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Journal articles on the topic 'Bernoullian Statistics'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Karssenberg, Frederik G., Christian Piel, Andreas Hopf, Vincent B. F. Mathot, and Walter Kaminsky. "Bernoullian, Terminal, Penultimate or Third Order Markov Statistics?" Macromolecular Theory and Simulations 14, no. 5 (2005): 295–99. http://dx.doi.org/10.1002/mats.200500005.

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2

Dong, Shen, and André M. Striegel. "Monte Carlo Simulation of the Sequence Length and Junction Point Distributions in Random Copolymers Obeying Bernoullian Statistics." International Journal of Polymer Analysis and Characterization 17, no. 4 (2012): 247–56. http://dx.doi.org/10.1080/1023666x.2012.653100.

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3

Yushkevich, A. P. "Nicholas Bernoulli and the Publication of James Bernoulli’s Ars Conjectandi." Theory of Probability & Its Applications 31, no. 2 (1987): 286–303. http://dx.doi.org/10.1137/1131034.

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4

Bolthausen, Erwin, and Mario V. Wüthrich. "BERNOULLI'S LAW OF LARGE NUMBERS." ASTIN Bulletin 43, no. 2 (2013): 73–79. http://dx.doi.org/10.1017/asb.2013.11.

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AbstractThis year we celebrate the 300th anniversary of Jakob Bernoulli's path-breaking work Ars conjectandi, which appeared in 1713, eight years after his death. In Part IV of his masterpiece, Bernoulli proves the law of large numbers which is one of the fundamental theorems in probability theory, statistics and actuarial science. We review and comment on his original proof.

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5

Rawlings, Don. "Bernoulli trials and permutation statistics." International Journal of Mathematics and Mathematical Sciences 15, no. 2 (1992): 291–311. http://dx.doi.org/10.1155/s0161171292000371.

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Several coin-tossing games are surveyed which, in a natural way, give rise to statistically induced probability measures on the set of permutations of{1,2,…,n}and on sets of multipermutations. The distributions of a general class of random variables known as binary tree statistics are also given.

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6

Suganuma, Koto, Tetsuo Asakura, Miyuki Oshimura, Tomohiro Hirano, Koichi Ute, and H. N. Cheng. "NMR Analysis of Poly(Lactic Acid) via Statistical Models." Polymers 11, no. 4 (2019): 725. http://dx.doi.org/10.3390/polym11040725.

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The physical properties of poly(lactic acid) (PLA) are influenced by its stereoregularity and stereosequence distribution, and its polymer stereochemistry can be effectively studied by NMR spectroscopy. In previously published NMR studies of PLA tacticity, the NMR data were fitted to pair-addition Bernoullian models. In this work, we prepared several PLA samples with a tin catalyst at different L,L-lactide and D,D-lactide ratios. Upon analysis of the tetrad intensities with the pair-addition Bernoullian model, we found substantial deviations between observed and calculated intensities due to the presence of transesterification and racemization during the polymerization processes. We formulated a two-state (pair-addition Bernoullian and single-addition Bernoullian) model, and it gave a better fit to the observed data. The use of the two-state model provides a quantitative measure of the extent of transesterification and racemization, and potentially yields useful information on the polymerization mechanism.

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7

Dobrow, Robert P. "On the distribution of distances in recursive trees." Journal of Applied Probability 33, no. 3 (1996): 749–57. http://dx.doi.org/10.2307/3215356.

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Recursive trees have been used to model such things as the spread of epidemics, family trees of ancient manuscripts, and pyramid schemes. A tree Tn with n labeled nodes is a recursive tree if n = 1, or n > 1 and Tn can be constructed by joining node n to a node of some recursive tree Tn–1. For arbitrary nodes i < n in a random recursive tree we give the exact distribution of Xi,n, the distance between nodes i and n. We characterize this distribution as the convolution of the law of Xi,j+1 and n – i – 1 Bernoulli distributions. We further characterize the law of Xi,j+1 as a mixture of sums of Bernoullis. For i = in growing as a function of n, we show that is asymptotically normal in several settings.

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8

Fu, James C., Tung-Lung Wu, and W. Y. Wendy Lou. "Continuous, Discrete, and Conditional Scan Statistics." Journal of Applied Probability 49, no. 01 (2012): 199–209. http://dx.doi.org/10.1017/s0021900200008949.

