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

Geometric Mean01:15

Geometric Mean

2.7K
The mean is a measure of the central tendency of a data set. In some data sets, the data is inherently multiplicative, and the arithmetic mean is not useful. For example, the human population multiplies with time, and so does the credit amount of financial investment, as the interest compounds over successive time intervals.
In cases of multiplicative data, the geometric mean is used for statistical analysis. First, the product of all the elements is taken. Then, if there are n elements in the...
2.7K
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

13.7K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
13.7K
Area Computation by the Alternative Coordinate Method01:24

Area Computation by the Alternative Coordinate Method

860
The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
860
Statistical Analysis: Overview01:11

Statistical Analysis: Overview

14.6K
When we take repeated measurements on the same or replicated samples, we will observe inconsistencies in the magnitude. These inconsistencies are called errors. To categorize and characterize these results and their errors, the researcher can use statistical analysis to determine the quality of the measurements and/or suitability of the methods.
One of the most commonly used statistical quantifiers is the mean, which is the ratio between the sum of the numerical values of all results and the...
14.6K
Outliers and Influential Points01:08

Outliers and Influential Points

5.1K
An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the...
5.1K
Geometric Sequences01:30

Geometric Sequences

394
In systems where values diminish by a constant proportion at each stage, the resulting sequence follows a geometric structure. Each new value in the sequence is obtained by applying a fixed multiplier to the preceding term. This regular, proportional decline type is often used to represent processes involving gradual loss, such as energy dissipation or reduction in amplitude over time.When analyzing the total effect of such a process across unlimited iterations, the series of values is referred...
394

You might also read

Related Articles

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

Sort by
Same author

Statistics and AI - A Fireside Conversation.

Harvard data science review·2026
Same author

Cardiovascular-Kidney-Metabolic Syndrome: Conceptualising an Approach to Health Economic Modelling.

Diabetes, obesity & metabolism·2026
Same author

Artificial Intelligence in Image-Based Cardiovascular Disease Analysis.

Annual review of biomedical data science·2026
Same author

Multi-organ imaging and genetics show the impact of sleep patterns on the human brain and body.

Communications medicine·2026
Same author

Scalable subclonal reconstruction of cancer cells in DNA sequencing data using a penalized likelihood model.

bioRxiv : the preprint server for biology·2026
Same author

Connectome-based spatial statistics enabling large-scale population analyses of human connectome across cohorts.

bioRxiv : the preprint server for biology·2026
Same journal

Individualized dynamic latent factor model for multi-resolutional data with application to mobile health.

Biometrika·2026
Same journal

Functional principal component analysis forsparse censored data.

Biometrika·2026
Same journal

Finding distributions that differ, with false discovery rate control.

Biometrika·2026
Same journal

Sequential Gibbs posteriors with applications to principal component analysis.

Biometrika·2026
Same journal

Comparing causal parameters with many treatments and positivity violations.

Biometrika·2026
Same journal

Leveraging External Data for Testing Experimental Therapies with Biomarker Interactions in Randomized Clinical Trials.

Biometrika·2026
See all related articles

Related Experiment Video

Updated: May 3, 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

2.1K

Bayesian influence analysis: a geometric approach.

Hongtu Zhu1, Joseph G Ibrahim1, Niansheng Tang2

  • 1Department of Biostatistics, CB# 7420, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27516, U.S.A., hzhu@bios.unc.edu , ibrahim@bios.unc.edu.

Biometrika
|January 24, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces Bayesian influence analysis to assess data and model perturbations. It uses a geometric framework, the Bayesian perturbation manifold, to quantify these effects in statistical models.

Keywords:
Influence measurePerturbation manifoldPerturbation modelPrior distribution

More Related Videos

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

2.9K
Methods to Explore the Influence of Top-down Visual Processes on Motor Behavior
09:49

Methods to Explore the Influence of Top-down Visual Processes on Motor Behavior

Published on: April 16, 2014

24.7K

Related Experiment Videos

Last Updated: May 3, 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

2.1K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

2.9K
Methods to Explore the Influence of Top-down Visual Processes on Motor Behavior
09:49

Methods to Explore the Influence of Top-down Visual Processes on Motor Behavior

Published on: April 16, 2014

24.7K

Area of Science:

  • Statistics
  • Bayesian Analysis
  • Geometric Methods

Background:

  • Assessing the impact of perturbations in statistical models is crucial for robust analysis.
  • Existing methods for Bayesian influence analysis may not fully capture the intrinsic structure of perturbation schemes.

Purpose of the Study:

  • To develop a general framework for Bayesian influence analysis.
  • To introduce a geometric approach for characterizing and quantifying perturbations in statistical models.

Main Methods:

  • Developed a perturbation model to define various perturbation schemes.
  • Introduced the Bayesian perturbation manifold, utilizing metric tensors and geodesics.
  • Derived intrinsic and local influence measures based on the manifold.

Main Results:

  • The Bayesian perturbation manifold provides a geometric structure for understanding perturbation models.
  • Intrinsic and local influence measures quantify the impact of perturbations on statistical models.
  • Demonstrated broad applicability through theoretical and numerical examples.

Conclusions:

  • The proposed geometric framework offers a novel approach to Bayesian influence analysis.
  • The developed influence measures enhance the understanding of model sensitivity to perturbations.
  • This methodology is broadly applicable to formal Bayesian analysis.