Parameterization of the Stochastic Model for Evaluating Variable Small Data in the Shannon Entropy Basis.

Area of Science:

• Information Theory
• Statistical Modeling
• Data Science

Background:

• Stochastic models are crucial for evaluating variable small data.
• Measurement interferences introduce uncertainty and variability in parameter estimation.
• Existing methods may not fully account for these uncertainties.

Purpose of the Study:

• To apply Shannon's entropy maximization principle to small data evaluation.
• To develop an information technology for parameter and non-parametric evaluation under interference.
• To formalize methods for estimating probability density functions and generating parameter ensembles.

Main Methods:

• Analytical transition from likelihood function to Shannon entropy functional.
• Utilizing Shannon entropy to quantify uncertainty from parameter probabilities and measurement interferences.
• Developing parametric and non-parametric evaluation techniques based on entropy maximization.

Main Results:

• Shannon entropy quantifies uncertainty from both model parameters and measurement distortions.
• Entropy maximization provides robust parameter estimates that account for measurement variability.
• Formalized methods for probability density estimation and parameter vector generation are presented.

Conclusions:

• Entropy maximization offers a principled approach to robust small data evaluation under uncertainty.
• The developed information technology enhances the reliability of stochastic model parameter estimation.
• This framework is applicable to small data measured with significant interferences.