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

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

665
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
665
Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

124
Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
124
Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

139
Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any...
139
Estimation of the Physical Quantities01:05

Estimation of the Physical Quantities

5.0K
On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
5.0K
Phase-lead and Phase-lag Controllers01:22

Phase-lead and Phase-lag Controllers

212
Understanding the working function of different types of controllers can be illustrated with practical analogies, such as adjusting a stereo's volume equalizer. Cranking up the bass involves a phase-lead controller, which functions as a high-pass filter, while increasing the treble uses a phase-lag controller, which acts as a low-pass filter. PD controllers, similar to high-pass filters, enhance the system's response to high-frequency components. PI controllers, akin to low-pass...
212
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

98
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...
98

You might also read

Related Articles

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

Sort by
Same authorSame journal

Correction to: A uniformisation-driven algorithm for inference-related estimation of a phase-type ageing model.

Lifetime data analysis·2026
Same author

A computing platform for pairs-trading online implementation via a blended Kalman-HMM filtering approach.

Journal of big data·2020
See all related articles

Related Experiment Video

Updated: Aug 27, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

10.7K

A uniformisation-driven algorithm for inference-related estimation of a phase-type ageing model.

Boquan Cheng1, Rogemar Mamon2,3

  • 1Department of Statistical and Actuarial Sciences, The University of Western Ontario, 1151 Richmond Street, London, Ontario, N6A 5B7, Canada.

Lifetime Data Analysis
|October 2, 2022
PubMed
Summary
This summary is machine-generated.

We developed an efficient algorithm for calculating phase-type ageing model likelihood. This new method is faster and more accurate than traditional approaches, offering improved numerical stability and reliability.

Keywords:
Coxian modelMatrix exponentialMaximum likelihoodRate of algorithm’s successUniformisation method

More Related Videos

Author Spotlight: Unveiling Prognostic Indicators in Heart Failure - The Role of Phase Angle and Bioelectrical Impedance Analysis
04:05

Author Spotlight: Unveiling Prognostic Indicators in Heart Failure - The Role of Phase Angle and Bioelectrical Impedance Analysis

Published on: June 30, 2023

2.1K
Cutoff Value of Phase Angle by Bioelectrical Impedance Analysis at Admission as a Prognostic Factor in Patients with Acute Heart Failure
05:16

Cutoff Value of Phase Angle by Bioelectrical Impedance Analysis at Admission as a Prognostic Factor in Patients with Acute Heart Failure

Published on: June 10, 2025

197

Related Experiment Videos

Last Updated: Aug 27, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

10.7K
Author Spotlight: Unveiling Prognostic Indicators in Heart Failure - The Role of Phase Angle and Bioelectrical Impedance Analysis
04:05

Author Spotlight: Unveiling Prognostic Indicators in Heart Failure - The Role of Phase Angle and Bioelectrical Impedance Analysis

Published on: June 30, 2023

2.1K
Cutoff Value of Phase Angle by Bioelectrical Impedance Analysis at Admission as a Prognostic Factor in Patients with Acute Heart Failure
05:16

Cutoff Value of Phase Angle by Bioelectrical Impedance Analysis at Admission as a Prognostic Factor in Patients with Acute Heart Failure

Published on: June 10, 2025

197

Area of Science:

  • Probability theory
  • Computational statistics
  • Reliability engineering

Background:

  • Phase-type ageing models are crucial in reliability and survival analysis.
  • Calculating the likelihood for these models can be computationally intensive and numerically unstable.
  • Existing methods often rely on matrix exponentiation, which can be slow and prone to errors.

Purpose of the Study:

  • To develop an efficient and numerically stable algorithm for computing the likelihood of phase-type ageing models.
  • To compare the performance of the proposed algorithm against traditional methods.
  • To provide guidance on optimizing the likelihood estimation process.

Main Methods:

  • Development of a novel algorithm utilizing the uniformisation method for numerical stability.
  • Implementation of a vectorised formula to compute only essential probability distribution elements.
  • Comparative analysis of speed and accuracy against the matrix exponential method.

Main Results:

  • The proposed algorithm demonstrates superior speed and accuracy compared to the matrix exponential method.
  • The algorithm incorporates an adjustable upper bound for errors, enhancing reliability.
  • It can be readily adapted for likelihood calculations in Coxian models.

Conclusions:

  • The new algorithm offers a significant improvement for phase-type and Coxian model likelihood computation.
  • The uniformisation and vectorisation techniques enhance efficiency and numerical stability.
  • Using 20 random initial values for optimization is recommended for reliable maximum likelihood estimates.