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Quantifying uncertainty in the estimation of probability distributions.
1North Carolina State University, Raleigh, North Carolina 27695-8205, USA. htbanks@ncsu.edu
This study introduces a computational framework for estimating probability distributions using ordinary least squares. It quantifies uncertainty in parameter estimation, providing standard errors for the results.
Area of Science:
- Statistics
- Computational Mathematics
Background:
- Ordinary least squares (OLS) is a standard method for parameter estimation.
- Estimating probability distributions presents unique challenges in statistical modeling.
Purpose of the Study:
- To develop a computational framework for parameter estimation problems where parameters are probability distributions.
- To provide a method for quantifying uncertainty, such as standard errors, associated with these estimations.
Main Methods:
- Utilizing ordinary least squares for parameter estimation.
- Developing a computational framework for uncertainty quantification.
Main Results:
- A framework for estimating probability distributions via OLS was established.
- Numerical findings demonstrating the quantification of uncertainty were presented.
Conclusions:
- The proposed computational framework effectively addresses uncertainty in estimating probability distributions using OLS.
- The findings support the application of this method in statistical modeling and analysis.
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