yamasaki’s example is used for the construction of such a Moore–Yamasaki–Kharazishvili type measure that is equivalent to the product of a certain infinite family of Borel probability measures with a strictly positive density function on R. By virtue the properties of real-valued sequences equidistributed on the real axis, it is demonstrated that an arbitrary family of infinite powers of Borel diffused probability measures with strictly positive density functions on R is strongly separated and, accordingly, has an i...