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The distributions for continuous, discrete, and conditional discrete scan statistics are studied. The approach of finite Markov chain imbedding, which has been applied to random permutations as well as to runs and patterns, is extended to compute the distribution of the conditional discrete scan statistic, defined from a sequence of Bernoulli trials. It is shown that the distribution of the continuous scan statistic induced by a Poisson process defined on (0, 1] is a limiting distribution of weighted distributions of conditional discrete scan statistics. Comparisons of rates of convergence as well as numerical comparisons of various bounds and approximations are provided to illustrate the theoretical results.

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9

Fu, James C., Tung-Lung Wu, and W. Y. Wendy Lou. "Continuous, Discrete, and Conditional Scan Statistics." Journal of Applied Probability 49, no. 1 (2012): 199–209. http://dx.doi.org/10.1239/jap/1331216842.

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The distributions for continuous, discrete, and conditional discrete scan statistics are studied. The approach of finite Markov chain imbedding, which has been applied to random permutations as well as to runs and patterns, is extended to compute the distribution of the conditional discrete scan statistic, defined from a sequence of Bernoulli trials. It is shown that the distribution of the continuous scan statistic induced by a Poisson process defined on (0, 1] is a limiting distribution of weighted distributions of conditional discrete scan statistics. Comparisons of rates of convergence as well as numerical comparisons of various bounds and approximations are provided to illustrate the theoretical results.

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10

Fu, James C. "Distribution of the scan statistic for a sequence of bistate trials." Journal of Applied Probability 38, no. 4 (2001): 908–16. http://dx.doi.org/10.1239/jap/1011994181.

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Let be the scan statistic of window size r for a sequence of n bistate trials . The scan statistic Sn(r) has been successfully used in various fields of applied probability and statistics, and its distribution has been studied extensively in the literature. Currently, all existing formulae for the distribution of Sn(r) are rather complex, and they can only be numerically implemented when is a sequence of Bernoulli trials, the window size r is less than 20 and the length of the sequence n is not too large. Hence, these formulae have been limiting the practical applications of the scan statistic. In this article, we derive a simple and effective formula for the distribution of Sn(r) via the finite Markov chain embedding technique to overcome some of the limitations of the existing complex formulae. This new formula can be applied when is either a sequence of Bernoulli trials or a sequence of Markov dependent bistate trials. Selected numerical examples are given to illustrate our results.

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11

Edwards, A. W. R. "Bernoulli: Official Journal of the Bernoulli Society for Mathematical Statistics and Probability." Nature 383, no. 6595 (1996): 40. http://dx.doi.org/10.1038/383040a0.

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12

Mahler, Ronald. "Exact Closed-Form Multitarget Bayes Filters." Sensors 19, no. 12 (2019): 2818. http://dx.doi.org/10.3390/s19122818.

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The finite-set statistics (FISST) foundational approach to multitarget tracking and information fusion has inspired work by dozens of research groups in at least 20 nations; and FISST publications have been cited tens of thousands of times. This review paper addresses a recent and cutting-edge aspect of this research: exact closed-form—and, therefore, provably Bayes-optimal—approximations of the multitarget Bayes filter. The five proposed such filters—generalized labeled multi-Bernoulli (GLMB), labeled multi-Bernoulli mixture (LMBM), and three Poisson multi-Bernoulli mixture (PMBM) filter variants—are assessed in depth. This assessment includes a theoretically rigorous, but intuitive, statistical theory of “undetected targets”, and concrete formulas for the posterior undetected-target densities for the “standard” multitarget measurement model.

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13

Deshmukh, Shailaja R. "BERNOULLI SAMPLING." Australian Journal of Statistics 33, no. 2 (1991): 167–76. http://dx.doi.org/10.1111/j.1467-842x.1991.tb00424.x.

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14

Fu, James C. "Distribution of the scan statistic for a sequence of bistate trials." Journal of Applied Probability 38, no. 04 (2001): 908–16. http://dx.doi.org/10.1017/s0021900200019124.

