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LOCATING A CHANGED SEGMENT IN A SEQUENCE OF bernoulli variableS

BIOMETRIKA 1990年第2期77卷 295-304页

作者： FU, YX CURNOW, RN Department of Applied Statistics University of ReadingReading RG62AN U.K.

The theory underlying inferences about a single change point in a sequence of independent bernoulli variables is extended to the two change points problem where the distance between the two change points is known, namely a changed segment. Both null and nonnull distributions of the log likelihood ratio for testing the hypothesis that there is no changed segment against the alternative that there is one of specified length are derived using recurrence equations. The distribution of the maximum likelihood estimator of the location of the changed segment is derived. Some numerical results for changed segments of length up to 20 are given and computational methods are presented.

关键词： bernoulli variable Change point Changed segment Markov chain Protein structure

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Application of the weighted binomial in quality control

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 1997年第7期30卷 4025-4032页

作者： Papayanopoulos, L Rutgers State Univ Grad Sch Management Newark NJ 07102 USA

No abstract available

关键词： weighted binomial weighted multinomial combinatorial distribution omega function induced distribution probability density mass function discrete random variable bernoulli variable quality control process drift hypothesis test control chart asymmetric control limits computer graphics prior distribution posterior distribution

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FLOW BEHAVIOR IN REARWARD-FACING CAVITIES

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APPLIED MATHEMATICAL MODELLING 1986年第3期10卷 176-184页

作者： FLETCHER, CAJ BARBUTO, J Department of Mechanical Engineering University of Sydney New South Wales 2006Australia

A group finite element method is described for the prediction of steady, incompressible, laminar flow in rearward-facing cavities with blowing and suction, The cavity is formed by a downstream lip extension to a reaward-facing step. The steady-state solution is obtained as the converged solution of a consistent pseudo-transient approximate factorization of the stream-function vorticity equations. Subsequently the global pressure distribution is obtained from a poisson equation for the bernoulli energy variable. The flow over reaward-facing cavities with depth/breadth ratios of 0.56 and 1.18 is compared with the flow ever a reaward-facing step. The flowfield is dominated by a bubble of slowly recirculating fluid which grows in downstream extent with increasing Reynolds number, almost independently of lip length. The recirculation bubble extends slightly upstream of the lip and, for the longer lip, induces a very weak counter-rotating flow in the base of the cavity. The use of equal magnitude blowing and suction in the base of the cavity under the longer lip sets up a two cell structure in the cavity for clockwise blowing and suction and a single cell structure for anticlockwise blowing and suction. These additional cells appear to limit the influence of the blowing and suction on the strength and orientation of the main recirculation region downstream of the lip.

关键词： group finite element method reaward-facing cavity laminar flow blowing and suction bernoulli variable

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New power limits for extremes

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EXTREMES 2013年第4期16卷 457-485页

作者： Balkema, Guus Univ Amsterdam Amsterdam Netherlands

For order statistics there is a deceptively simple link between affine and power norming, using exponential transforms. This link does not tell the whole story about limit distributions. The exponential transforms and yield limit variables which are either positive or negative. Under power norming there exist discrete limit distributions for maxima. The corresponding limit variables assume two values, one of which is zero. All variables with two values, one positive, one zero, are power limits for maxima. They are of different power type if they give different weight to zero, but they all have the same domain, the set of dfs with finite positive upper endpoint and an upper tail which varies slowly. So we see that convergence of types does not hold for power norming. This paper gives a classification of the power limits and their domains for maxima, variables conditioned to be large, and POTs (where power limits may assume three values). Convergence of sample clouds under power norming is studied, and of intermediate upper order statistics. The new power limits do not affect applications. Power norming is a viable alternative to classic extreme value theory. The extra norming constant in the exponent automatically improves the rate of convergence. Hill plots are a good instrument to determine this norming constant. It will be shown how to eliminate the bias of Hill plots and estimate high upper quantiles when the tail does not vary regularly or when convergence is slow.

关键词： bernoulli variable Convergence of types g-and-h distribution High risk scenario Hill plot Intermediate order statistics Maxima Non-linear normalization Peaks over thresholds Residual life time Weibull tail

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A POLYA APPROXIMATION TO THE POISSON-BINOMIAL LAW

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JOURNAL OF APPLIED PROBABILITY 2012年第3期49卷 745-757页

作者： Skipper, Max Univ Sydney Sch Math & Stat Sydney NSW 2006 Australia Univ Oxford Oxford OX1 2JD England

Using Stein's method, we derive explicit upper bounds on the total variation distance between a Poisson-binomial law (the distribution of a sum of independent but not necessarily identically distributed bernoulli random variables) and a Polya distribution with the same support, mean, and variance;a nonuniform bound on the pointwise distance between the probability mass functions is also given. A numerical comparison of alternative distributional approximations on a somewhat representative collection of case studies is also exhibited. The evidence proves that no single one is uniformly most accurate, though it suggests that the Polya approximation might be preferred in several parameter domains encountered in practice.

