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 Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

164
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...
164
Quadratic Models01:23

Quadratic Models

55
Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
55
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

889
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...
889
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

176
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
176
Determination of Multiple Dosing Parameters: Steady-State, Minimum and Maximum Concentrations01:15

Determination of Multiple Dosing Parameters: Steady-State, Minimum and Maximum Concentrations

80
Gentamicin, an aminoglycoside antibiotic, is commonly administered via intermittent intravenous infusion to treat severe infections. An intermittent one-hour infusion of gentamicin, administered at eight-hour intervals, allows for precise control of plasma drug concentrations, minimizing toxicity while ensuring therapeutic efficacy. Pharmacokinetic principles govern the dynamics of plasma concentrations and can be mathematically described using specific equations.The plasma drug concentration...
80
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

159
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...
159

You might also read

Related Articles

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

Sort by
Same author

ebnm: An R Package for Solving the Empirical Bayes Normal Means Problem Using a Variety of Prior Families.

Journal of statistical software·2026
Same authorSame journal

Empirical Bayes Covariance Decomposition, and a Solution to the Multiple Tuning Problem in Sparse PCA.

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·2026
Same author

Non-negative matrix factorization algorithms generally improve topic model fits.

Statistics and computing·2026
Same author

Generation of aptamers for the selective detection and neutralization of soluble lymphotoxin alpha.

Molecular therapy. Nucleic acids·2026
Same author

Differential disease tolerance mediates sex-biased illness severity in sepsis.

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

Integrating multi-omics and multi-context QTL data with GWAS reveals the genetic architecture of complex traits and improves the discovery of risk genes.

medRxiv : the preprint server for health sciences·2026
Same journal

Probabilistic Joint and Individual Variation Explained (ProJIVE) for Data Integration.

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·2026
Same journal

fastkqr: A Fast Algorithm for Kernel Quantile Regression.

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·2026
Same journal

Joint Registration and Conformal Prediction for Partially Observed Functional Data.

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·2026
Same journal

Efficient Decision Trees for Tensor Regressions.

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·2026
Same journal

Distributed Nonparametric Regression with Heterogeneity Through Prediction-Based Aggregation.

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·2026
See all related articles

Related Experiment Video

Updated: Nov 11, 2025

A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM
13:54

A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM

Published on: August 18, 2023

5.3K

A Fast Algorithm for Maximum Likelihood Estimation of Mixture Proportions Using Sequential Quadratic Programming.

Youngseok Kim1, Peter Carbonetto1, Matthew Stephens1

  • 1Department of Statistics, Department of Human Genetics and the Research Computing Center at the University of Chicago, and Mathematics and Computer Science Division at Argonne National Laboratory.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|March 25, 2021
PubMed
Summary
This summary is machine-generated.

A new sequential quadratic programming (SQP) method significantly speeds up maximum likelihood estimation of mixture proportions, offering a faster and equally accurate alternative to existing convex optimization techniques for statistical modeling.

Keywords:
active set methodsconvex optimizationmixture modelsnonparametric empirical Bayesnonparametric maximum likelihoodrank-revealing QR decompositionsequential quadratic programming

More Related Videos

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.7K
Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.5K

Related Experiment Videos

Last Updated: Nov 11, 2025

A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM
13:54

A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM

Published on: August 18, 2023

5.3K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.7K
Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.5K

Area of Science:

  • Statistics
  • Computational Statistics
  • Optimization

Background:

  • Maximum likelihood estimation of mixture proportions is crucial for statistical modeling.
  • Traditional methods like the expectation-maximization (EM) algorithm have limitations.
  • Convex optimization, specifically interior point methods, offer improvements over EM.

Purpose of the Study:

  • To develop a novel and more efficient algorithm for maximum likelihood estimation of mixture proportions.
  • To leverage sequential quadratic programming (SQP) for enhanced computational performance.

Main Methods:

  • A new solution based on sequential quadratic programming (SQP) is developed.
  • The approach reformulates the problem and utilizes an active set method for efficiency.
  • Low-rank approximations are employed for faster gradient and Hessian computations.

Main Results:

  • The SQP method demonstrates substantial speed improvements over interior point methods.
  • Accuracy is maintained, comparable to existing state-of-the-art solvers.
  • For large datasets, a 100-fold reduction in runtime was achieved compared to interior point solvers.

Conclusions:

  • The proposed SQP approach offers a significantly faster and accurate solution for mixture proportion estimation.
  • This method provides a powerful new tool for statistical analysis, particularly for large-scale problems.
  • Implementations are available in Julia and an R package (mixsqp).