scholarly journals Boolean Monte Carlo Method

2019 ◽  
Author(s):  
Takuma Usuzaki ◽  
Minoru Shimoyama ◽  
Shuji Chiba ◽  
Naoko Mori
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Contingency Table ◽  
Contingency Tables ◽  
Medical Test ◽  
Frequentist Approach ◽  
Large Numbers ◽  
Result Analysis ◽  
Variable Analysis

A medical test and accuracy of diagnosis are often discussed with contingency tables. However, it is difficult to apply a contingency table to multivariate cases because the number of possible categories increases exponentially. We hypothesize that randomly assigning Boolean operators and focusing on frequencies of Boolean operators could explain the outcome correctly, obtain the tendencies of operators, and overcome difficulties in analyzing large numbers of variables and categories. The aims of this paper are introducing a method to obtain tendencies of Boolean operators and expanding 2 by 2 contingency tables to multivariate cases. To test this method, we construct two types of data: 1) when variables and outcome were randomly determined and 2) when the outcome depends on one variable. Analysis of the first type of data by this method showed that there was no significant result. Analysis of the second type of data reflected the bias of the data. As far as we know, this is the first attempt to use a frequentist approach to randomly assigned Boolean operators.

Multiway Contingency Tables: Monte Carlo Resampling Probability Values for the Chi-Squared and Likelihood-Ratio Tests

2010 ◽  
Vol 107 (2) ◽  
pp. 501-510 ◽  
Author(s):  
Michael A. Long ◽  
Kenneth J. Berry ◽  
Paul W. Mielke
Keyword(s):  
Monte Carlo ◽  
Likelihood Ratio ◽  
Contingency Table ◽  
Contingency Tables ◽  
Likelihood Ratio Tests ◽  
Ratio Test ◽  
Test Statistics ◽  
Test Statistic ◽  
Resampling Methods ◽  
Chi Squared

Monte Carlo resampling methods to obtain probability values for chi-squared and likelihood-ratio test statistics for multiway contingency tables are presented. A resampling algorithm provides random arrangements of cell frequencies in a multiway contingency table, given fixed marginal frequency totals. Probability values are obtained from the proportion of resampled test statistic values equal to or greater than the observed test statistic value.

Tests’ power for independence in the two-way contingency table

2016 ◽  
Vol 61 (8) ◽  
pp. 1-17
Author(s):  
Piotr Sulewski
Keyword(s):  
Monte Carlo ◽  
Statistical Analysis ◽  
Monte Carlo Methods ◽  
Null Hypothesis ◽  
Contingency Table ◽  
Contingency Tables ◽  
Critical Values ◽  
The Family ◽  
Chi Squared ◽  
Simulation Monte Carlo

In the statistical literature there are many test measures to study the independence of features in the two-way contingency tables. For statistical analysis, the family of six so-called ”chi-squared statistic” was selected — including Pearson’s X² statistics — and the proposal of the author in the form of modular statistics. In order to free themselves from the limitations of the applicability of the ”chi-squared statistic”, critical values for all analyzed statistics were determined by simulation Monte Carlo methods. In order to compare the tests, the measure of untruthfulness of H₀ was proposed and calculated the power of the tests which is the ability of two-way contingency tables to reject null hypothesis which says that between features X and Y there is no relation.

scholarly journals A New Test for Independence in 2×2 Contingency Tables

2017 ◽  
Vol 4 (330) ◽  
Author(s):  
Piotr Sulewski
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Contingency Tables ◽  
Critical Values ◽  
Chi Square ◽  
The Monte Carlo Method ◽  
Qualitative Variables ◽  
Chi Square Test ◽  
Divergence Statistics ◽  
Power Divergence

