Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

65
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
65
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

84
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
84
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

99
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
99
Poisson Probability Distribution01:09

Poisson Probability Distribution

8.3K
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
8.3K
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

3.1K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
3.1K
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

488
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
488

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Rectangular multivariate normal prediction regions for setting reference regions in laboratory medicine.

Journal of biopharmaceutical statistics·2022
Same author

A mixture model with Poisson and zero-truncated Poisson components to analyze road traffic accidents in Turkey.

Journal of applied statistics·2022
Same author

Nonparametric hyperrectangular tolerance and prediction regions for setting multivariate reference regions in laboratory medicine.

Statistical methods in medical research·2020
Same author

Improving coverage probabilities for parametric tolerance intervals via bootstrap calibration.

Statistics in medicine·2020
Same author

Integrin subtype-dependent CD18 cleavage under shear and its influence on leukocyte-platelet binding.

Journal of leukocyte biology·2012
Same author

Two-dimensional kinetics of beta 2-integrin and ICAM-1 bindings between neutrophils and melanoma cells in a shear flow.

American journal of physiology. Cell physiology·2008

Related Experiment Video

Updated: Jul 25, 2025

Assembly and Characterization of Polyelectrolyte Complex Micelles
08:44

Assembly and Characterization of Polyelectrolyte Complex Micelles

Published on: March 2, 2020

10.8K

Finite mixtures of mean-parameterized Conway-Maxwell-Poisson models.

Dongying Zhan1, Derek S Young1

  • 1Dr. Bing Zhang Department of Statistics, University of Kentucky, 725 Rose Street, Lexington, KY 40536-0082 USA.

Statistical Papers (Berlin, Germany)
|June 26, 2023
PubMed
Summary
This summary is machine-generated.

We introduce a flexible finite mixture model using mean-parameterized Conway-Maxwell-Poisson (CMP) distributions to analyze count data with varying dispersion across subpopulations. This approach offers improved modeling compared to standard Poisson or negative binomial mixtures.

Keywords:
BootstrappingCount dataData dispersionEM algorithmNegative binomial

More Related Videos

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.4K
Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures
10:56

Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures

Published on: May 20, 2014

12.2K

Related Experiment Videos

Last Updated: Jul 25, 2025

Assembly and Characterization of Polyelectrolyte Complex Micelles
08:44

Assembly and Characterization of Polyelectrolyte Complex Micelles

Published on: March 2, 2020

10.8K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.4K
Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures
10:56

Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures

Published on: May 20, 2014

12.2K

Area of Science:

  • Statistics
  • Biostatistics
  • Computational Statistics

Background:

  • The Conway-Maxwell-Poisson (CMP) distribution generalizes the Poisson distribution for over- or under-dispersed count data.
  • Classic CMP parameterization does not directly model the mean, necessitating mean-parameterized versions.
  • Analyzing count data with subpopulations exhibiting heterogeneous dispersion requires advanced statistical models.

Purpose of the Study:

  • To propose a finite mixture of mean-parameterized CMP distributions for modeling complex count data.
  • To develop an EM algorithm for maximum likelihood estimation and use bootstrapping for standard errors.
  • To evaluate the proposed model's flexibility against existing mixture models using simulations and real-world data.

Main Methods:

  • Finite mixture modeling using mean-parameterized Conway-Maxwell-Poisson distributions.
  • Expectation-Maximization (EM) algorithm for parameter estimation.
  • Bootstrapping for standard error estimation.
  • Simulation studies and analysis of dog mortality data.

Main Results:

  • The proposed mixture model demonstrates flexibility in handling count data with varying dispersion across subpopulations.
  • Simulation studies show superior performance compared to mixtures of Poissons and negative binomials.
  • The model is successfully applied to analyze dog mortality data.

Conclusions:

  • The finite mixture of mean-parameterized CMP distributions provides a powerful tool for analyzing complex count data.
  • This approach effectively captures heterogeneity in dispersion across different subpopulations.
  • The model offers a valuable alternative to traditional mixture models for count data analysis.