scholarly journals Poisson statistics of eigenvalues in the hierarchical Dyson model

2018 ◽  
Vol 63 (1) ◽  
pp. 117-144 ◽  
Author(s):  
Александр Давидович Бендиков ◽  
Alexander Davidovich Bendikov ◽  
Anton Braverman ◽  
Anton Braverman ◽  
John Pike ◽  
...  
Keyword(s):  
Poisson Statistics ◽  
Dyson Model

scholarly journals Poisson statistics of eigenvalues in the hierarchical Dyson model

2018 ◽  
Vol 63 (1) ◽  
pp. 94-116
Author(s):  
A. Bendikov ◽  
A. Braverman ◽  
J. Pike
Keyword(s):  
Poisson Statistics ◽  
Dyson Model

Bayesian Estimation of Stimulus Responses in Poisson Spike Trains

2004 ◽  
Vol 16 (7) ◽  
pp. 1325-1343 ◽  
Author(s):  
Sidney R. Lehky
Keyword(s):  
Bayesian Method ◽  
Significant Degree ◽  
Spike Trains ◽  
Neural Responses ◽  
Interval Estimates ◽  
Poisson Statistics ◽  
Likelihood Functions ◽  
Bayesian Estimates ◽  
Mean And Variance ◽  
The Mean

A Bayesian method is developed for estimating neural responses to stimuli, using likelihood functions incorporating the assumption that spike trains follow either pure Poisson statistics or Poisson statistics with a refractory period. The Bayesian and standard estimates of the mean and variance of responses are similar and asymptotically converge as the size of the data sample increases. However, the Bayesian estimate of the variance of the variance is much lower. This allows the Bayesian method to provide more precise interval estimates of responses. Sensitivity of the Bayesian method to the Poisson assumption was tested by conducting simulations perturbing the Poisson spike trains with noise. This did not affect Bayesian estimates of mean and variance to a significant degree, indicating that the Bayesian method is robust. The Bayesian estimates were less affected by the presence of noise than estimates provided by the standard method.

scholarly journals Integration of macromolecular diffraction data

1999 ◽  
Vol 55 (10) ◽  
pp. 1696-1702 ◽  
Author(s):  
A. G. W. Leslie
Keyword(s):  
Diffraction Data ◽  
Standard Error ◽  
Standard Errors ◽  
X Ray ◽  
Poisson Statistics ◽  
Profile Fitting ◽  
X Ray Background

Diffraction intensities can be evaluated by two distinct procedures: summation integration and profile fitting. Equations are derived for evaluating the intensities and their standard errors for both cases, based on Poisson statistics. These equations highlight the importance of the contribution of the X-ray background to the standard error and give an estimate of the improvement which can be achieved by profile fitting. Profile fitting offers additional advantages in allowing estimation of saturated reflections and in dealing with incompletely resolved diffraction spots.

Deconvolution of blurred images using photon counting statistics and maximum probability

1989 ◽  
Vol 67 (1) ◽  
pp. 89-94 ◽  
Author(s):  
N. D. Lloyd ◽  
E. J. Llewellyn
Keyword(s):  
Photon Counting ◽  
Final Solution ◽  
Maximum Probability ◽  
Poisson Statistics ◽  
True Answer ◽  
Counting Statistics ◽  
Blurred Images ◽  
Photon Counting Statistics ◽  
Good Agreement

A method for the deconvolution of blurred images that uses photon counting Poisson statistics to determine the most probable solution is described. The method ensures that the final solution is physically meaningful and consistent with the observations. The developed algorithm is tested with real blurred data, and the result is compared with other methods. These tests show that the algorithm produces stable results that are in good agreement with the true answer.

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