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Let be the scan statistic of window size r for a sequence of n bistate trials . The scan statistic S n (r) has been successfully used in various fields of applied probability and statistics, and its distribution has been studied extensively in the literature. Currently, all existing formulae for the distribution of S n (r) are rather complex, and they can only be numerically implemented when is a sequence of Bernoulli trials, the window size r is less than 20 and the length of the sequence n is not too large. Hence, these formulae have been limiting the practical applications of the scan statistic. In this article, we derive a simple and effective formula for the distribution of S n (r) via the finite Markov chain embedding technique to overcome some of the limitations of the existing complex formulae. This new formula can be applied when is either a sequence of Bernoulli trials or a sequence of Markov dependent bistate trials. Selected numerical examples are given to illustrate our results.

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15

Sharyn, Campbell A., Anant P. Godbole, and Stephanie Schaller. "Discriminating between sequences of bernoulli and markov-bernoulli trials." Communications in Statistics - Theory and Methods 23, no. 10 (1994): 2787–814. http://dx.doi.org/10.1080/03610929408831416.

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16

Chen, Jinshu. "Invariant States for a Quantum Markov Semigroup Constructed from Quantum Bernoulli Noises." Open Systems & Information Dynamics 25, no. 04 (2018): 1850019. http://dx.doi.org/10.1142/s1230161218500191.

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Quantum Bernoulli noises are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation (CAR) in equal-time. In this paper, we consider a quantum Markov semigroup constructed from quantum Bernoulli noises. Among others, we show that the semigroup has infinitely many faithful invariant states that are diagonal, and satisfies the quantum detailed balance condition.

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17

Giraudo, Davide. "Limit theorems for U-statistics of Bernoulli data." Latin American Journal of Probability and Mathematical Statistics 18, no. 1 (2021): 793. http://dx.doi.org/10.30757/alea.v18-29.

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18

Boutsikas, M. V., M. V. Koutras, and F. S. Milienos. "Asymptotic results for the multiple scan statistic." Journal of Applied Probability 54, no. 1 (2017): 320–30. http://dx.doi.org/10.1017/jpr.2016.102.

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AbstractThe contribution of the theory of scan statistics to the study of many real-life applications has been rapidly expanding during the last decades. The multiple scan statistic, defined on a sequence of n Bernoulli trials, enumerates the number of occurrences of k consecutive trials which contain at least r successes among them (r≤k≤n). In this paper we establish some asymptotic results for the distribution of the multiple scan statistic, as n,k,r→∞ and illustrate their accuracy through a simulation study. Our approach is based on an appropriate combination of compound Poisson approximation and random walk theory.

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19

Gnedin, Alexander V. "The Bernoulli sieve." Bernoulli 10, no. 1 (2004): 79–96. http://dx.doi.org/10.3150/bj/1077544604.

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20

Dai, Bin, Shilin Ding, and Grace Wahba. "Multivariate Bernoulli distribution." Bernoulli 19, no. 4 (2013): 1465–83. http://dx.doi.org/10.3150/12-bejsp10.

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21

Golodets, Valentin Y., and Sergey V. Neshveyev. "Non-Bernoullian Quantum K-Systems." Communications in Mathematical Physics 195, no. 1 (1998): 213–32. http://dx.doi.org/10.1007/s002200050386.

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22

Stigler, Stephen. "Statisticians and the History of Economics." Journal of the History of Economic Thought 24, no. 2 (2002): 155–64. http://dx.doi.org/10.1080/10427710220134349.

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Over twenty years ago, I had the pleasure of speaking to the Royal Statistical Society about the life and work in statistics of Francis Ysidro Edgeworth. In a preamble to that talk, I commented upon some similarities between Edgeworth and an even earlier scientist, Daniel Bernoulli, who lived from 1700 to 1782. One similarity I mentioned would be so well-known to this audience that it scarcely bears repetition: Both Edgeworth and Bernoulli were important in the histories of both economics and statistics. Of Edgeworth's work in economics I need not comment—I expect that his work on taxation, price theory, international trade, and index numbers is familiar to many in this audience. Edgeworth's work in statistics was no less important in at least four ways: (1) He was an astute and original philosopher of the application of probability and quantitative thinking in social science; (2) he had sufficient mathematical genius to situate Galton's concept of correlation in the framework of the multivariate normal distribution, thereby pointing the way for Karl Pearson to develop correlational analysis—Edgeworth even has a claim on being the inventor of the product moment correlation coefficient; (3) he pioneered the exploration of many topics, such as variance component estimation, the theory of maximum likelihood, and series expansions for sampling distributions; and (4) he had an amazing ability to explore the limits of statistical concepts by constructing subtle and surprising counterexamples to widely accepted truths.

