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 Experiment Videos

Applying the saddlepoint approximation to bivariate stochastic processes.

E Renshaw1

  • 1Department of Statistics and Modelling Science, University of Strathclyde, Glasgow, UK. eric@stams.strath.ac.uk

Mathematical Biosciences
|December 21, 2000
PubMed
Summary

This study extends the truncated saddlepoint procedure to multivariate scenarios for stochastic population dynamics. The method provides an algebraic probability density function without distributional assumptions, overcoming limitations of normal approximations.

Related Concept Videos

You might also read

Related Articles

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

Sort by
Same author

Spatio-temporal stochastic modelling of Clostridium difficile.

The Journal of hospital infection·2008
Same author

Stochastic modelling of environmental variation for biological populations.

Theoretical population biology·2000
Same author

Stochastic effects in a model of nematode infection in ruminants.

IMA journal of mathematics applied in medicine and biology·1998
Same author

Chaos in biometry.

IMA journal of mathematics applied in medicine and biology·1994
Same author

Tracer studies to locate the site of platinum ions within filamentous and inhibited cells of Escherichia coli.

Journal of bacteriology·1967
Same author

Platinum-induced filamentous growth in Escherichia coli.

Journal of bacteriology·1967

Area of Science:

  • Stochastic processes
  • Population dynamics
  • Statistical inference

Background:

  • Moment closure is crucial for multitype stochastic population dynamics.
  • Standard normal approximations require replacing higher-order moments with zero, which is often too restrictive.
  • Existing methods lack flexibility in handling unknown cumulant structures.

Purpose of the Study:

  • To extend the univariate truncated saddlepoint procedure to multivariate settings.
  • To develop a method for approximating probability density functions (p.d.f.) in complex population dynamics.
  • To overcome limitations of existing moment closure techniques.

Main Methods:

  • Extension of the univariate truncated saddlepoint procedure to multivariate cases.
  • Development of an algorithm for algebraic p.d.f. computation.

Related Experiment Videos

  • Analysis of a challenging test case to determine operational limits.

    • Main Results:

    • The proposed method requires no distributional assumptions.
    • It provides an algebraic form for the p.d.f. regardless of cumulant knowledge.
    • The algorithm generally converges rapidly to the target p.d.f.

    Conclusions:

    • The multivariate truncated saddlepoint procedure offers a flexible alternative to normal approximations in stochastic population dynamics.
    • This approach is valuable when dealing with unknown or incomplete cumulant information.
    • The method demonstrates practical utility, though its operational limits require further investigation.