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

Dimensional Analysis01:23

Dimensional Analysis

2.5K
Dimensional analysis is a powerful tool that is used in physics and engineering to understand and predict the behavior of physical systems. The basic idea behind dimensional analysis is to express physical quantities in terms of fundamental dimensions such as the mass, length, and time. Derived dimensions like the velocity, acceleration, and force are derived from the combinations of these fundamental dimensions.
Dimensional analysis allows us to analyze and compare physical quantities on a...
2.5K
Dimensional Analysis03:40

Dimensional Analysis

68.5K
Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
Conversion Factors and Dimensional Analysis
The unit...
68.5K
Dimensional Analysis01:27

Dimensional Analysis

827
Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.
In fluid mechanics, dimensional...
827
Dimensional Analysis02:19

Dimensional Analysis

26.8K
The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
26.8K
Problem Solving: Dimensional Analysis01:08

Problem Solving: Dimensional Analysis

7.7K
Every mathematical equation that connects separate distinct physical quantities must be dimensionally consistent, which implies it must abide by two rules. For this reason, the concept of dimension is crucial. The first rule is that an equation's expressions on either side of an equality must have the exact same dimension, i.e., quantities of the same dimension can be added or removed. The second rule stipulates that all popular mathematical functions, such as exponential, logarithmic, and...
7.7K
Cartesian Vector Notation01:28

Cartesian Vector Notation

1.9K
Cartesian vector notation is a valuable tool in mechanical engineering for representing vectors in three-dimensional space, performing vector operations such as determining the gradient, divergence, and curl, and expressing physical quantities such as the displacement, velocity, acceleration, and force. By using Cartesian vector notation, engineers can more easily analyze and solve problems in various areas of mechanical engineering, including dynamics, kinematics, and fluid mechanics. This...
1.9K

You might also read

Related Articles

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

Sort by
Same author

Estimating Finite Mixtures of Ordinal Graphical Models.

Psychometrika·2021
Same author

Noncontact Synergistic Effect between Au Nanoparticles and the Fe<sub>2</sub>O<sub>3</sub> Spindle Inside a Mesoporous Silica Shell as Studied by the Fenton-like Reaction.

Langmuir : the ACS journal of surfaces and colloids·2016
Same author

An elaborate landscape of the human antibody repertoire against enterovirus 71 infection is revealed by phage display screening and deep sequencing.

mAbs·2016
Same author

The role of size of input box, location of input box, input method and display size in Chinese handwriting performance and preference on mobile devices.

Applied ergonomics·2016
Same author

Apelin/APJ System: A Novel Therapeutic Target for Myocardial Ischemia/Reperfusion Injury.

DNA and cell biology·2016
Same author

A New Soft Computing Method for K-Harmonic Means Clustering.

PloS one·2016

Related Experiment Video

Updated: Apr 16, 2026

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

3.1K

A Bayesian Vector Multidimensional Scaling Procedure Incorporating Dimension Reparameterization with Variable

Duncan K H Fong1, Wayne S DeSarbo2, Zhe Chen3

  • 1Department of Marketing, Pennsylvania State University, University Park, PA, 16802, USA. i2v@psu.edu.

Psychometrika
|March 4, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a novel Bayesian spatial procedure for determining data dimensions and identifying key variables. The new method offers improved interpretability and performance over existing models, as shown in simulations and a vehicle rating analysis.

Keywords:
QR decompositionbayesian analysisconsumer psychologymultidimensional scalingreparameterizationvariable selectionvector model

More Related Videos

Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.5K
Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
03:14

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness

Published on: December 6, 2024

1.3K

Related Experiment Videos

Last Updated: Apr 16, 2026

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

3.1K
Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.5K
Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
03:14

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness

Published on: December 6, 2024

1.3K

Area of Science:

  • Multivariate statistics
  • Bayesian inference
  • Dimensionality reduction

Background:

  • Traditional spatial models face challenges in determining dimensionality and identifying influential covariates.
  • Existing methods may lack interpretability and robust variable selection capabilities.

Purpose of the Study:

  • To develop a two-way Bayesian vector spatial procedure with variable selection.
  • To address identifiability issues in Bayesian spatial models.
  • To enhance the interpretability of derived dimensions in joint space maps.

Main Methods:

  • A novel two-way Bayesian vector spatial procedure incorporating dimension reparameterization.
  • Variable selection option for identifying significant covariates.
  • Simulation studies to compare performance against benchmark models.
  • Empirical application using consumer ratings of sport utility vehicles.

Main Results:

  • The proposed model effectively determines dimensionality and identifies significant covariates.
  • The Bayesian approach successfully resolves identifiability problems.
  • Simulation results demonstrate superior performance compared to a popular benchmark model.
  • The empirical application yields interpretable and managerially insightful results.

Conclusions:

  • The proposed Bayesian spatial procedure with variable selection provides a robust framework for dimensionality determination and covariate interpretation.
  • The method offers significant advantages in interpretability and performance over existing approaches.
  • This methodology is valuable for analyzing complex datasets and deriving actionable insights.