PET measurements are usually precorrected for accidental coincidence events by real-time subtraction of the delayed window coincidences. Randoms subtraction compensates in mean for accidental coincidences but destroys the Poisson statistics. We propose and analyze two new approximations to the exact log-likelihood of the precorrected measurements, one based on a \shifted Poisson" model, the oth...

Positron emission tomography (PET) measurements are usually precorrected for accidental coincidence events by real-time subtraction of the delayed-window coincidences. Randoms subtraction compensates on average for accidental coincidences but destroys the Poisson statistics. We propose and analyze two new approximations to the exact log-likelihood of the precorrected measurements, one based on ...

PET measurements are usually precorrected for accidental coincidence events by real-time subtraction of the delayed window coincidences. Randoms subtraction compensates in mean for accidental coincidences but destroys the Poisson statistics. We propose and analyze two new approximations to the exact log-likelihood of the precorrected measurements, one based on a “shifted Poisson” model, the oth...

Count data are common in many fields and often modelled with the Poisson model. However, equidispersion assumption (variance = mean) related to model is violated practice. While much research has focused on modelling overdispersed count data, underdispersion received relatively little attention. Alternative models therefore needed handle overdispersion > < mean). This study assessed relat...

We present and discuss a variance-reduced stochastic particle method for simulating the relaxation-time model of the Boltzmann transport equation. The present paper focuses on the dilute gas case, although the method is expected to directly extend to all fields (carriers) for which the relaxation-time approximation is reasonable. The variance reduction, achieved by simulating only the deviation...

This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional variance, implying an interpretation as an integer valued GARCH process. In a nonlinear conditional Pois...

In this paper, we develop a new approximation for nonstationary multiserver queues with abandonment. Our method uses the Poisson–Charlier polynomials, which are a discrete orthogonal polynomial sequence that is orthogonal with respect to the Poisson distribution. We show that by appealing to the Poisson–Charlier polynomials that we can estimate the mean, variance, and probability of delay of ou...

We consider a point process i + ξi, where i ∈ Z and the ξi’s are i.i.d. random variables with variance σ. This process, with a suitable rescaling of the distribution of ξi’s, converges to the Poisson process in total variation for large σ. We then study a simple queueing system with our process as arrival process, and we provide a complete analytical description of the system. Although the arri...

Relative risk is usually the parameter of interest in epidemiologic and medical studies. In this paper, the author proposes a modified Poisson regression approach (i.e., Poisson regression with a robust error variance) to estimate this effect measure directly. A simple 2-by-2 table is used to justify the validity of this approach. Results from a limited simulation study indicate that this appro...

The paper deals with the limit behavior of a compound Poisson process switching between finite number sequences i.i.d. random variables. is provided by Bernoulli’s Under suitable normalization, Brownian motion variance.