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conditional independence Leads to Satisfaction of the Bell Inequality without Assuming Non-Locality or Non-Reality

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Advances in Pure Mathematics 2022年第5期12卷 405-417页

作者： Louis Sica Institute for Quantum Studies Chapman University Orange USA Inspire Institute Inc. Alexandria USA

The original Bell inequality was obtained in a statistical derivation assuming three mutually cross-correlated random variables (four in the later version). Given that observations destroy the particles, the physical realization of three variables from an experiment producing two particles per trial requires two separate trial runs. One assumed variable value (for particle 1) occurs at a fixed instrument setting in both trial runs while a second variable (for particle 2) occurs at alternative instrument settings in the two trial runs. Given that measurements on the two particles occurring in each trial are themselves correlated, measurements from independent realizations at mutually exclusive settings on particle 2 are conditionally independent, i.e., conditionally dependent on particle 1, through probability. This situation is realized from variables defined by Bell using entangled particle pairs. Two correlations have the form that Bell computed from entanglement, but a third correlation from conditionally independent measurements has a different form. When the correlations are computed using quantum probabilities, the Bell inequality is satisfied without recourse to assumptions of non-locality, or non-reality.

关键词： Bell Theorem Bell Inequality Entanglement Cross-Correlations conditional independence

Testing conditional independence with data missing at random

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Applied Mathematics(A Journal of Chinese Universities) 2018年第3期33卷 298-312页

作者： LIU Yi LIU Xiao-hui College of Science China University of Petroleum (East China) School of Statistics Jiangxi University of Finance and Economics Research Center of Applied Statistics Jiangxi University of Finance and Economics

It is known that conditional independence is a quite basic assumption in many fields of statistics. How to test its validity is of great importance and has been extensively studied by the literature. Nevertheless, all of the existing methods focus on the case that data are fully observed, but none of them seems having taken into account of the scenario when missing data are present. Motivated by this, this paper develops two testing statistics to handle such a situation relying on the idea of inverse probability weighted and augmented inverse probability weighted techniques. The asymptotic distributions of the proposed statistics are also derived under the null hypothesis. The simulation studies indicate that both testing statistics perform well in terms of size and power.

关键词： conditional independence cumulative sum process of residuals missing at random inverse probability weighting re-sampling

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c-CSN:Single-cell RNA Sequencing Data Analysis by conditional Cell-specific Network

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Genomics, Proteomics & Bioinformatics 2021年第2期19卷 319-329页

作者： Lin Li Hao Dai Zhaoyuan Fang Luonan Chen Key Laboratory of Systems Biology Shanghai Institute of Biochemistry and Cell BiologyCenter for Excellence in Molecular Cell ScienceChinese Academy of SciencesShanghai 200031China University of Chinese Academy of Sciences Beijing 100049China Shanghai Research Center for Brain Science and Brain-Inspired Intelligence Shanghai 201210China CAS Center for Excellence in Animal Evolution and Genetics Chinese Academy of SciencesKunming 650223China Hangzhou Institute for Advanced Study Chinese Academy of SciencesHangzhou 310024China

t The rapid advancement of single-cell technologies has shed new light on the complex mechanisms of cellular ***,compared to bulk RNA sequencing(RNA-seq),single-cell RNA-seq(scRNA-seq)suffers from higher noise and lower coverage,which brings new computational *** on statistical independence,cell-specific network(CSN)is able to quantify the overall associations between genes for each cell,yet suffering from a problem of overestimation related to indirect *** overcome this problem,we propose the c-CSN method,which can construct the conditional cell-specific network(CCSN)for each cell.c-CSN method can measure the direct associations between genes by eliminating the indirect associations.c-CSN can be used for cell clustering and dimension reduction on a network basis of single ***,each CCSN can be viewed as the transformation from less“reliable”gene expression to more“reliable”gene–gene associations in a *** on CCSN,we further design network flow entropy(NFE)to estimate the differentiation potency of a single cell.A number of scRNA-seq datasets were used to demonstrate the advantages of our approach.1)One direct association network is generated for one cell.2)Most existing scRNA-seq methods designed for gene expression matrices are also applicable to c-CSN-transformed degree matrices.3)CCSN-based NFE helps resolving the direction of differentiation trajectories by quantifying the potency of each cell.c-CSN is publicly available at https://***/LinLi-0909/c-CSN.

关键词： Network flow entropy Cell-specific network Single-cell network Direct association conditional independence

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On collapsibilities of Yule's measure

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Science China Mathematics 2001年第7期44卷 829-836页

作者：郭建华史宁中耿直 Department of Mathematics Northeast Normal University Changchun China Department of Probability and Statistics Peking University Beijing China Institute of Mathematics Jilin University Changchun China

impson's paradox reminds people that the statistical inference in a low-dimensional space probably distorts the reality in a high one *** study the paradox with respect to Yule's measure,this paper discusses simple collapsibility,strong collapsibility and consecutive collapsibility,and presents necessary and sufficient conditions of *** fact,these conditions are of great importance for observational and experimental designs,eliminating confounding bias,categorizing discrete variables and so on.

关键词： collapsibility conditional independence Simpson’ s paradox Yule’ s measure.

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有向图模型的模型解释

有向图模型的模型解释