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

Divergence and Curl01:15

Divergence and Curl

3.2K
The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as the volume tends to zero. More practically, divergence measures how much a vector field spreads out or diverges from a given point. For an outgoing flux, conventionally, the divergence is positive. The diverging point is often called the "source" of the field. Meanwhile, the negative divergence of a vector field at a point means that the vector...
3.2K
Introduction to Nonparametric Statistics01:28

Introduction to Nonparametric Statistics

1.4K
Nonparametric statistics offer a powerful alternative to traditional parametric methods, useful when assumptions about the population distribution cannot be made. Unlike parametric tests, which require data to follow a specific distribution with well-defined parameters (such as the mean and standard deviation), nonparametric tests do not require such constraints. This makes them particularly valuable when dealing with small sample sizes, skewed data, or ordinal and categorical variables.
One of...
1.4K
Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

3.7K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
3.7K
Gene Duplication and Divergence02:37

Gene Duplication and Divergence

8.0K
The seminal work of Ohno in 1970 popularized the idea of gene duplication and divergence. DNA sequence comparison studies reveal that a large portion of the genes in bacteria, archaebacteria, and eukaryotes was  generated by gene duplication and divergence, indicating its critical role in evolution.
The duplicated copies of the gene are called Paralogs. Paralogs with similar sequences and functions form a gene family. Across several species, a large number of gene families are...
8.0K
Divergence and Curl of Electric Field01:25

Divergence and Curl of Electric Field

7.2K
The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
7.2K
Divergence and Curl of Magnetic Field01:26

Divergence and Curl of Magnetic Field

4.0K
The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
4.0K

You might also read

Related Articles

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

Sort by
Same author

Effects of <i>Lactobacillus plantarum</i> P9 Probiotics on Defecation and Quality of Life of Individuals with Chronic Constipation: Protocol for a Randomized, Double-Blind, Placebo-Controlled Clinical Trial.

Evidence-based complementary and alternative medicine : eCAM·2022
Same author

Super-taxon in human microbiome are identified to be associated with colorectal cancer.

BMC bioinformatics·2022
Same author

Pre-IVF treatment with a GnRH antagonist in women with endometriosis (PREGNANT): study protocol for a prospective, double-blind, placebo-controlled trial.

BMJ open·2022
Same author

Comparative genomic analysis revealed genetic divergence between Bifidobacterium catenulatum subspecies present in infant versus adult guts.

BMC microbiology·2022
Same author

Probiotics synergized with conventional regimen in managing Parkinson's disease.

NPJ Parkinson's disease·2022
Same author

Protocol of a randomized, double-blind, placebo-controlled study of the effect of probiotics on the gut microbiome of patients with gastro-oesophageal reflux disease treated with rabeprazole.

BMC gastroenterology·2022
Same journal

Towards a Unified Theory for Semiparametric Data Fusion with Individual-Level Data.

Annals of statistics·2026
Same journal

One-Step Estimation of Differentiable Hilbert-Valued Parameters.

Annals of statistics·2026
Same journal

GENERALIZATION ERROR BOUNDS OF DYNAMIC TREATMENT REGIMES IN PENALIZED REGRESSION-BASED LEARNING.

Annals of statistics·2026
Same journal

EFFICIENT AND MULTIPLY ROBUST RISK ESTIMATION UNDER GENERAL FORMS OF DATASET SHIFT.

Annals of statistics·2026
Same journal

TESTING HIGH-DIMENSIONAL REGRESSION COEFFICIENTS IN LINEAR MODELS.

Annals of statistics·2026
Same journal

COUNTERFACTUAL INFERENCE IN SEQUENTIAL EXPERIMENTS.

Annals of statistics·2026
See all related articles

Related Experiment Video

Updated: Feb 3, 2026

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task
05:04

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task

Published on: September 21, 2017

6.4K

BALL DIVERGENCE: NONPARAMETRIC TWO SAMPLE TEST.

Wenliang Pan1, Yuan Tian1, Xueqin Wang1

  • 1Sun Yat-sen University.

Annals of Statistics
|October 23, 2018
PubMed
Summary
This summary is machine-generated.

We introduce Ball Divergence, a new statistical measure for comparing probability distributions. This novel method offers a robust, consistent, and powerful two-sample test applicable to imbalanced datasets.

Keywords:
Ball divergenceFinite dimensional Banach spaceMetric rankPermutation procedure

More Related Videos

Presynapse Formation Assay Using Presynapse Organizer Beads and &ldquo;Neuron Ball&rdquo; Culture
10:17

Presynapse Formation Assay Using Presynapse Organizer Beads and “Neuron Ball” Culture

Published on: August 2, 2019

8.6K
Reliable Mechanochemistry: Protocols for Reproducible Outcomes of Neat and Liquid Assisted Ball-mill Grinding Experiments
13:05

Reliable Mechanochemistry: Protocols for Reproducible Outcomes of Neat and Liquid Assisted Ball-mill Grinding Experiments

Published on: January 23, 2018

11.2K

Related Experiment Videos

Last Updated: Feb 3, 2026

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task
05:04

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task

Published on: September 21, 2017

6.4K
Presynapse Formation Assay Using Presynapse Organizer Beads and &ldquo;Neuron Ball&rdquo; Culture
10:17

Presynapse Formation Assay Using Presynapse Organizer Beads and “Neuron Ball” Culture

Published on: August 2, 2019

8.6K
Reliable Mechanochemistry: Protocols for Reproducible Outcomes of Neat and Liquid Assisted Ball-mill Grinding Experiments
13:05

Reliable Mechanochemistry: Protocols for Reproducible Outcomes of Neat and Liquid Assisted Ball-mill Grinding Experiments

Published on: January 23, 2018

11.2K

Area of Science:

  • Probability theory
  • Statistical inference
  • Functional analysis

Background:

  • Comparing probability distributions is crucial in statistical analysis.
  • Existing methods often require moment assumptions or struggle with outliers and imbalanced data.
  • Novel divergence measures are needed for robust and generalizable statistical testing.

Purpose of the Study:

  • Introduce Ball Divergence, a new measure for probability differences in Banach spaces.
  • Develop a robust multivariate two-sample test based on Ball Divergence.
  • Demonstrate the test's consistency, applicability to imbalanced data, and superiority over existing methods.

Main Methods:

  • Defined Ball Divergence for probability measures in separable Banach spaces.
  • Developed a metric rank test statistic based on Ball Divergence.
  • Analyzed the asymptotic distribution under null (mixture of chi-squared) and alternative (normal) hypotheses.
  • Proved consistency against general alternatives and independence from sample size ratios.

Main Results:

  • Ball Divergence is zero if and only if probability measures are identical, without moment assumptions.
  • The proposed two-sample test is robust to outliers and heavy-tail data.
  • The test statistic shows desirable convergence properties and is consistent under general alternatives.
  • Numerical simulations indicate superior Type I error control and power compared to existing tests.
  • The method is effective for imbalanced datasets.

Conclusions:

  • Ball Divergence provides a powerful and generalizable tool for comparing probability distributions.
  • The developed multivariate two-sample test is robust, consistent, and performs well on imbalanced data.
  • The method has practical applications in drug development (virtual screening) and genomics (gene expression analysis).