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23

Smith, Laurel, and Persi Diaconis. "Honest bernoulli excursions." Journal of Applied Probability 25, no. 3 (1988): 464–77. http://dx.doi.org/10.2307/3213976.

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For simple random walk on the integers, consider the chance that the walk has traveled distance k from its start given that its first return is at time 2n. We derive a limiting approximation accurate to order 1/n. We give a combinatorial explanation for a functional equation satisfied by the limit and show this yields the functional equation of Riemann's zeta function.

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24

Smith, Laurel, and Persi Diaconis. "Honest bernoulli excursions." Journal of Applied Probability 25, no. 03 (1988): 464–77. http://dx.doi.org/10.1017/s002190020004119x.

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For simple random walk on the integers, consider the chance that the walk has traveled distance k from its start given that its first return is at time 2n. We derive a limiting approximation accurate to order 1/n. We give a combinatorial explanation for a functional equation satisfied by the limit and show this yields the functional equation of Riemann's zeta function.

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25

Gnedin, Alexander V., Alexander M. Iksanov, Pavlo Negadajlov, and Uwe Rösler. "The Bernoulli sieve revisited." Annals of Applied Probability 19, no. 4 (2009): 1634–55. http://dx.doi.org/10.1214/08-aap592.

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26

Treadway, Jennifer, and Don Rawlings. "Bernoulli Trials and Mahonian Statistics: A Tale of Twoq's." Mathematics Magazine 67, no. 5 (1994): 345–54. http://dx.doi.org/10.1080/0025570x.1994.11996247.

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27

Raper, Simon. "Turning points: Bernoulli's golden theorem." Significance 15, no. 4 (2018): 26–29. http://dx.doi.org/10.1111/j.1740-9713.2018.01171.x.

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28

Matveichuk, S. A., and Yu I. Petunin. "A generalization of Bernoulli's model occurring in order statistics II." Ukrainian Mathematical Journal 43, no. 6 (1991): 728–34. http://dx.doi.org/10.1007/bf01058940.

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29

SPANÒ, M., F. LILLO, S. MICCICHÈ, and R. N. MANTEGNA. "INVERTED REPEATS IN VIRAL GENOMES." Fluctuation and Noise Letters 05, no. 02 (2005): L193—L200. http://dx.doi.org/10.1142/s0219477505002550.

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We investigate 738 complete genomes of viruses to detect the presence of short inverted repeats. The number of inverted repeats found is compared with the prediction obtained for a Bernoullian and for a Markovian control model. We find as a statistical regularity that the number of observed inverted repeats is often greater than the one expected in terms of a Bernoullian or Markovian model in several of the viruses and in almost all those with a genome longer than 30,000 bp.

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30

GUILLOTIN-PLANTARD, NADINE, and RENÉ SCHOTT. "DYNAMIC QUANTUM BERNOULLI RANDOM WALKS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, no. 02 (2008): 213–29. http://dx.doi.org/10.1142/s021902570800304x.

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Quantum Bernoulli random walks can be realized as random walks on the dual of SU(2). We use this realization in order to study a model of dynamic quantum Bernoulli random walk with time-dependent transitions. For the corresponding dynamic random walk on the dual of SU(2), we prove several limit theorems (local limit theorem, central limit theorem, law of large numbers, large deviation principle). In addition, we characterize a large class of transient dynamic random walks.

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31

Altoum, Sami H., Aymen Ettaieb, and Hafedh Rguigui. "Generalized Bernoulli Wick differential equation." Infinite Dimensional Analysis, Quantum Probability and Related Topics 24, no. 01 (2021): 2150008. http://dx.doi.org/10.1142/s0219025721500089.

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Based on the distributions space on [Formula: see text] (denoted by [Formula: see text]) which is the topological dual space of the space of entire functions with exponential growth of order [Formula: see text] and of minimal type, we introduce a new type of differential equations using the Wick derivation operator and the Wick product of elements in [Formula: see text]. These equations are called generalized Bernoulli Wick differential equations which are the analogue of the classical Bernoulli differential equations. We solve these generalized Wick differential equations. The present method is exemplified by several examples.

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32

Harel, Arie. "On honest Bernoulli excursions." Journal of Applied Probability 27, no. 2 (1990): 475–76. http://dx.doi.org/10.2307/3214670.

