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

Bonferroni Test01:10

Bonferroni Test

2.8K
The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
The means of different samples are first paired in all possible combinations.
The null hypothesis of the...
2.8K
Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data01:16

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

157
Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...
157
Statistical Significance01:50

Statistical Significance

20.2K
Once data is collected from both the experimental and the control groups, a statistical analysis is conducted to find out if there are meaningful differences between the two groups. A statistical analysis determines how likely any difference found is due to chance (and thus not meaningful). In psychology, group differences are considered meaningful, or significant, if the odds that these differences occurred by chance alone are 5 percent or less. Stated another way, if we repeated this...
20.2K
Significance Testing: Overview01:04

Significance Testing: Overview

3.4K
Significance testing is a set of statistical methods used to test whether a claim about a parameter is valid. In analytical chemistry, significance testing is used primarily to determine whether the difference between two values comes from determinate or random errors. The effect of a particular change in the measurement protocol, analyst, or sample itself can cause a deviation from the expected result. In the case of a suspected deviation/outlier, we need to be able to confirm mathematically...
3.4K
Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

3.4K
A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
3.4K
Statistical Hypothesis Testing01:16

Statistical Hypothesis Testing

2.0K
Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...
2.0K

You might also read

Related Articles

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

Sort by
Same author

Reassessment of Kepler's habitable zone Earth-like exoplanets with data-driven null signal templates.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same author

Multiscale Flow for robust and optimal cosmological analysis.

Proceedings of the National Academy of Sciences of the United States of America·2024
Same author

Estimating COVID-19 mortality in Italy early in the COVID-19 pandemic.

Nature communications·2021
Same author

Learning effective physical laws for generating cosmological hydrodynamics with Lagrangian deep learning.

Proceedings of the National Academy of Sciences of the United States of America·2021
Same author

Limits on Stellar-Mass Compact Objects as Dark Matter from Gravitational Lensing of Type Ia Supernovae.

Physical review letters·2018
Same author

Primordial Non-Gaussianities and Zero-Bias Tracers of the Large-Scale Structure.

Physical review letters·2018

Related Experiment Video

Updated: Jul 24, 2025

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
12:39

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types

Published on: December 10, 2012

11.4K

Statistical Significance Testing for Mixed Priors: A Combined Bayesian and Frequentist Analysis.

Jakob Robnik1, Uroš Seljak1,2

  • 1Physics Department, University of California at Berkeley, Berkeley, CA 94720, USA.

Entropy (Basel, Switzerland)
|July 8, 2023
PubMed
Summary

Combining Bayesian and frequentist hypothesis testing improves statistical power when prior information is incomplete. This approach uses the Bayes factor within frequentist analysis, enhancing power over standard methods, especially in complex scenarios like exoplanet detection.

Keywords:
Bayesian statisticsexoplanet transit searchfrequentist statisticshypothesis testinglook-elsewhere effectstatistical mechanics

More Related Videos

Using the FishSim Animation Toolchain to Investigate Fish Behavior: A Case Study on Mate-Choice Copying In Sailfin Mollies
10:50

Using the FishSim Animation Toolchain to Investigate Fish Behavior: A Case Study on Mate-Choice Copying In Sailfin Mollies

Published on: November 8, 2018

10.9K
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

3.4K

Related Experiment Videos

Last Updated: Jul 24, 2025

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
12:39

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types

Published on: December 10, 2012

11.4K
Using the FishSim Animation Toolchain to Investigate Fish Behavior: A Case Study on Mate-Choice Copying In Sailfin Mollies
10:50

Using the FishSim Animation Toolchain to Investigate Fish Behavior: A Case Study on Mate-Choice Copying In Sailfin Mollies

Published on: November 8, 2018

10.9K
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

3.4K

Area of Science:

  • Statistics
  • Astrophysics
  • Statistical Mechanics

Background:

  • Hypothesis testing often involves mixed priors, where some parameters have informative priors and others do not.
  • Bayesian methods use Bayes factors, incorporating Occam's razor, while frequentist tests rely on false-positive rates, being less sensitive to prior choice when priors are incomplete.
  • Combining both methodologies offers a robust approach for hypothesis testing with partial prior information.

Purpose of the Study:

  • To propose and validate a hybrid methodology for hypothesis testing that leverages both Bayesian and frequentist approaches.
  • To demonstrate that using the Bayes factor as a test statistic in frequentist analysis enhances statistical power, particularly with mixed priors.
  • To develop an analytic formalism for this hybrid approach, generalizing existing theorems and avoiding computationally expensive simulations.

Main Methods:

  • The study combines the Bayes factor (Bayesian) with frequentist hypothesis testing frameworks.
  • It shows the equivalence of the maximum likelihood-ratio test statistic to the Bayes factor with a non-informative Jeffrey's prior.
  • An analytic formalism is developed, generalizing Wilks' theorem and applicable to scenarios with partial prior information, avoiding simulations.

Main Results:

  • Mixed priors increase statistical power in frequentist analyses compared to standard maximum likelihood tests.
  • The developed analytic formalism reproduces existing expressions for p-values in linear models and periodograms in specific limits.
  • The formalism accurately reproduces p-values from numerical simulations in an exoplanet transit detection example, even with high multiplicity.

Conclusions:

  • Combining Bayesian Bayes factors with frequentist analysis provides a powerful tool for hypothesis testing, especially with incomplete prior knowledge.
  • The developed analytic formalism offers a computationally efficient and accurate method for statistical inference in complex problems.
  • The study provides a novel interpretation linking hypothesis testing (p-value, Bayes factor) to statistical mechanics concepts like energy and entropy competition.