分类: 数学 >> 统计和概率 分类: 统计学 >> 数理统计学 分类: 信息科学与系统科学 >> 信息科学与系统科学基础学科 提交时间: 2024-05-22
摘要: 统计独立性是统计学和机器学习领域的基础性概念,如何表示和度量统计独立性是该领域的基本问题。Copula理论提供了统计相关关系表示的理论工具,而Copula熵理论则给出了度量统计独立性的概念工具。本文综述了Copula熵的理论和应用,概述了其基本概念定义、定理和性质,以及估计方法。介绍了Copula熵研究的最新进展,包括其在统计学的十个基本问题(结构学习、关联发现、变量选择、因果发现、系统辨识、时延估计、域自适应、正态性检验、双样本检验和变点检测等)上的理论应用。讨论了理论应用之间的联系,以及其对应的深层次的相关性和因果性概念之间的联系,并将Copula熵的(条件)独立性度量框架与基于核函数和距离相关的同类框架进行了理论对比。通过仿真和实际数据实验评估验证了Copula熵方法体系相对于同类方法的实际优越性。简述了Copula熵在理论物理学、天体物理学、地球物理学、理论化学、化学信息学、材料学、水文学、气候学、气象学、环境学、生态学、动物形态学、农学、认知神经学、运动神经学、计算神经学、心理学、系统生物学、生物信息学、临床诊断学、老年医学、精神病学、公共卫生学、经济学、管理学、社会学、教育学、计算语言学、新闻传播学、法学、政治学、军事学、情报学,以及能源工程、食品工程、土木建筑、交通运输、制造工程、可靠性工程、冶金工程、化学工程、航空航天、兵器工程、车辆工程、电子工程、通信工程、高性能计算、信息安全、测绘遥感、海洋工程和金融工程等领域的实际应用。
分类: 数学 >> 统计和概率 提交时间: 2024-02-04
摘要: 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 Entropypartition of complex system in present article. Human brains system self-organizably andadaptively 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
分类: 数学 >> 统计和概率 提交时间: 2024-01-23
摘要: The nineties of the 20th century, I have proposed and constructed theory of Abstract Neural Automata (ANA) 1 .Aim of present manu
分类: 数学 >> 统计和概率 分类: 心理学 >> 心理统计 提交时间: 2023-07-02
摘要: 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).
分类: 医学、药学 >> 基础医学 分类: 数学 >> 统计和概率 提交时间: 2023-04-19
摘要: 目的 考察当前单个率Meta分析的文献中对率的数据转换的实际使用情况。方法 在PubMed中检索2017年发表的单个率Meta分析的文献,从481条记录中筛选出145篇纳入分析。结果 在有全文的123篇文献中只有33篇(26.8%)文献交代了率的转换方法的使用,其中双重反正弦法20篇,logit转换8篇,平方根反正弦法3篇,对数转换1篇,直接使用原始率1篇。在这33篇文献中,率的转换方法的使用与汇总率的大小无关(P=0.217)。结论 单个率的Meta分析中率的转换方法是较为重要的因素,但各种转换方法的优劣尚无定论,发表的文献应加强对于率的数据转换等方法的说明。
分类: 医学、药学 >> 基础医学 分类: 数学 >> 统计和概率 提交时间: 2023-04-19
摘要: 目的 在单个率Meta分析中对率的不同转换方法进行比较。方法 构造两套模拟数据进行单个率的Meta分析,考察5种数据转换方法(不转换、对数转换、logit转换、平方根反正弦转换及双重反正弦转换)下的结果,兼顾固定效应模型和随机效应模型,及事件数为零时增加不同的固定值。计算汇总的率的均值(Mean),偏倚值(Bias)、偏倚率(Proportion Bias)、误差均方(Mean Squared Error, MSE)、误差均方百分比(Proportion MSE)及95%可信区间的覆盖率(Coverage)。结果 对基于二项分布的单个率进行Meta分析时,平方根反正弦转换总体表现最佳。当事件数为零时,增加不同的固定值对结果影响较大,但这种校正对不转换的策略没有帮助,甚至有损;对于对数转换和logit转换的改善也非常有限。总体率<0.05时,单个率Meta分析汇总的率偏倚较大。结论 单个率的Meta分析中平方根反正弦转换表现最佳。总体率<0.05时使用Meta分析宜谨慎。
分类: 医学、药学 >> 基础医学 分类: 数学 >> 统计和概率 提交时间: 2023-04-19
摘要: 单样本率比较(单组目标值法)的样本量计算常见的方法为正态近似法,有时伴相应的数据转换如平方根反正弦转换,而确切概率法通常需要商业统计软件寻值或编程实现。本文利用免费软件R语言编程实现单样本率比较确切概率法计算样本量,并且考虑到了确切概率法计算时检验效能与样本量非单调递增的关系,直接给出计算结果,也可作图直观显示检验效能与样本量的关系,希望能有助于这类研究的有效开展。
分类: 数学 >> 统计和概率 提交时间: 2022-05-12
摘要: 设 Zn 是一个独立同分布环境下的上临界分支过程. 本文得到了两个关于 Zn 的非一致性 Berry-Esseen 估计. 该结果把 Grama et al. [Stochastic,Process.,Appl.,127(4),1255-1281,2017] 的 Berry-Esseen 估计推广到了非一致性的情形. 最后, 我们讨论了这些结果在区间估计方面的应用.
分类: 数学 >> 统计和概率 分类: 数学 >> 应用数学 提交时间: 2022-03-30
摘要: 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 constantfrom the perspective of stochastic analysis.To address this issue, we deduce the price process of assetsfrom 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 pricesexisting 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 optionsbased on our model.This formula has an elegant form convenient to calculate,which is similarly to the renowned Black-Scholes formulaand of great significance to the research of derivatives market.
分类: 数学 >> 统计和概率 提交时间: 2021-12-16
摘要: 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.
分类: 数学 >> 统计和概率 提交时间: 2019-10-14
摘要: 已有的关于模型平均估计渐近分布理论的研究多是基于局部误设定的假设,[1] 是其中开创性的且最著名的文章之一. 虽然利用局部误设定的假设可以证明模型平均估计渐近分布理论, 但是 [2] 等对此假设提出了不合理性质疑和解释. 本文我们研究[1]中的置信区间估计方法. 证明了在一般参数设定下, 虽然 [1]中的渐近分布理论不一定成立, 但是关于不确定参数的线性函数的置信区间在正态分布误差、线性回归模 型下是有效的, 即置信区间的覆盖率趋于预设定的名义水平. 我们通过模拟研究进一步验证了理论结果.
分类: 数学 >> 统计和概率 提交时间: 2019-07-21
摘要: 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.
分类: 数学 >> 统计和概率 提交时间: 2018-11-07
摘要: 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.