Andrey Gorshenin

Modelling Of Statistical Fluctuations Of Information Flows By Mixtures Of Gamma Distributions.

The paper describes statistical approach to the analysis of traffic of information flows. Stochastic structure of traffic process can be modelled by finite probability mixtures, e.g., mixtures of gamma distributions. The approach is demonstrated on real data from the official website of the Russian Academy of Sciences.

Statistical analysis of precipitation events

In the present paper we demonstrate the results of a statistical analysis of some characteristics of precipitation events and propose a kind of a theoretical explanation of the proposed models in terms of mixed Poisson and mixed exponential distributions based on the information-theoretical entropy reasoning. The proposed models can be also treated as the result of following the popular Bayesian approach.

The probability distribution of extreme precipitation

On the basis of the negative binomial distribution of the duration of wet periods calculated per day, an asymptotic model is proposed for distributing the maximum daily rainfall volume during the wet period, having the form of a mixture of Frechet distributions and coinciding with the distribution of the positive degree of a random variable having the Fisher–Snedecor distribution. The method of proving the corresponding result is based on limit theorems for extreme order statistics in samples of a random volume with a mixed Poisson distribution. The adequacy of the models proposed and methods of their statistical analysis is demonstrated by the example of estimating the extreme distribution parameters based on real data.

On an interface of the online system for a stochastic analysis of the varied information flows

The article describes a possible approach to the construction of an interface of an online asynchronous system that allows researchers to analyse varied information flows. The implemented stochastic methods are based on the mixture models and the method of moving separation of mixtures. The general ideas of the system functionality are demonstrated on an example for some moments of a finite normal mixture.

On implementation of EM-type algorithms in the stochastic models for a matrix computing on GPU

The paper discusses the main ideas of an implementation of EM-type algorithms for computing on the graphics processors and the application for the probabilistic models based on the Cox processes. An example of the GPU’s adapted MATLAB source code for the finite normal mixtures with the expectation-maximization matrix formulas is given. The testing of computational efficiency for GPU vs CPU is illustrated for the different sample sizes.

The evolution of probability characteristics of low-frequency plasma turbulence

The technique of the analysis of statistical characteristics of turbulent fluctuation based on volatility decomposition by using EM-type algorithms is presented. The changes of these characteristics in the case of variations in the conditions of microwave field excitation are analyzed. Good consistency between the results obtained using the EM algorithm and its stochastic modification (SEM algorithm) and actually observed processes in a turbulent plasma is demonstrated.

Research support system for stochastic data processing

The paper describes a research support system named “MSM Tools” that can be used for stochastic modelling of real processes in various information systems and implements the heterogeneous computing paradigm. The proposed approach to data mining is based on method of moving separation of probability mixtures. To obtain statistical estimations of the unknown parameters of mixed probability models, the system implements several modifications of so-called EM algorithm (including grid modifications for the NVIDIA CUDA architecture) that are commonly used in such areas as pattern recognition, clustering, classification, processing of censored and/or truncated data. An example of real data analysis via “MSM Tools” service is given.

Coordinate-Wise Versions of The Grid Method for the Analysis of Intensities of Non-Stationary Information Flows by Moving Separation of Mixtures of Gamma-distribution

A coordinate-wise modification of the grid method for separation of mixtures is proposed in the problem of the dynamical monitoring of the stochastic structure of information flows.

On non-parametric methodology of the plasma turbulence research

A non-parametric approach to the estimation of plasma turbulence spectra is propesed in the paper. The basic model for description of the fine structure of stochastic processes is a finite location-scale normal mixture. The classical EM-algorithm is used for estimating the unknown parameters. The explanation of empirical results are given for the evolution of one-side Fourier spectra obtained in different modes of low-frequency plasma turbulence. Such kind of analysis allows to identify typical structures of processes forming plasma turbulence.

Modelling stock order flows with non-homogeneous intensities from high-frequency data

A micro-scale model is proposed for the evolution of such information system as the limit order book in financial markets. Within this model, the flows of orders (claims) are described by doubly stochastic Poisson processes taking account of the stochastic character of intensities of buy and sell orders that determine the price discovery mechanism. The proposed multiplicative model of stochastic intensities makes it possible to analyze the characteristics of the order flows as well as the instantaneous proportion of the forces of buyers and sellers, that is, the imbalance process, without modelling the external information background. The proposed model gives the opportunity to link the micro-scale (high-frequency) dynamics of the limit order book with the macro-scale models of stock price processes of the form of subordinated Wiener processes by means of limit theorems of probability theory and hence, to use the normal variance-mean mixture models of the corresponding heavy-tailed distributions. The approach can be useful in different areas with similar properties (e.g., in plasma physics).