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33

Euán, Carolina, and Ying Sun. "Bernoulli vector autoregressive model." Journal of Multivariate Analysis 177 (May 2020): 104599. http://dx.doi.org/10.1016/j.jmva.2020.104599.

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34

Harel, Arie. "On honest Bernoulli excursions." Journal of Applied Probability 27, no. 02 (1990): 475–76. http://dx.doi.org/10.1017/s0021900200038961.

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35

Tikhomirov. "Singularity of random Bernoulli matrices." Annals of Mathematics 191, no. 2 (2020): 593. http://dx.doi.org/10.4007/annals.2020.191.2.6.

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36

Timár, Adám. "Neighboring clusters in Bernoulli percolation." Annals of Probability 34, no. 6 (2006): 2332–43. http://dx.doi.org/10.1214/009117906000000485.

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37

Vos, J. C., and W. Vervaat. "Local Times of Bernoulli Walk." Statistica Neerlandica 42, no. 1 (1988): 1–16. http://dx.doi.org/10.1111/j.1467-9574.1988.tb01516.x.

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38

D’Ovidio, Mirko, Anna Chiara Lai, and Paola Loreti. "Solutions of Bernoulli Equations in the Fractional Setting." Fractal and Fractional 5, no. 2 (2021): 57. http://dx.doi.org/10.3390/fractalfract5020057.

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We present a general series representation formula for the local solution of the Bernoulli equation with Caputo fractional derivatives. We then focus on a generalization of the fractional logistic equation and present some related numerical simulations.

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39

Treadway, Jennifer, and Don Rawlings. "Bernoulli Trials and Mahonian Statistics: A Tale of Two q's." Mathematics Magazine 67, no. 5 (1994): 345. http://dx.doi.org/10.2307/2690993.

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40

Christofides, Tasos C. "A Kolmogorov inequality for U-statistics based on Bernoulli kernels." Statistics & Probability Letters 21, no. 5 (1994): 357–62. http://dx.doi.org/10.1016/0167-7152(94)00031-x.

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41

Privault, Nicolas. "Stochastic analysis of Bernoulli processes." Probability Surveys 5 (2008): 435–83. http://dx.doi.org/10.1214/08-ps139.

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42

Paetzold, Kamona L., and H. Fenwick Huss. "Bernoulli processes interrelated by constrain." Communications in Statistics - Theory and Methods 17, no. 5 (1988): 1377–83. http://dx.doi.org/10.1080/03610928808829686.

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43

Priezzhev, V. B., and G. M. Schütz. "Exact solution of the Bernoulli matching model of sequence alignment." Journal of Statistical Mechanics: Theory and Experiment 2008, no. 09 (2008): P09007. http://dx.doi.org/10.1088/1742-5468/2008/09/p09007.

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44

Joner, Michael D., William H. Woodall, and Marion R. Reynolds. "Detecting a rate increase using a Bernoulli scan statistic." Statistics in Medicine 27, no. 14 (2008): 2555–75. http://dx.doi.org/10.1002/sim.3081.

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45

Heicklen, Deborah, and Christopher Hoffman. "Rational Maps Are d-Adic Bernoulli." Annals of Mathematics 156, no. 1 (2002): 103. http://dx.doi.org/10.2307/3597185.

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46

Khrennikov, Andrew. "p-Adic behaviour of Bernoulli probabilities." Statistics & Probability Letters 37, no. 4 (1998): 375–79. http://dx.doi.org/10.1016/s0167-7152(97)00140-5.

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47

Khrennikov, A. Yu. "p-adic Behavior of Bernoulli Probabilities." Theory of Probability & Its Applications 42, no. 4 (1998): 689–94. http://dx.doi.org/10.1137/s0040585x97976581.

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48

Tang, Pengfei. "Heavy Bernoulli-percolation clusters are indistinguishable." Annals of Probability 47, no. 6 (2019): 4077–115. http://dx.doi.org/10.1214/19-aop1354.

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49

Breuillard, Emmanuel, and Péter P. Varjú. "On the dimension of Bernoulli convolutions." Annals of Probability 47, no. 4 (2019): 2582–617. http://dx.doi.org/10.1214/18-aop1324.

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50

Lovison, Gianfranco. "A matrix-valued Bernoulli distribution." Journal of Multivariate Analysis 97, no. 7 (2006): 1573–85. http://dx.doi.org/10.1016/j.jmva.2005.06.008.

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