Comments on statistical independence for linear stochastic multicompartmental systems

1983 ◽  
Vol 45 (3) ◽  
pp. 431-435
Author(s):  
V. Capasso ◽  
S. L. Paveri-Fontana
Keyword(s):  
Statistical Independence

The Constructive Thinking Inventory: Factorial Structure in Healthy Individuals and Patients with Chronic Skin Diseases

1998 ◽  
Vol 14 (3) ◽  
pp. 226-233 ◽  
Author(s):  
Jürgen Hoyer ◽  
Mechthild Averbeck ◽  
Thomas Heidenreich ◽  
Ulrich Stangier ◽  
Karin Pöhlmann ◽  
...  
Keyword(s):  
Skin Diseases ◽  
Principal Component ◽  
Initial Study ◽  
Statistical Independence ◽  
Constructive Thinking ◽  
Global Factor ◽  
Emotional Coping ◽  
Factor Congruence ◽  
Chronic Skin ◽  
Chronic Skin Diseases

Epstein's “Constructive Thinking Inventory” (CTI) was developed to measure the construct of experiential intelligence, which is based on his cognitive-experiential self-theory. Inventory items were generated by sampling naturally occurring automatic cognitions. Using principal component analysis, the findings showed a global factor of coping ability as well as six main factors: Emotional Coping, Behavioral Coping, Categorical Thinking, Personal Superstitious Thinking, Esoteric Thinking, and Naive Optimism. We tested the replicability of this factor structure and the amount of statistical independence (nonredundancy) between these factors in an initial study of German students (Study 1, N = 439) and in a second study of patients with chronic skin disorders (Study 2, N = 187). Factor congruence with the original (American) data was determined using a formula proposed by Schneewind and Cattell (1970) . Our findings show satisfactory factor congruence and statistical independence for Emotional Coping and Esoteric Thinking in both studies, while full replicability or independence could not be found in both for the other factors. Implications for the use and further development of the CTI are discussed.

Reasoning About Measurements

2021 ◽  
pp. 31-92
Author(s):  
Jochen Rau
Keyword(s):  
Probability Theory ◽  
Quantum Theory ◽  
Physical Theory ◽  
Logical Structure ◽  
Statistical Independence ◽  
Classical Probability ◽  
Multiple Systems ◽  
Classical Probability Theory ◽  
Operational Requirement

This chapter explains the approach of ‘operationalism’, which in a physical theory admits only concepts associated with concrete experimental procedures, and lays out its consequences for propositions about measurements, their logical structure, and states. It illustrates these with toy examples where the ability to perform measurements is limited by design. For systems composed of several constituents this chapter introduces the notions of composite and reduced states, statistical independence, and correlations. It examines what it means for multiple systems to be prepared identically, and how this is represented mathematically. The operational requirement that there must be procedures to measure and prepare a state is examined, and the ensuing constraints derived. It is argued that these constraint leave only one alternative to classical probability theory that is consistent, universal, and fully operational, namely, quantum theory.

Appendix: A Brief Introduction to Analyzing Categorical Data and Finding More Data

2018 ◽  
pp. 302-326
Author(s):  
Quan Li
Keyword(s):  
Logistic Regression ◽  
Categorical Data ◽  
Public Domain ◽  
Statistical Independence ◽  
Discrete Variables ◽  
Short List ◽  
The Public ◽  
Independent Variables ◽  
Dichotomous Variable ◽  
Chi Squared

This chapter provides a brief introduction to two techniques often used with discrete data: testing statistical independence between two discrete variables with Chi-squared statistics, and testing the effects of some independent variables on the probability of a dependent variable taking on the value of one rather than zero with logistic regression. Both are illustrated by focusing on a dichotomous variable measuring self-reported happiness by survey respondents in World Value Surveys. In addition, the chapter also provides a short list of publicly available data resources that help to familiarize readers with the wealth of data in the public domain.

scholarly journals Random Permutations, Non-Decreasing Subsequences and Statistical Independence

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1415
Author(s):  
Jesús E. García ◽  
Verónica A. González-López
Keyword(s):  
Random Variables ◽  
Continuous Data ◽  
Random Permutations ◽  
Statistical Independence ◽  
Independence Test ◽  
Independence Tests ◽  
Present Procedure ◽  
Longest Increasing Subsequence

In this paper, we show how the longest non-decreasing subsequence, identified in the graph of the paired marginal ranks of the observations, allows the construction of a statistic for the development of an independence test in bivariate vectors. The test works in the case of discrete and continuous data. Since the present procedure does not require the continuity of the variables, it expands the proposal introduced in Independence tests for continuous random variables based on the longest increasing subsequence (2014). We show the efficiency of the procedure in detecting dependence in real cases and through simulations.

scholarly journals Statistical independence in mathematics–the key to a Gaussian law

2020 ◽  
Author(s):  
Gunther Leobacher ◽  
Joscha Prochno
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Historical Context ◽  
Lacunary Series ◽  
Statistical Independence ◽  
Binary Expansion ◽  
Sum Of Digits ◽  
Sum Of Digits Function ◽  
Kolmogorov Axioms

Abstract In this manuscript we discuss the notion of (statistical) independence embedded in its historical context. We focus in particular on its appearance and role in number theory, concomitantly exploring the intimate connection of independence and the famous Gaussian law of errors. As we shall see, this at times requires us to go adrift from the celebrated Kolmogorov axioms, which give the appearance of being ultimate ever since they have been introduced in the 1930s. While these insights are known to many a mathematician, we feel it is time for both a reminder and renewed awareness. Among other things, we present the independence of the coefficients in a binary expansion together with a central limit theorem for the sum-of-digits function as well as the independence of divisibility by primes and the resulting, famous central limit theorem of Paul Erdős and Mark Kac on the number of different prime factors of a number $$n\in{\mathbb{N}}$$ n ∈ N . We shall also present some of the (modern) developments in the framework of lacunary series that have its origin in a work of Raphaël Salem and Antoni Zygmund.

Sign in / Sign up

Export Citation Format

Share Document