Related Experiment Video
Updated: Oct 2, 2025
08:12
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
Published on: March 1, 2022
2.6K
Coming Together of Bayesian Inference and Skew Spherical Data
Najmeh Nakhaei Rad1,2,3, Andriette Bekker3, Mohammad Arashi3,4
1Department of Mathematics and Statistics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
Frontiers in Big Data
|February 28, 2022
Summary
This study introduces Bayesian modeling for directional data using a novel skew-rotationally-symmetric Fisher-von Mises-Langevin distribution. The research quantifies prior impact and uses advanced sampling for analyzing circular and spherical data.
Area of Science:
- Statistics
- Bayesian Inference
- Directional Data Analysis
Background:
- Directional data analysis is crucial in various scientific fields.
- Existing models may not fully capture skewness and rotational symmetry.
- Bayesian methods offer a robust framework for parameter estimation.
Purpose of the Study:
- To introduce a new Bayesian framework for modeling skew-rotationally-symmetric directional data.
- To develop and apply novel prior distributions for Bayesian analysis.
- To provide practical guidance for implementing these methods.
Main Methods:
- Utilized the skew-rotationally-symmetric Fisher-von Mises-Langevin (FvML) distribution.
- Quantified prior impact using the Wasserstein Impact Measure (WIM).
- Employed modified Gibbs and slice samplings for posterior computation.
Main Results:
- Demonstrated the applicability of the FvML distribution for directional data.
- Showcased the utility of WIM in guiding prior selection.
- Successfully analyzed both synthetic and real-world datasets.
Conclusions:
- The proposed Bayesian approach effectively models skew and rotational symmetry in directional data.
- The methodology provides a valuable tool for practitioners in statistics and related fields.
- This work opens new avenues for Bayesian analysis of complex circular and spherical data.
Related Concept Videos
01:06Skewness
13.4K
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...
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...
13.4K
01:09Types of Skewness
13.3K
If the frequency distribution of a data set is more inclined towards smaller or larger values, the distribution is said to be skewed. If data values are skewed to the right, then the distribution is called positively skewed. Conversely, if the plot is skewed to the left, the distribution is called negatively skewed.
For instance, in the middle of a pandemic, the geographical distribution of vaccine coverage may be positively skewed towards populations in the global north countries. However,...
For instance, in the middle of a pandemic, the geographical distribution of vaccine coverage may be positively skewed towards populations in the global north countries. However,...
13.3K
01:23Spherical Coordinates
11.5K
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
11.5K
01:16Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data
242
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,...
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,...
242
01:26Gauss's Law: Spherical Symmetry
8.1K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...
8.1K
01:28Introduction to Nonparametric Statistics
933
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...
One of...
933