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

Accuracy, limits, and approximation01:28

Accuracy, limits, and approximation

545
Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
545
Skewness01:06

Skewness

12.7K
The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.
The longer the tail of the plot on one side, the more skewed it is. The skewness of a data set’s values suggests that the measures of central tendency...
12.7K
Chebyshev's Theorem to Interpret Standard Deviation01:15

Chebyshev's Theorem to Interpret Standard Deviation

4.5K
Chebyshev’s theorem, also known as Chebyshev’s Inequality, states that the proportion of values of a dataset for K standard deviation is calculated using the equation:
4.5K
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

887
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
887
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

1.1K
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
1.1K
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

8.3K
In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
8.3K

You might also read

Related Articles

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

Sort by
Same author

Real-world effectiveness of tezepelumab on clinical remission and small airway dysfunction in severe asthma: a 52-week prospective study.

Expert opinion on biological therapy·2026
Same author

Quantitative Conspicuity of Pancreatic Canine Insulinoma: A Comparison of Dynamic 4D CT and Dual-Source, Dual-Energy Bolus-Triggered Multiphase CT Imaging.

Veterinary sciences·2025
Same author

The Learning Curve of Reverdin-Isham and Akin Percutaneous Osteotomies for Hallux Valgus Correction: A Bayesian Approach.

Journal of clinical medicine·2025
Same author

Short Term Treatment Monitoring of Renal and Inflammatory Biomarkers with Naturally Occurring Leishmaniosis: A Cohort Study of 30 Dogs.

Veterinary sciences·2024
Same author

Objective Priors for Invariant <i>e</i>-Values in the Presence of Nuisance Parameters.

Entropy (Basel, Switzerland)·2024
Same author

The Importance of Reading the Skin: Cutaneous Metastases of Pancreatic Cancer, a Systematic Review.

Journal of clinical medicine·2024

Related Experiment Video

Updated: Sep 13, 2025

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

2.6K

Bayesian Discrepancy Measure: Higher-Order and Skewed Approximations.

Elena Bortolato1, Francesco Bertolino2, Monica Musio2

  • 1Barcelona School of Economics, Universitat Pompeu Fabra, 08005 Barcelona, Spain.

Entropy (Basel, Switzerland)
|July 29, 2025
PubMed
Summary

This study introduces advanced Bayesian methods for hypothesis testing, offering more accurate posterior distribution approximations with minimal computational increase. These techniques enhance statistical inference for both simple and complex models.

Keywords:
Bayesian discrepancy measurecredible regionsevidencehigher-order asymptoticsmatching priorsnuisance parameteroptimal transport mapprecise null hypothesisskew-normal distributionskewed approximationstail area probability

More Related Videos

Measuring Delay Discounting in Humans Using an Adjusting Amount Task
07:47

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Published on: January 9, 2016

15.5K
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: Sep 13, 2025

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

2.6K
Measuring Delay Discounting in Humans Using an Adjusting Amount Task
07:47

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Published on: January 9, 2016

15.5K
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
  • Bayesian Inference
  • Hypothesis Testing

Background:

  • Accurate approximation of posterior distributions is crucial for Bayesian hypothesis testing.
  • Existing first-order approximations may lack sufficient precision for complex statistical models.
  • The Bayesian discrepancy measure is a key tool for precise hypothesis testing.

Purpose of the Study:

  • To develop and evaluate higher-order asymptotic and skewed approximations for the Bayesian discrepancy measure.
  • To extend these approximations to both univariate and multivariate settings, including nuisance parameters.
  • To demonstrate improved accuracy and practical benefits over existing methods.

Main Methods:

  • Derivation of third-order asymptotic approximations for univariate posterior distributions.
  • Development of skewed approximations using skew-normal distributions via derivative matching.
  • Extension to multivariate settings using optimal transport maps for accurate credible regions.

Main Results:

  • Third-order and skewed approximations show improved accuracy in capturing posterior shape.
  • These advanced approximations offer greater precision with little additional computational cost.
  • Connections between Bayesian higher-order approximations and frequentist inference are established.

Conclusions:

  • Higher-order asymptotic and skewed approximations provide a significant improvement for Bayesian hypothesis testing.
  • The proposed methods are computationally efficient and practically beneficial.
  • The study successfully extends accurate approximation techniques to complex multivariate scenarios.