Category Archives: Disease

Limitations of the negative binomial distribution in spatial models

Galaxies, trees, and influenza cases have something in common: they tend to occur in clusters. The issue of how to model clustered spatial patterns is thus of interest to a variety of scientific disciplines. For many people, the mention of spatial clumping brings to mind the negative binomial distribution. This is appropriate, because the negative binomial distribution is overdispersed, meaning its variance is greater than its mean (in contrast to the Poisson distribution, which has equal variance and mean). Unfortunately, there are some difficulties in using the negative binomial distribution in spatial modeling, which we attempt to explain in this post.

Suppose that you want to create a model that generates spatial locations of trees. You want the model to be stochastic, so that each time you generate a forest, you end up with a different configuration of trees. The relevant tool is a spatial point process; mathematical details are described in books such as Daley and Veres-Jones. Each forest that you generate is called a realization of the process.

Continue reading “Limitations of the negative binomial distribution in spatial models” »

Six little data points and one huge story

It has been an exciting summer in science news. In early July, CERN announced the probable discovery of a Higgs-like particle at the Large Hadron Collider, filling a long open hole in the standard model of physics. On Sunday, the Curiosity rover successfully executed a phenomenally difficult landing on Mars.

Sandwiched between these headline-grabbing events, a story of arguably equal significance has been overshadowed: evidence from the remote Amazon that unvaccinated humans can develop antibodies to rabies.

Rabies is a scary disease (jokes on The Office notwithstanding). It causes approximately 55,000 deaths annually. Victims suffer anxiety, hallucinations, delirium, paralysis and eventually death. It is hard to imagine a more horrific way to die.

Continue reading “Six little data points and one huge story” »