ЭБ Коллекция: Proceedings of the XIII International Conference, Minsk, September 6–10, 2022

Statistical estimation of high-order dependencies in discrete-valued time series

Sat, 01 Jan 2022 00:00:00 GMT

Заглавие документа: Statistical estimation of high-order dependencies in discrete-valued time series Авторы: Kharin, Yu. S. Аннотация: Any digital society generates a lot of discrete-valued data. If this discrete-valued data are considered in dynamics (in dependence on time t ∈ Z) we get discrete-valued time series x t ∈ A, where A is some discrete set. This paper is devoted to probabilistic modeling and statistical analysis of high order stochastic dependencies of x t on its prehistory {x τ : τ < t}. The outline of the paper is as follows: Markov chain of order s and its parsimonious (small-parametric) models; approaches to construction of parsimonious models; FBE-method for statistical estimation of parameters in parsimonious models; robustness in statistical estimation of parameters for parsimonious models; application to computer data analysis

On software library for statistical classification of discrete-valued multivariate data, time series and random fields

Sat, 01 Jan 2022 00:00:00 GMT

Заглавие документа: On software library for statistical classification of discrete-valued multivariate data, time series and random fields Авторы: Kharin, Yu. S.; Voloshko, V. A.; Staleuskaya, S. N.; Sinkevich, N. V. Аннотация: We present a new software for statistical classification and visualization of discrete-valued data of various types: multivariate data, time series and random fields

Notes on the independence of tests and on completeness of NIST package

Sat, 01 Jan 2022 00:00:00 GMT

Заглавие документа: Notes on the independence of tests and on completeness of NIST package Авторы: Zubkov, A. M.; Serov, A. A. Аннотация: We discuss two problems arising when several statistical tests are applied to the same data. Some examples of binary sequences which consist of dependent or nonrandom elements but pass all tests of the NIST Statistical Test Suite are described

Orthogonal decomposition of bivariate densities using the Bayes space methodology

Sat, 01 Jan 2022 00:00:00 GMT

Заглавие документа: Orthogonal decomposition of bivariate densities using the Bayes space methodology Авторы: Hron, K. Аннотация: Bivariate probability densities capture relationships within and between two continuous random variables. As such, they carry essentially relative information and follow the scale invariance property which is widely recognized in Bayesian statistics (e.g., when normalizing constant are neglected from computations). Both these properties are captured by the so called Bayes spaces, which are spaces of positive measures equipped with a Hilbert space structure built as a generalization of the log-ratio methodology for compositional data. In fact, Bayes spaces form a natural sample space for “scale invariant” measures and their respective densities. It is possible to decompose the bivariate densities orthogonally into independent and interactive parts, the former being product of revised definitions of marginal densities and the latter capturing the relationships between the random variables. This has several important consequences in the probability context. For instance, this yields the marginal invariance, i.e., when the bivariate density is shifted (in the Bayes space sense) by marginal densities, the interaction density is not changed. Furthermore, the centred logratio transformation of bivariate densities enables to move them from the Bayes space to the standard L 2 space where popular methods of functional data analysis can be applied. The novel theoretical framework here proposed has thus clear potential on the application side, allowing to analyse samples of densities arising, for example, as a result of aggregation of massive data coming from large-scale studies or automated collection of data