Some generalizations of Bernoulli and Polya-Eggenberger contagion models

Artificial Intelligence for COVID-19

2021

The rapid spread of the COVID-19 pandemic has revealed an acute problem associated with forecasting the development of epidemics in different countries and assessing the accuracy of these forecasts. The most widely used models for predicting viral outbreaks are the SIR and SEIR models and their modifications. The complexity of predicting the development of epidemics using these models is associated with the large uncertainty of the parameters included in these models; therefore, many researchers have attempted to apply machine learning methods for forecasting. The objects of our study were the Grey Wolf Optimizer (GOW) methods, as well as two machine learning models (MLP multilayer perceptron and ANFIS adaptive network fuzzy inference system). Ranking the models in increasing order of their accuracy is not difficult, but in many cases it makes no sense, since the model predictions in the statistical sense differ little from each other (homogeneous) and therefore such models can be considered equivalent. The chapter describes an effective nonparametric tests both traditional and new for comparing the results of time series prediction, which makes it possible to assess their homogeneity and identify groups of forecasting methods whose forecast results differ statistically significantly from each other. The results of comparison of forecasting machine learning models for different countries are presented. The effectiveness of the applied method of nonparametric testing of the homogeneity of models is shown.

Section: Klyushin-petunin Nonparametric Test For Homogeneitymentioning

confidence: 99%

Nonparametric Tests for Comparing COVID-19 Machine Learning Forecasting Models

Artificial Intelligence for COVID-19

2021

“…The confidence intervals I (n) i j = p (1) i j , p 2 i j and I = ( p 1 , p 2 ) are called intervals based on the 3 s-rule. The scheme of trials, where the events A (k) i j can arise when the hypothesis that distributions are identical holds is true, called a generalized Bernoulli scheme [36][37][38]. If the hypothesis does not hold, this scheme is called a modified Bernoulli scheme.…”

Section: Homogeneity Measure For Samples Without Tiesmentioning

confidence: 99%

Nonparametric Analysis of Tracking Data in the Context of COVID-19 Pandemic

2020

Studies in Big Data

Methods of statistical pattern recognition are powerful tools for analysis of statistical data on COVID-19 pandemic. In this chapter, we offer a new effective online algorithm for detection of change-points in tracking data (movement data, health rate data etc.). We developed a non-parametric test for evaluation of the statistical hypothesis that data in two adjacent time intervals have the same distribution. In the context of the mobile phone tracking this means that the coordinates of the tracked object does not deviated from the base point significantly. For estimation of the health rate it means the absence of significant deviations from the norm. The significance level for the test is less than 0.05. The test permits ties in samples. Also, we show that results of comparison of the test with well-known Kolmogorov-Smirnov test. These results show that the proposed test is more robust, sensitive and accurate than the alternative ones. In addition, the new method does not require high computational capacity.

“…This method is based on the concept of the Petunin statistics [3], which is a measure of samples' homogeneity and plays a role of coordinate at the plane. In the turn, the Petunin statistics uses the MP-model and Hill' assumption A (n) [4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

Classification of Multivariate Samples Using Petunin Ellipses

Shtyk

2020

JNAM

The method of classification multivariate samples using Petunin ellipses is investigated in the paper. Several different types of samples were generated for testing. Based on the calculated accuracy of the criteria advantages and disadvantages of each of the linear and quadratic criteria and the specifics of the method as a whole were discovered. It has been found that both linear and quadratic criteria give high accuracy for samples with small variance. As the variance increases, the accuracy of the linear criterion remains high, the accuracy of the quadratic criterion decreases. Both criteria are resistant to sample noise.