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Poisson distribution
About: Poisson distribution is a research topic. Over the lifetime, 16314 publications have been published within this topic receiving 363895 citations.
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TL;DR: A novel foam structure is presented, which exhibits a negative Poisson's ratio, and such a material expands laterally when stretched, in contrast to ordinary materials.
Abstract: A novel foam structure is presented, which exhibits a negative Poisson's ratio. Such a material expands laterally when stretched, in contrast to ordinary materials.
2,871 citations
TL;DR: In this article, a classical confidence belt construction is proposed to unify the treatment of upper confidence limits for null results and two-sided confidence intervals for non-null results for Gaussian processes with background and Gaussian errors with a bounded physical region.
Abstract: We give a classical confidence belt construction which unifies the treatment of upper confidence limits for null results and two-sided confidence intervals for non-null results. The unified treatment solves a problem (apparently not previously recognized) that the choice of upper limit or two-sided intervals leads to intervals which are not confidence intervals if the choice is based on the data. We apply the construction to two related problems which have recently been a battle-ground between classical and Bayesian statistics: Poisson processes with background, and Gaussian errors with a bounded physical region. In contrast with the usual classical construction for upper limits, our construction avoids unphysical confidence intervals. In contrast with some popular Bayesian intervals, our intervals eliminate conservatism (frequentist coverage greater than the stated confidence) in the Gaussian case and reduce it to a level dictated by discreteness in the Poisson case. We generalize the method in order to apply it to analysis of experiments searching for neutrino oscillations. We show that this technique both gives correct coverage and is powerful, while other classical techniques that have been used by neutrino oscillation search experiments fail one or both of these criteria.
2,830 citations
26 Jun 2006
TL;DR: A spatially adaptive multiscale algorithm whose time and space complexities are proportional to the size of the reconstructed model, and which reduces to a well conditioned sparse linear system.
Abstract: We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function schemes, our Poisson approach allows a hierarchy of locally supported basis functions, and therefore the solution reduces to a well conditioned sparse linear system. We describe a spatially adaptive multiscale algorithm whose time and space complexities are proportional to the size of the reconstructed model. Experimenting with publicly available scan data, we demonstrate reconstruction of surfaces with greater detail than previously achievable.
2,712 citations
TL;DR: The calculation of limits for small numbers of astronomical counts is based on standard equations derived from Poisson and binomial statistics; although the equations are straightforward, their direct use is cumbersome and involves both table-interpolations and several mathematical operations as discussed by the authors.
Abstract: The calculation of limits for small numbers of astronomical counts is based on standard equations derived from Poisson and binomial statistics; although the equations are straightforward, their direct use is cumbersome and involves both table-interpolations and several mathematical operations Convenient tables and approximate formulae are here presented for confidence limits which are based on such Poisson and binomial statistics The limits in the tables are given for all confidence levels commonly used in astrophysics
2,415 citations
TL;DR: In an exponentially growing population in which the product of the current population size and the growth rate is substantially larger than one, the analytical and simulation results show that most coalescent events occur relatively early and in a restricted range of times.
Abstract: We consider the distribution of pairwise sequence differences of mitochondrial DNA or of other nonrecombining portions of the genome in a population that has been of constant size and in a population that has been growing in size exponentially for a long time. We show that, in a population of constant size, the sample distribution of pairwise differences will typically deviate substantially from the geometric distribution expected, because the history of coalescent events in a single sample of genes imposes a substantial correlation on pairwise differences. Consequently, a goodness-of-fit test of observed pairwise differences to the geometric distribution, which assumes that each pairwise comparison is independent, is not a valid test of the hypothesis that the genes were sampled from a panmictic population of constant size. In an exponentially growing population in which the product of the current population size and the growth rate is substantially larger than one, our analytical and simulation results show that most coalescent events occur relatively early and in a restricted range of times. Hence, the "gene tree" will be nearly a "star phylogeny" and the distribution of pairwise differences will be nearly a Poisson distribution. In that case, it is possible to estimate r, the population growth rate, if the mutation rate, mu, and current population size, N0, are assumed known. The estimate of r is the solution to ri/mu = ln(N0r) - gamma, where i is the average pairwise difference and gamma approximately 0.577 is Euler's constant.
2,260 citations