Апробация методов математической статистики при атрибуции текста в рамках судебного автороведения
Developing a new approach to the problem of optimal control in the open dynamical model of a three-sector economy
The article is devoted to pattern recognition task with the database containing small number of samples per class. By mapping of local continuous feature vectors to a discrete range, this problem is reduced to statistical classification of a set of discrete finite patterns. It is demonstrated that Bayesian decision under the assumption that probability distributions can be estimated using the Parzen kernel and the Gaussian window with a fixed variance for all the classes, implemented in the PNN, is not optimal in the classification of a set of patterns. We presented here the novel modification of the PNN with homogeneity testing which gives an optimal solution of the latter task under the same assumption about probability densities. By exploiting the discrete nature of patterns our modification prevents the well-known drawbacks of the memory-based approach implemented in both the PNN and the PNN with homogeneity testing, namely, low classification speed and high requirements to the memory usage. Our modification only requires the storage and processing of the histograms of input and training samples. We present the results of an experimental study in two practically important tasks: 1) the problem of Russian text authorship attribution with character n-grams features; and 2) face recognition with well-known datasets (AT&T, FERET and JAFFE) and comparison of color- and gradient-orientation histograms. Our results support the statement that the proposed network provides better accuracy (1-7%) and is much more resistant to change of the smoothing parameter of Gaussian kernel function in comparison with the original PNN.
We study the problem of testing composite hypotheses versus composite alternatives when there is a slight deviation between the model and the real distribution. The used approach, which we called sub-optimal testing, implies an extension of the initial model and a modification of a sequential statistically significant test for the new model. The sub-optimal test is proposed and a non-asymptotic border for the loss function is obtained. Also we investigate correlation between the sub-optimal test and the sequential probability ratio test for the initial model.
The article studies forensic methods which are a prerequisite to properly arrange the investigation of crimes connected with illegal corporate raids. Having outlined in this perspective the key directions in forensic methods, the author interprets them it as a set of organizational, legal, informational and other events specially aimed at teaching and applying expertise, guidelines on forensic studies, tools and methods in different departments of RF internal affairs bodies, i.e. investigative, special investigative techniques and analytics departments. The staff of the bodies is obliged to be involved in exposing, preventing, detecting and investigating crimes connected with corporate raids.
The complexity of today’s statistical data calls for modern mathematical tools. Many fields of science make use of mathematical statistics and require continuous updating on statistical technologies. Practice makes perfect, since mastering the tools makes them applicable. Our book of exercises and solutions offers a wide range of applications and numerical solutions based on R. In modern mathematical statistics, the purpose is to provide statistics students with a number of basic exercises and also an understanding of how the theory can be applied to real-world problems. The application aspect is also quite important, as most previous exercise books are mostly on theoretical derivations. Also we add some problems from topics often encountered in recent research papers. The book was written for statistics students with one or two years of coursework in mathematical statistics and probability, professors who hold courses in mathematical statistics, and researchers in other fields who would like to do some exercises on math statistics.
The purpose of this paper is the presentation of the ideas and concepts that
form the basis of the concept of mathematical model control some processes
occurring in the Russian market of cereals. The estimated model must have a
stochastic nature, i.e. constitute some random process. Indeed, in a free market
there are objectively random factors that cannot be described by deterministic.
The functionals related to the quality of the system control are obtained
in the analytic form. The statement that the optimal strategy of controlling
the system is a deterministic strategy is proved. Analytic form representation
for the function the absolute extremum of which is determined as the optimal
control strategy is obtained also.