Subjects: Mathematics >> Statistics and Probability Subjects: Statistics >> Mathematical Statistics Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science submitted time 2024-05-22
Abstract: Statistical independence is a core concept in statistics and machine learning. Representing and measuring independence are of fundamental importance in related fields. Copula theory provides the tool for representing statistical independence, while Copula Entropy (CE) presents the tool for measuring statistical independence. This paper first introduces the theory of CE, including its definition, theorem, properties, and estimation method. The theoretical applications of CE to structure learning, association discovery, variable selection, causal discovery, system identification, time lag estimation, domain adaptation, multivariate normality test, two-sample test, and change point detection are reviewed. The relationships between the theoretical applications and their connection to correlation and causality are discussed. The frameworks based on CE, the kernel method, and distance correlation for measuring statistical independence and conditional independence are compared. The advantage of CE based on methods over the other comparable methods is evaluated with simulated and real data. The applications of CE in theoretical physics, astrophysics, geophysics, theoretical chemistry, cheminformatics, materials science, hydrology, climatology, meteorology, environmental science, ecology, animal morphology, agronomy, cognitive neuroscience, motor neuroscience, computational neuroscience, psychology, system biology, bioinformatics, clinical diagnostics, geriatrics, psychiatry, public health, economics, management, sociology, pedagogy, computational linguistics, mass media, law, political science, military science, informatics, energy, food engineering, architecture, civil engineering, transportation, manufacturing, reliability, metallurgy, chemical engineering, aeronautics and astronautics, weapon, automobile, electronics, communication, high performance computing, cybersecurity, remote sensing, ocean, and finance are briefly introduced.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Statistics and Probability submitted time 2024-02-04
Abstract: The three frameworks for theories of consciousness taken most seriously by neuroscientists are that consciousness is a biological state of the brain,the global workspace perspective,and the perspective of higher state.Consciousness is discussed from viewpoint of theory of Entropy—partition of complex system in present article. Human brain’s system self-organizably and adaptively implements partition 、 aggregation and integration, and consciousness emerges.The Gibss representation of consciousness is proved and That consciousness originates from quantum mechanical processes of brain activity is explained by means of SW entropy
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Subjects: Mathematics >> Statistics and Probability submitted time 2024-01-23
Abstract: The nineties of the 20th century, I have proposed and constructed theory of Abstract Neural Automata (ANA) 1 .Aim of present manu
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Subjects: Mathematics >> Statistics and Probability Subjects: Psychology >> Statistics in Psychology submitted time 2023-07-02
Abstract: Taking the goodness of fit test (Chi test) as an example, this paper attempts to calculate the Bayesian factor BF10 of n-fold Bernoulli test by the Excel software (using JASP software as the evidence). The results showed that in the range of 0.15-0.55 (the rate of samples which are all "true"), the calculated results of Excel were more accurate, and the differences between the two (Excel and JASP) were not statistically significant (P>0.3).
Peer Review Status:Awaiting Review
Subjects: Medicine, Pharmacy >> Preclinical Medicine Subjects: Mathematics >> Statistics and Probability submitted time 2023-04-19
Abstract: Objective To investigate the current status of data transformation in Meta analysis of single proportions. Methods A literature search in PubMed was performed to retrieve researches of Meta analysis of single proportions published in 2017, and 481 records were returned. Results In 123 researches with full texts, only 33 (26.8%) described data transformation for proportions. Among which, double arcsine transformation was used 20 times, logit transformation 8, squared arcsine transformation 3, log transformation 1 and raw proportion 1. There was no relation between pooled portions and data transformation method (P=0.217). Conclusion Data transformation is important in Meta analysis of single proportions, however, it is yet to determined which transformation method is best. So, data transformation should be clarified in published papers.
Peer Review Status:Awaiting Review
Subjects: Medicine, Pharmacy >> Preclinical Medicine Subjects: Mathematics >> Statistics and Probability submitted time 2023-04-19
Abstract: Objective To compare different data transformations in Meta analysis for single proportions. Methods Two simulation data were constructed for Meta analysis under fixed effect model and random effect model, different adding values when event number was zero, and five different data transformation methods (raw proportion, log transformation, logit transformation, arcsine transformation and double arcsine transformation). Mean of pooled portion, bias, proportion bias, mean squared error, proportion mean squared error, proportion mean squared error and 95% confidence coverage were calculated. Results For Meta analysis of single proportions based on binomial distribution, generally, arcsine transformation performed best. When event number was zero, different values added to it did not improve the result much. Bias of pooled proportion was rather big when the population proportion is below 0.05. Conclusion Arcsine data transformation performed best during the simulation study for Meta analysis of single proportions. Caution should be used when dealing with population proportion less than 0.05.