In statistical literature there exist many tests to reveal the independence of two qualitative variables in two‑way contingency tables (CTs), in particular in 2×2 CTs. In this paper four independence tests were compared. These are: the chi‑square test, being the most popular type of power divergence statistics; the modular test and the d‑square test, which is a modification of the Pearson’s test; the logarithmic minimum test which is a new proposal. Critical values for the tests listed above were determined with the Monte Carlo method. In order to compare the tests, the measure of untruthfulness of H0 was proposed and the power of the tests was calculated. 

scholarly journals The LMS for testing independence in two-way contingency tables

2019 ◽  
Vol 56 (1) ◽  
pp. 17-43 ◽  
Author(s):  
Piotr Sulewski
Keyword(s):  
Monte Carlo ◽  
Statistical Analysis ◽  
Monte Carlo Method ◽  
Contingency Tables ◽  
Critical Values ◽  
Testing Independence ◽  
The Monte Carlo Method ◽  
Qualitative Variables ◽  
Chi Squared

SummaryIn the statistical literature there are proposed many test measures to determine the independence of two qualitative variables in contingency tables, in particular in two-way contingency tables larger than 2×2. For statistical analysis, three of the so-called “chi-squared tests”—the T3 test, BP test and |χ| test—were selected. These tests were compared with a logarithmic minimum test, which is the author’s proposal. Critical values for the tests were determined with the Monte Carlo method. To compare the tests, an appropriate measure of untruthfulness of H0 was used and the power of the tests was calculated.

Outbursts of comet Schwassmann-Wachmann 1, and the cloud of interplanetary boulders

1974 ◽  
Vol 22 ◽  
pp. 307 ◽  
Author(s):  
Zdenek Sekanina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Interplanetary Space ◽  
Porous Matrix ◽  
Maximum Diameter ◽  
Expansion Velocity ◽  
Solid Constituent ◽  
Meteoric Material ◽  
Periodic Comet

AbstractIt is suggested that the outbursts of Periodic Comet Schwassmann-Wachmann 1 are triggered by impacts of interplanetary boulders on the surface of the comet’s nucleus. The existence of a cloud of such boulders in interplanetary space was predicted by Harwit (1967). We have used the hypothesis to calculate the characteristics of the outbursts – such as their mean rate, optically important dimensions of ejected debris, expansion velocity of the ejecta, maximum diameter of the expanding cloud before it fades out, and the magnitude of the accompanying orbital impulse – and found them reasonably consistent with observations, if the solid constituent of the comet is assumed in the form of a porous matrix of lowstrength meteoric material. A Monte Carlo method was applied to simulate the distributions of impacts, their directions and impact velocities.

Structures and crystallization of vacuum-deposited amorphous Se and Sb films

1990 ◽  
Vol 48 (4) ◽  
pp. 140-141
Author(s):  
Makoto Shiojiri ◽  
Toshiyuki Isshiki ◽  
Tetsuya Fudaba ◽  
Yoshihiro Hirota
Keyword(s):  
Monte Carlo ◽  
Electron Microscope ◽  
Monte Carlo Method ◽  
Computer Program ◽  
Radial Distribution ◽  
Film Formation ◽  
Amorphous State ◽  
Two Dimensional ◽  
Amorphous Films ◽  
Binding Condition

In hexagonal Se crystal each atom is covalently bound to two others to form an endless spiral chain, and in Sb crystal each atom to three others to form an extended puckered sheet. Such chains and sheets may be regarded as one- and two- dimensional molecules, respectively. In this paper we investigate the structures in amorphous state of these elements and the crystallization.HRTEM and ED images of vacuum-deposited amorphous Se and Sb films were taken with a JEM-200CX electron microscope (Cs=1.2 mm). The structure models of amorphous films were constructed on a computer by Monte Carlo method. Generated atoms were subsequently deposited on a space of 2 nm×2 nm as they fulfiled the binding condition, to form a film 5 nm thick (Fig. 1a-1c). An improvement on a previous computer program has been made as to realize the actual film formation. Radial distribution fuction (RDF) curves, ED intensities and HRTEM images for the constructed structure models were calculated, and compared with the observed ones.

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