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

Truncation in Survival Analysis01:09

Truncation in Survival Analysis

705
Truncation in survival analysis refers to the exclusion of individuals or events from the dataset based on specific criteria related to the time of the event. This exclusion can happen in two primary forms: left truncation and right truncation.
Left truncation occurs when individuals who experienced the event of interest before a certain time are not included in the study. This is often due to a "delayed entry" into the study where only those who survive until a certain entry point are...
705
Modeling with Differential Equations01:25

Modeling with Differential Equations

227
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
227
Applications of Life Tables01:22

Applications of Life Tables

416
Life tables are versatile across various fields, providing a quantitative basis for analyzing mortality and survival rates. Whether used by demographers, actuaries, epidemiologists, or sociologists, life tables offer valuable insights into the dynamics of life and death, facilitating informed decisions in public health, insurance, conservation, and beyond. Their broad applicability highlights the interconnectedness of demographic data with practical outcomes in everyday life and strategic...
416
Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

427
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
427
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

1.3K
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...
1.3K
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

4.6K
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.
4.6K

You might also read

Related Articles

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

Sort by
Same author

mGEM: multigraph estimation models for pattern analysis.

BMC bioinformatics·2026
Same author

An approximate-copula distribution for statistical modeling.

PLoS computational biology·2026
Same author

Generalizations of the quadratic bound optimization principle.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Closest Farthest Widest.

Algorithms·2025
Same author

A Cornucopia of Maximum Likelihood Algorithms.

The American statistician·2025
Same author

Bootstrap estimation of the proportion of outliers in robust regression.

Statistics and computing·2025
Same journal

Bandwidth of gamma-distribution-shaped functions via Lambert W function.

Statistics & probability letters·2026
Same journal

Directional replicability: When can the factor of two be omitted.

Statistics & probability letters·2026
Same journal

Approximating win-loss probabilities based on the overall and event-free survival functions.

Statistics & probability letters·2025
Same journal

On exact Bayesian credible sets for discrete parameters.

Statistics & probability letters·2025
Same journal

On critical points of Gaussian random fields under diffeomorphic transformations.

Statistics & probability letters·2024
Same journal

Universally Consistent K-Sample Tests via Dependence Measures.

Statistics & probability letters·2024
See all related articles

Related Experiment Video

Updated: Mar 29, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

9.0K

Coupling bounds for approximating birth-death processes by truncation.

Forrest W Crawford1, Timothy C Stutz2, Kenneth Lange3

  • 1Departments of Biostatistics and Ecology & Evolutionary Biology, Yale University, 60 College St, PO Box 208034 New Haven, CT 06510 USA, phone: (203) 785-6125.

Statistics & Probability Letters
|December 2, 2015
PubMed
Summary
This summary is machine-generated.

This study analyzes birth-death processes, which are Markov counting processes. We establish bounds for the accuracy of finite approximations used in computing their moments.

More Related Videos

Measurement of Survival Time in Brachionus Rotifers: Synchronization of Maternal Conditions
05:18

Measurement of Survival Time in Brachionus Rotifers: Synchronization of Maternal Conditions

Published on: July 22, 2016

9.0K
Establishing a Competing Risk Regression Nomogram Model for Survival Data
04:57

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

11.0K

Related Experiment Videos

Last Updated: Mar 29, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

9.0K
Measurement of Survival Time in Brachionus Rotifers: Synchronization of Maternal Conditions
05:18

Measurement of Survival Time in Brachionus Rotifers: Synchronization of Maternal Conditions

Published on: July 22, 2016

9.0K
Establishing a Competing Risk Regression Nomogram Model for Survival Data
04:57

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

11.0K

Area of Science:

  • Stochastic processes
  • Applied mathematics
  • Computational biology

Background:

  • Birth-death processes are fundamental continuous-time Markov counting processes.
  • Approximating moments of these processes often involves truncating the transition rate matrix.
  • Assessing the accuracy of such finite approximations is crucial for reliable analysis.

Purpose of the Study:

  • To derive rigorous bounds for the error introduced by finite approximations of birth-death processes.
  • To quantify the total variation distance between the true process and its truncated approximation.
  • To provide a theoretical foundation for the use of truncated matrices in moment computations.

Main Methods:

  • Utilizing a coupling argument to compare the continuous-time process with its finite approximation.
  • Developing mathematical inequalities to bound the total variation distance.
  • Analyzing the properties of continuous-time Markov chains.

Main Results:

  • Established bounds for the total variation distance between birth-death processes and their finite approximations.
  • Demonstrated the effectiveness of coupling arguments in error analysis for stochastic processes.
  • Provided a quantitative measure of approximation accuracy.

Conclusions:

  • The derived bounds offer a theoretical guarantee for the accuracy of moment computations using truncated matrices.
  • Coupling methods are a powerful tool for analyzing approximations in continuous-time Markov processes.
  • This work contributes to the reliable application of mathematical models in fields utilizing birth-death processes.