Bayesian analysis of robust Poisson geometric process model using heavy-tailed distributions

Area of Science:

• Statistics
• Probability Theory
• Data Analysis

Background:

• Outliers can significantly skew statistical analyses, leading to overestimation of mean and variance.
• Traditional Poisson geometric process models may not adequately handle data with extreme values.
• Accurate interpretation of data requires robust statistical methods that account for outliers.

Purpose of the Study:

• To develop a robust Poisson geometric process model capable of handling outliers.
• To improve the accuracy of statistical interpretations in the presence of extreme data points.
• To incorporate heavy-tailed distributions for enhanced outlier detection.

Main Methods:

• Proposed a robust Poisson geometric process model.
• Utilized heavy-tailed distributions: Student's t-distribution and exponential power distribution.
• Represented distributions using scale mixture of normal and scale mixture of uniform.
• Employed mixing parameters for outlier detection.

Main Results:

• The proposed model effectively describes data trends while identifying outlying observations.
• Simulations demonstrated the model's capability in handling heavy-tailed data.
• Real data analysis confirmed the practical utility of the robust model.

Conclusions:

• The robust Poisson geometric process model with heavy-tailed distributions provides a more accurate approach to data analysis.
• The model's ability to detect outliers enhances the reliability of statistical interpretations.
• This methodology offers a valuable tool for researchers dealing with datasets containing extreme values.