A new bin size index method for statistical analysis of multimodal datasets from materials characterization

Area of Science:

• Materials Science
• Statistical Analysis
• Data Mining

Background:

• Histogram construction is crucial for data analysis in materials characterization.
• Determining optimal bin size objectively is a significant challenge.
• Existing methods often struggle with multimodal datasets and overfitting.

Purpose of the Study:

• To introduce a novel, objective statistical data binning method called the bin size index (BSI).
• To enable rational histogram construction for effective deconvolution of multimodal datasets.
• To accurately determine underlying probability density functions in materials characterization.

Main Methods:

• Developed a normalized standard error-based statistical data binning method (BSI).
• Applied BSI to synthetic and real-world datasets (rock elasticity, clay suspensions).
• Compared BSI performance against other widely used binning methods.

Main Results:

• BSI successfully determined optimal bin sizes for histograms.
• The method accurately deconvoluted multimodal datasets and identified probability density functions.
• BSI outperformed other methods, yielding higher BSI values and smaller normalized standard errors.
• BSI effectively penalized overfitting and determined the number of modes in datasets.

Conclusions:

• The BSI method provides an objective and accurate approach to data binning for materials characterization.
• It enhances the deconvolution of complex, multimodal datasets.
• BSI offers a robust solution for determining probability density functions and avoiding overfitting.