Don't Count on Poisson: Flexible Alternatives for Modeling Count Data
While the Poisson distribution is a popular distribution for modeling count data, it is constrained by the "equi-dispersion assumption" (i.e. that the variance equals the mean). Real data oftentimes do not adhere to this restriction in that the data are found to be either over- or under-dispersed. The Conway-Maxwell-Poisson (COM-Poisson) distribution is a flexible, two-parameter alternative that not only generalizes the Poisson distribution, but also captures the Bernoulli and geometric distributions as special case distributions. Various works center around the development of related distributions and statistical methods that are motivated by the COM-Poisson distribution. This and related works have culminated into the book, The Conway-Maxwell-Poisson Distribution (Cambridge University Press).
Computing in R
Researchers can analyze their dispersed count data via various R packages available on the Comprehensive R Archive Network (CRAN). Several R packages have been developed to perform count data modeling via the Conway-Maxwell-Poisson (CMP) distribution, including regression analysis, count processes, bivariate modeling, and control chart theory.
Proteomic Data Analysis
Proteomic data analysis describes the collaborative study of protein change via differential expression and modification. Two-dimensional gel electrophoresis methods separate the proteins by pH and molecular weight to better study protein change on a large scale. Statistical methods provide scientists with the ability to quantitatively study these proteins and detect statistically significant protein change through two-dimensional polyacrylamide gel electroresis (2D-PAGE) and two-dimensional difference gel electrophoresis (2D-DIGE) images, where the proteins appear as spots in the images. The number and size of the images are a nice "Big Data" example.
