BACKGROUND When summary results from studies of counts of events in time contain zeros, the study-specific incidence rate ratio (IRR) and its standard error cannot be calculated because the log of zero is undefined. This poses problems for the widely used inverse-variance method that weights the study-specific IRRs to generate a pooled estimate. METHODS We conducted a simulation study to comp...

In this paper, a total variation (TV) minimization strategy is proposed to overcome the problem of sparse spatial resolution and large amounts of noise in low dose positron emission tomography (PET) imaging reconstruction. Two types of objective function were established based on two statistical models of measured PET data, least-square (LS) TV for the Gaussian distribution and Poisson-TV for t...

Quasi-Poisson and negative binomial regression models have equal numbers of parameters, and either could be used for overdispersed count data. While they often give similar results, there can be striking differences in estimating the effects of covariates. We explain when and why such differences occur. The variance of a quasi-Poisson model is a linear function of the mean while the variance of...

Average response properties of cortical sensory neurons such as firing rate and feature tuning are known to change with behavioral state. Here, we show anesthetic state also modifies the tuning of the variance of spiking responses in a fashion that is neither predicted by a Poisson model of spike count variance nor the neuron’s tuning curve. Neurons recorded in the visual motion-sensitive middl...

Neurons in many brain areas exhibit high trial-to-trial variability, with spike counts that are overdispersed relative to a Poisson distribution. Recent work (Goris, Movshon, & Simoncelli, 2014 ) has proposed to explain this variability in terms of a multiplicative interaction between a stochastic gain variable and a stimulus-dependent Poisson firing rate, which produces quadratic relationships...

A familiär relation links the densities that result for the intersection of a convex body and straight lines under uniform isotropic randomness with those that result under weighted randomness. An extension of this relation to the intersection of more general domains is utilized to obtain the variance of the n-dimensional measure of the intersection of two bodies under uniform isotropic randomn...

We consider a class of spherical processes rapidly converging to the boundary (so called Decentred Random Walks on Spheres or spherical processes with shifted centres) in comparison with the standard walk on spheres. The aim is to compare costs of the corresponding Monte Carlo estimates for the Poisson equation. Generally, these costs depend on the cost of simulation of one trajectory and on th...

We show that the random point measures induced by vertices in the convex hull of a Poisson sample on the unit ball, when properly scaled and centered, converge to those of a mean zero Gaussian field. We establish limiting variance and covariance asymptotics in terms of the density of the Poisson sample. Similar results hold for the point measures induced by the maximal points in a Poisson sampl...