关键词： Stein's method Poisson-binomial approximation bernoulli variable

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POWER OF THE SCAN STATISTIC IN DETECTING A CHANGED SEGMENT IN A bernoulli SEQUENCE

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BIOMETRIKA 1994年第3期81卷 595-601页

作者： WALLENSTEIN, S NAUS, J GLAZ, J RUTGERS STATE UNIV DEPT STATNEW BRUNSWICKNJ 08903 UNIV CONNECTICUT DEPT STATSTORRSCT 06269

Fu & Curnow (1990) derive recursive equations to find the level of significance and power of a likelihead ratio test for a changed segment of specified length, based on the scan statistic, the maximum number of successes within the specified length. Their method is computationally feasible for segment lengths of 20 or less. We present and evaluate highly accurate approximations as well as bounds for the power function of this test that are computationally feasible even for very large segment lengths. We also evaluate power when the duration of the increased length used in the test statistic does not correspond to the actual length.

关键词： bernoulli variable CHANGE-POINT DNA SEQUENCE MATCHING SCAN STATISTIC

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A Novel Adaptive Extended Target Tracking Algorithm Based-on Variational Bayes Within Unknown Probability of Measurement Loss 10

A Novel Adaptive Extended Target Tracking Algorithm Based-on...

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10th International Conference on Electrical Engineering, Control and Robotics (EECR)

作者： He, Wenbo Henan Univ Artificial Intelligence Coll Zhengzhou Peoples R China

ISBN: (纸本)9798350370010;9798350370003

A novel variational Bayes based adaptive extended target tracking algorithm is proposed to solve the problem of extended target tracking with an unknown probability of measurement loss. Firstly, in the random matrix theoretical framework, an unknown positive semi-definite matrix represents the range of the target. In addition, the rotation matrix represents the change of the target direction. Secondly, the bernoulli random variable with binary sequence properties is used to determine whether measurement loss occurs. Thirdly, The Beta distribution is chosen as the prior distribution for the probability of measurement loss. Lastly, the kinematic state, the extended information and the probability of measurement loss are jointly estimated based on the VB approach.

关键词： Extended target tracking Measurement loss Variational Bayes bernoulli variable Random matrix

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Stochastic stabilization of complex networks with randomly topological structure 28

Stochastic stabilization of complex networks with randomly t...

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28th Chinese Control and Decision Conference

作者： Yan, Tingting Wang, Guoliang Feng, Bo Cai, Hongyang Liaoning Shihua Univ Sch Informat & Control Engn Fushun 113001 Peoples R China

ISBN: (纸本)9781467397148

In this paper, the stabilization problem of complex networks is realized by a stochastically stabilizing controller, where the desired controller is added in terms of Brownian noise perturbation. Compared with the traditional methods on stabilizing controller, the stabilization scheme named to be stochastic pinning control in this paper is closely related to the bernoulli variable and is only in the diffusion part. Moreover, the topological structure of the presented stochastic pinning controller is not constant but in terms of coupling matrix changing randomly, which is handled by the robust method. It is shown that the probability in addition to the switching between such different topological structures both play important roles in stochastic stabilization. Based on the obtained result, a more general case that the expectation of the bernoulli variable having uncertainty is considered too. Finally, the correctness and effectiveness of the research results are verified by a numerical simulation.

关键词： complex networks stochastic stabilization stochastic pinning control Brownian noise bernoulli variable

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A Comparative Study of Four Change Detection Methods for Aerial Photography Applications

A Comparative Study of Four Change Detection Methods for Aer...

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Conference on Airborne Intelligence, Surveillance, Reconnaissance (ISR) Systems and Applications VII

作者： Abramovich, Gil Brooksby, Glen Bush, Stephen F. Manickam, Swaminathan Ozcanli, Ozge Garrett, Benjamin D. GE Global Res One Res Circle Niskayuna NY 12309 USA Brown Univ Div Engn Providence RI 02912 USA Lockheed Martin Corp IS&GS Gaithersburg MD 20879 USA

ISBN: (纸本)9780819481320

We present four new change detection methods that create an automated change map from a probability map. In this case, the probability map was derived from a 3D model. The primary application of interest is aerial photographic applications, where the appearance, disappearance or change in position of small objects of a selectable class (e.g., cars) must be detected at a high success rate in spite of variations in magnification, lighting and background across the image. The methods rely on an earlier derivation of a probability map. We describe the theory of the four methods, namely bernoulli variables, Markov Random Fields, connected change, and relaxation-based segmentation, evaluate and compare their performance experimentally on a set probability maps derived from aerial photographs.

关键词： Markov Random Field bernoulli variable relaxation connected change

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A composite binomial model derived from correlated random variables

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2000年第5-6期29卷 1179-1195页

作者： Song, R Schlecht, PC Groff, JH NIOSH HGO Cincinnati OH 45226 USA

Motivated by a correlation problem in a power calculation of proficiency testing, a composite binomial model is developed to describe the distribution for the number of outliers from measurement results of multiple analytes contained in a single sampler. This model is different from other binomial models in that its component bernoulli variables are derived from correlated random variables. By modeling the correlated random variables and selecting a binary link function to convert these correlated random variables to bernoulli variables, various composite binomial distributions can be derived. Formulas for calculating the probabilities of the composite binomial distribution are provided. Although the composite binomial model is developed for a power calculation, it can be applied to other problems related to a sum of correlated bernoulli variables.

关键词： outlier bernoulli variable exchangeable link function

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