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| | ''' Poisson regression and negative binomial regression 泊松回归与负二项回归'''分析是有用的，其中依赖(响应)变量是计数(0,1,2，...)的在一个区间内事件发生的数量。 | | ''' Poisson regression and negative binomial regression 泊松回归与负二项回归'''分析是有用的，其中依赖(响应)变量是计数(0,1,2，...)的在一个区间内事件发生的数量。 |
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| − | === Other applications in science 科学上的其他应用=== | + | ===科学上的其他应用=== |
| | + | 在泊松过程中，观察到的事件数目在其平均值''λ''上下波动，波动标准<math>\sigma_k =\sqrt{\lambda}</math>差为。这些波动被称为泊松噪声或（特别是在电子学中）散粒噪声。 |
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| | + | 在计算独立的离散事件时，平均数和标准差的相关性是有科学价值的。通过监测波动是如何随着平均信号而变化的，我们可以估计单一事件的贡献，即使这个贡献太小而不能直接检测到。例如，电子的电荷''e''可以通过将电流的大小与散粒噪声相关联来估计。如果''N''个电子在给定时间''t''平均通过一个点，那么平均电流为<math>I=eN/t</math>； 因为当前的波动应该是<math>\sigma_I=e\sqrt{N}/t</math>(即 Poisson 过程的标准差) ，所以电荷<math>e</math>可以通过数学比率<math>t\sigma_I^2/I</math>来估计。 |
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| − | In a Poisson process, the number of observed occurrences fluctuates about its mean ''λ'' with a [[standard deviation]] <math>\sigma_k =\sqrt{\lambda}</math>. These fluctuations are denoted as ''Poisson noise'' or (particularly in electronics) as ''[[shot noise]]''.
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| − | In a Poisson process, the number of observed occurrences fluctuates about its mean λ with a standard deviation <math>\sigma_k =\sqrt{\lambda}</math>. These fluctuations are denoted as Poisson noise or (particularly in electronics) as shot noise.
| + | 一个日常的例子是放大照片时出现的颗粒状；颗粒状是由于减少的银粒数量的泊松波动，而不是单个颗粒本身。通过将颗粒度与放大程度相关联，我们可以估算出单个颗粒的贡献（否则颗粒太小，无法单独看到）。泊松噪声的许多其他分子应用已经发展起来，例如，估计细胞膜上受体分子的数量密度。 |
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| − | 在泊松过程中，观察到的事件数目在其平均值上下波动，波动标准差为1/2。这些波动被称为泊松噪声或(特别是在电子学中)散粒噪声。
| + | : <math> \Pr(N_t=k) = f(k;\lambda t) = \frac{(\lambda t)^k e^{-\lambda t}}{k!}.</math> |
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| | + | 在''' 因果集合论 Causal Set theory'''中，时空的离散元素在集合中遵循一个泊松分布。 |
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| − | The correlation of the mean and standard deviation in counting independent discrete occurrences is useful scientifically. By monitoring how the fluctuations vary with the mean signal, one can estimate the contribution of a single occurrence, ''even if that contribution is too small to be detected directly''. For example, the charge ''e'' on an electron can be estimated by correlating the magnitude of an [[electric current]] with its [[shot noise]]. If ''N'' electrons pass a point in a given time ''t'' on the average, the [[mean]] [[Electric current|current]] is <math>I=eN/t</math>; since the current fluctuations should be of the order <math>\sigma_I=e\sqrt{N}/t</math> (i.e., the standard deviation of the [[Poisson process]]), the charge <math>e</math> can be estimated from the ratio <math>t\sigma_I^2/I</math>.{{Citation needed|date=April 2012}}
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| − | The correlation of the mean and standard deviation in counting independent discrete occurrences is useful scientifically. By monitoring how the fluctuations vary with the mean signal, one can estimate the contribution of a single occurrence, even if that contribution is too small to be detected directly. For example, the charge e on an electron can be estimated by correlating the magnitude of an electric current with its shot noise. If N electrons pass a point in a given time t on the average, the mean current is <math>I=eN/t</math>; since the current fluctuations should be of the order <math>\sigma_I=e\sqrt{N}/t</math> (i.e., the standard deviation of the Poisson process), the charge <math>e</math> can be estimated from the ratio <math>t\sigma_I^2/I</math>.
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| − | 在计算独立的离散事件时，平均数和标准差的相关性是有科学价值的。通过监测波动是如何随着平均信号而变化的，我们可以估计单一事件的贡献，即使这个贡献太小而不能直接检测到。例如，电子的电荷 e 可以通过将电流的大小与散粒噪声相关联来估计。如果 n 个电子在给定时间 t 平均通过一个点，那么平均电流为 < math > i = eN/t </math > ; 因为当前的波动应该是 < math > sigma i = e sqrt { n }/t </math > (即 Poisson 过程的标准差) ，所以电荷 < math > e </math > 可以通过数学比率 < t sigma _ i ^ 2/I </math > 来估计。
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| − | An everyday example is the graininess that appears as photographs are enlarged; the graininess is due to Poisson fluctuations in the number of reduced [[silver]] grains, not to the individual grains themselves. By [[Correlation|correlating]] the graininess with the degree of enlargement, one can estimate the contribution of an individual grain (which is otherwise too small to be seen unaided).{{Citation needed|date=April 2012}} Many other molecular applications of Poisson noise have been developed, e.g., estimating the number density of [[receptor (biochemistry)|receptor]] molecules in a [[cell membrane]].
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| − | An everyday example is the graininess that appears as photographs are enlarged; the graininess is due to Poisson fluctuations in the number of reduced silver grains, not to the individual grains themselves. By correlating the graininess with the degree of enlargement, one can estimate the contribution of an individual grain (which is otherwise too small to be seen unaided). Many other molecular applications of Poisson noise have been developed, e.g., estimating the number density of receptor molecules in a cell membrane.
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| − | 一个日常的例子是放大照片时出现的颗粒状; 颗粒状是由于减少的银粒数量的泊松波动，而不是单个颗粒本身。通过将颗粒度与放大程度相关联，我们可以估算出单个颗粒的贡献(否则颗粒太小，无法单独看到)。泊松噪声的许多其他分子应用已经发展起来，例如，估计细胞膜上受体分子的数量密度。
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| − | : <math>
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| − | <math>
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| − | 《数学》
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| − | \Pr(N_t=k) = f(k;\lambda t) = \frac{(\lambda t)^k e^{-\lambda t}}{k!}.</math>
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| − | \Pr(N_t=k) = f(k;\lambda t) = \frac{(\lambda t)^k e^{-\lambda t}}{k!}.</math>
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| − | Pr (n _ t = k) = f (k; lambda t) = frac {((lambda t) ^ k e ^ {-lambda t }}{ k！} . </math >
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| − | In [[Causal Set]] theory the discrete elements of spacetime follow a Poisson distribution in the volume.
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| − | In Causal Set theory the discrete elements of spacetime follow a Poisson distribution in the volume.
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| − | 在''' 因果集合论Causal Set theory'''中，时空的离散元素在集合中遵循一个泊松分布。
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| − | --[[用户:fairywang|fairywang]]([[用户讨论:fairywang|讨论]]) 【审校】“泊松分布”改为“泊松分布”
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| | ==计算方法== | | ==计算方法== |