Extended Poisson process modelling and analysis of grouped binary data

Biom J. 2012 May;54(3):426-35. doi: 10.1002/bimj.201100214.

Abstract

A simple extension of the Poisson process results in binomially distributed counts of events in a time interval. A further extension generalises this to probability distributions under- or over-dispersed relative to the binomial distribution. Substantial levels of under-dispersion are possible with this modelling, but only modest levels of over-dispersion - up to Poisson-like variation. Although simple analytical expressions for the moments of these probability distributions are not available, approximate expressions for the mean and variance are derived, and used to re-parameterise the models. The modelling is applied in the analysis of two published data sets, one showing under-dispersion and the other over-dispersion. More appropriate assessment of the precision of estimated parameters and reliable model checking diagnostics follow from this more general modelling of these data sets.

MeSH terms

  • Animals
  • Bacillus / physiology
  • Data Interpretation, Statistical*
  • Litter Size
  • Mice
  • Models, Statistical*
  • Poisson Distribution*
  • Probability
  • Solanum tuberosum / microbiology
  • Spores, Bacterial / physiology