Peer Review Status:Awaiting Review
Subjects: Medicine, Pharmacy >> Preclinical Medicine Subjects: Mathematics >> Statistics and Probability submitted time 2023-04-19
Abstract: The common method of sample size calculation for single proportion comparison (performance goal) is normal asymptotic approach, sometimes with corresponding data transformation such as squared arcsine, while exact probability usually needs commercial statistics software or programming. We use the free software R to calculate the sample size for single proportion via exact probability, and considering of the non-monotone increasing relationship between power and sample size with exact probability, we provide intuitive figure demonstration besides giving direct calculation results. We hope this will facilitate study design with performance goal.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Statistics and Probability submitted time 2022-05-12
Abstract:
Let Zn be a supercritical branching process in an independent and identically distributed random environment. We establish nonuniform Berry-Esseen bounds for the process Zn, which refine the Berry-Esseen bound of Grama et al. [Stochastic,Process.,Appl.,127(4),1255-1281,2017]. We also discuss an application of our result to constructing confidence interval for the criticality parameter.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Statistics and Probability Subjects: Mathematics >> Applied Mathematics submitted time 2022-03-30
Abstract:
In this paper, we propose and study a novel continuous-time model, based on the well-known constant elasticity of variance (CEV) model, to describe the asset price process. The basic idea is that the volatility elasticity of the CEV model can not be treated as a constant from the perspective of stochastic analysis. To address this issue, we deduce the price process of assets from the perspective of volatility elasticity, propose the constant volatility elasticity (CVE) model, and further derive a more general variable volatility elasticity (VVE) model. Moreover, our model can describe the positive correlation between volatility and asset prices existing in the commodity markets, while CEV model can only describe the negative correlation. Through the empirical research on the financial market, many assets, especially commodities, often show this positive correlation phenomenon in some time periods, which shows that our model has strong practical application value. Finally, we provide the explicit pricing formula of European options based on our model. This formula has an elegant form convenient to calculate, which is similarly to the renowned Black-Scholes formula and of great significance to the research of derivatives market.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Statistics and Probability submitted time 2021-12-16
Abstract: The paper considers Wasserstein metric between the empirical probability measure of n discrete random variables and a continuous uniform one on the d-dimensional ball and give the asymptotic estimation of their expectation as $n \to \infty$. Further We considers the above problem on a mixed process, i.e., n discrete random variables are produced by the Poisson process.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Statistics and Probability submitted time 2019-10-14
Abstract: Most authors have examined the inference of model averaging estima- tors under local misspecification assumption. [1] is one of the most groundbreaking and famous articles. However, although the local misspecification assumption pro- vides a suitable framework for studying the asymptotic theories of Frequentist Model Averaging estimators, it also draws comments from [2] because of its realism. In this paper, we prove that the confidence interval construction method for the linear function of parameters in [1] is still valid in linear regression with normally distributed error under general fixed parameter setup. It means that the coverage probability of the confidence interval can reach the nominal level. The simulation results support our theory conclusion. "
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Statistics and Probability submitted time 2019-07-21
Abstract: " Based on the point of view of neuroethology and cognition-psychology, general frame of theory for intelligent systems is presented by means of principle of relative entropy minimizing in this paper. Cream of the general frame of theory is to present and to prove basic principle of intelligent systems: entropy increases or decreases together with intelligence in the intelligent systems. The basic principle is of momentous theoretical significance and practical significance .From the basic principle can not only derive two kind of learning algorithms (statistical simulating annealing algorithms and annealing algorithms of mean-field theory approximation) for training large kinds of stochastic neural networks,but also can thoroughly dispel misgivings created by second law of thermodynamics on 'peoplespsychology ,hence make one be fully confident of facing life.Because of Human society, natural world, and even universe all are intelligent systems. "
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Statistics and Probability submitted time 2018-11-07
Abstract: Abstract. In studying of a class of random neural network, some of relative researchers have proposed Markov model of neural network. Wherein Markov property of the neural network is based on “assuming”. To reveal mechanism of generating of Markov property in neural network, it is studied how infinite-dimensional random neural network (IDRNN) forms inner Markov representation of environment information in this paper.Because of equivalence between markov property and Gibbsian our conclusion is that knowledge is eventually expressed by extreme Gibbs probability measure—ergodic Gibbs probability measure in IDRNN. This conclusion is also applicable to quantum mechanical level of IDRNN. Hence one can see “ concept “- “ consciousness” is generated at particle(ion) level in the brain and is experienced at the level of the neurons; We have discussed also ergodicity of IDRNN with random neural potential. " "
Peer Review Status:Awaiting Review