From the binomial to the Poisson distribution.
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Abstract In the mid-1970s, Ivan Lefkovits and co-workers introduced limiting dilution analysis of T and B cells as a method to quantify antigen-specific T and B cells. In this study, I describe how my co-operation with Ivan on the subject led not only to heated discussions on the validity of the approach but also to the identification of interleukin-2 as T-cell-derived factor, capable of replacing T-cell help required for the activation of B cells.
A procedure is proposed to compare single-unit spiking activity elicited in repetitive cycles with an inhomogeneous Poisson process (IPP). Each spike sequence in a cycle is discretized and represented as a point process on a circle. The interspike interval probability density predicted for an IPP is computed on the basis of the experimental firing probability density; differences from the experimental interval distribution are assessed. This procedure was applied to spike trains which were repetitively induced by opening-closing movements of the distal article of a lobster leg. As expected, the density of short interspike intervals, less than 20-40 ms in length, was found to lie greatly below the level predicted for an IPP, reflecting the occurrence of the refractory period. Conversely, longer intervals, ranging from 20-40 to 100-120 ms, were markedly more abundant than expected; this provided evidence for a time window of increased tendency to fire again after a spike. Less consistently, a weak depression of spike generation was observed for longer intervals. A Monte Carlo procedure, implemented for comparison, produced quite similar results, but was slightly less precise and more demanding as concerns computation time.
Geographic disease surveillance methods identify regions that have higher disease rates than expected. These approaches are generally applied to incident or prevalent cases of disease. In some contexts, disease-related events rather than individuals are the appropriate units of analysis for geographic surveillance. We propose a compound Poisson approach that detects event clusters by testing individual areas that may be combined with their nearest neighbors. The method is applicable to situations where the population sizes are diverse and the population distribution by important strata may differ by area. For example, a geographical region might have sparse population in the northern areas, and other areas which are predominantly retirement communities. The approach requires a coarse geographical relationship and administrative data for the numbers of population, cases, and events in each area. Pediatric self-inflicted injuries requiring presentation to Alberta emergency departments provide an illustration.
An empirical Bayes method is proposed for predicting the future performance of certain subgroups of a compound Poisson population.
Data on the distribution of dicentrics and acentrics observed when human lymphocytes are cultured for 48 h after irradiation by X-rays, gamma-rays, and neutrons are presented. Analysis shows that for dicentrics, the observed distribution for X-rays, gamma-rays, and fission neutrons may be described by Poisson statistics but for higher energy neutrons overdispersion is observed. The phenomenon of overdispersion is also observed for acentrics irrespective of the radiation used. The possibility that overdispersion results from the variations of dose in sensitive sites leads to the conclusion that for dicentrics the site size is considerably larger than the 1--2 micrometer diameter derived by applying the dual action theory to the dose effect relationships. This larger site may well be the cell nucleus.
Assessments of the penetrating potential of human spermatozoa were carried out using the zona-free hamster oocyte penetration test on 4 groups of subjects exhibiting normal fertility, idiopathic asthenozoospermia(less than 40% motility), asthenozoospermia associated with varicocele and oligoaesthenozoospermia (less than 20 X 10(6) spermatozoa/ml and less than 40% motility). When the Poisson model was used to correct the results of the in-vitro penetration experiments for differences in motile sperm concentration, significant differences were apparent between the normal fertile controls and all 3 categories of asthenozoospermic patient. Furthermore, the penetrating ability of the motile spermatozoa from patients presenting with a varicocele or oligoaesthenozoospermia was significantly less than that for the group in which asthenozoospermia was the only detectable defect. These results emphasize the practical significance of the Poisson model in the analysis of male fertility and demonstrate that the asthenozoospermic condition is associated with a significant reduction in the fertilizing potential of the motile spermatozoa.
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