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

Inertia Tensor01:24

Inertia Tensor

469
The concept of the inertia tensor is employed to depict the mass distribution and rotational inertia of a solid or rigid object. This tensor is expressed through a three-by-three matrix. Each component within this matrix corresponds to varying moments of inertia about specific axes.
The diagonal components of the inertia tensor matrix represent the moments of inertia concerning the principal axes of the object. These primary axes are defined as the axes where the object experiences the least...
469
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

13.9K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
13.9K
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

498
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...
498
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

1.5K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
1.5K
Scalar and Vector Triple Products01:06

Scalar and Vector Triple Products

2.4K
Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the resultant is a vector. These rules of the scalar or vector product between two vectors can be applied to multiple vectors to obtain meaningful combinations. The scalar triple product is the dot product of a vector with the cross product of two vectors.
The scalar triple product is the dot product of a vector with the cross product of two vectors....
2.4K
Cartesian Form for Vector Formulation01:26

Cartesian Form for Vector Formulation

641
The Cartesian form for vector formulation is a process to calculate  the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.
641

You might also read

Related Articles

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

Sort by
Same author

[Design and Application of 3D-Printed Individualized Pelvic Prostheses].

Zhongguo yi liao qi xie za zhi = Chinese journal of medical instrumentation·2026
Same author

Genomic reconstruction of upland cotton domestication uncovers staged selection, gene flow, and flowering-time adaptation.

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

RxMap: an LLM-assisted tool for medication normalization.

JAMIA open·2026
Same author

Rolling temperature affects green tea quality and non-volatile metabolites: Insights from integrated metabolomics and proteomics.

Food chemistry·2026
Same author

Multi-dimensional regulation of tea leaf development: morphogenesis, hormone-transcriptional networks, environmental factors, and artificial cultivation practices.

Frontiers in plant science·2026
Same author

Monocyte epigenetic age acceleration is linked to non-somatic depressive symptoms in women with and without HIV.

The journals of gerontology. Series A, Biological sciences and medical sciences·2026
Same journal

Improving Overall Risk Ranking via Subgroup-Level Information Borrowing in Survival Risk Stratification.

Statistics and its interface·2026
Same journal

High-dimensional Bayesian mediation analysis with adaptive Laplace priors.

Statistics and its interface·2026
Same journal

Imaging mediation analysis for longitudinal outcomes: a case study of childhood brain tumor survivorship.

Statistics and its interface·2025
Same journal

Variable selection for doubly robust causal inference.

Statistics and its interface·2025
Same journal

Smooth online parameter estimation for time varying VAR models with application to rat local field potential activity data.

Statistics and its interface·2025
Same journal

A Double Regression Method for Graphical Modeling of High-dimensional Nonlinear and Non-Gaussian Data.

Statistics and its interface·2025
See all related articles

Related Experiment Video

Updated: Jul 1, 2025

Author Spotlight: Analgesic Effect of Tuina on Rat Models with Compression of the Dorsal Root Ganglion Pain
05:49

Author Spotlight: Analgesic Effect of Tuina on Rat Models with Compression of the Dorsal Root Ganglion Pain

Published on: July 14, 2023

1.4K

Bayesian tensor-on-tensor regression with efficient computation.

Kunbo Wang1, Yanxun Xu1

  • 13400 N. Charles Street, Baltimore, MD 21218.

Statistics and Its Interface
|March 12, 2024
PubMed
Summary
This summary is machine-generated.

We introduce a Bayesian tensor-on-tensor regression method for predicting multidimensional arrays. This approach efficiently estimates both model dimensions and parameters, offering superior performance and uncertainty quantification for complex data.

Keywords:
Fractional Bayes FactorMarkov chain Monte CarloTensor-on-tensor regressionTucker decomposition

More Related Videos

Topographical Estimation of Visual Population Receptive Fields by fMRI
06:02

Topographical Estimation of Visual Population Receptive Fields by fMRI

Published on: February 3, 2015

9.3K
Image-based Lagrangian Particle Tracking in Bed-load Experiments
10:32

Image-based Lagrangian Particle Tracking in Bed-load Experiments

Published on: July 20, 2017

9.0K

Related Experiment Videos

Last Updated: Jul 1, 2025

Author Spotlight: Analgesic Effect of Tuina on Rat Models with Compression of the Dorsal Root Ganglion Pain
05:49

Author Spotlight: Analgesic Effect of Tuina on Rat Models with Compression of the Dorsal Root Ganglion Pain

Published on: July 14, 2023

1.4K
Topographical Estimation of Visual Population Receptive Fields by fMRI
06:02

Topographical Estimation of Visual Population Receptive Fields by fMRI

Published on: February 3, 2015

9.3K
Image-based Lagrangian Particle Tracking in Bed-load Experiments
10:32

Image-based Lagrangian Particle Tracking in Bed-load Experiments

Published on: July 20, 2017

9.0K

Area of Science:

  • Multivariate statistics
  • Machine learning
  • Data science

Background:

  • Tensor regression is crucial for analyzing multidimensional data.
  • Existing Tucker decomposition methods struggle to simultaneously estimate core tensor dimensions and parameters.
  • A need exists for robust methods addressing these limitations.

Purpose of the Study:

  • To propose a novel Bayesian tensor-on-tensor regression framework.
  • To develop methods for simultaneous estimation of model dimension and parameters.
  • To provide uncertainty quantification for tensor regression.

Main Methods:

  • Bayesian tensor-on-tensor regression utilizing Tucker decomposition.
  • Development of a Markov Chain Monte Carlo (MCMC) algorithm for posterior inference.
  • An optimization-based algorithm with simulated annealing for dimension optimization.

Main Results:

  • The proposed Bayesian framework enables joint estimation of model dimension and parameters.
  • Extensive simulations demonstrate superior performance over alternative methods.
  • The method shows practical effectiveness on facial imaging and 3D motion data.

Conclusions:

  • The developed Bayesian tensor-on-tensor regression offers a powerful tool for multidimensional data prediction.
  • The simultaneous estimation of dimensions and parameters addresses a key limitation in existing methods.
  • The approach provides reliable uncertainty quantification and practical applicability.