Research Areas & Select Publications

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• 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.
  
  Bridging the Gap: A Generalized Stochastic Process for Count Data
  Zhu et al. (2017)
  
  Bivariate Conway-Maxwell-Poisson distribution: Formulation, properties, and inference
  Sellers et al. (2016)
  
  A flexible zero-inflated model to address data dispersion
  Sellers and Raim (2016)
  
  Data Dispersion: Now You See It... Now You Don't
  Sellers and Shmueli (2013)
  
  The COM-Poisson model for count data: a survey of methods and applications (with discussion)
  Sellers et al. (2012) (with discussion)
  
  A Generalized Statistical Control Chart for Over- or Under-Dispersed Data
  Sellers (2012)

• 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.
  
  COMPoissonReg: Conway-Maxwell Poisson (COM-Poisson) Regression (Version 4.1)
  Sellers et al. (2017)
  
  cmpprocess: Flexible Modeling of Count Processes (Version 1.0)
  Zhu et al. (2017)
  
  multicmp: Flexible Modeling of Multivariate Count Data via the Multivariate Conway-Maxwell-Poisson Distribution (Version 1.0)
  Sellers et al. (2017)
  
  CMPControl: Control Charts for Conway-Maxwell-Poisson Distribution (Version 1.0)
  Sellers and Costa (2014)
• 

  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.
  
  Statistical Analysis of Gel Electrophoresis Data
  Sellers and Miecznikowski (2012)
  
  Multidimensional Median Filters for Finding Bumps in Chemical Sensor Datasets
  Miecznikowski, Sellers, and Eddy (2011)
  
  A comparison of imputation procedures and statistical tests for the analysis of two-dimensional electrophoresis data
  Miecznikowski et al. (2010)
  
  Feature Detection Techniques for Preprocessing Proteomic Data
  Sellers and Miecznikowski (2010)
  
  Lights, Camera, Action! Systematic variation in 2-D difference gel electrophoresis images
  Sellers et al. (2007)