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

Abstract

This paper presents a normalized standard error-based statistical data binning method, termed “bin size index” (BSI), which yields an optimized, objective bin size for constructing a rational histogram to facilitate subsequent deconvolution of multimodal datasets from materials characterization and hence the determination of the underlying probability density functions. Totally ten datasets, including four normally-distributed synthetic ones, three normally-distributed ones on the elasticity of rocks obtained by statistical nanoindentation, and three lognormally-distributed ones on the particle size distributions of flocculated clay suspensions, were used to illustrate the BSI’s concepts and algorithms. While results from the synthetic datasets prove the method’s accuracy and effectiveness, analyses of other real datasets from materials characterization and measurement further demonstrate its rationale, performance, and applicability to practical problems. The BSI method also enables determination of the number of modes via the comparative evaluation of the errors returned from different trial bin sizes. The accuracy and performance of the BSI method are further compared with other widely used binning methods, and the former yields the highest BSI and smallest normalized standard errors. This new method particularly penalizes the overfitting that tends to yield too many pseudo-modes via normalizing the errors by the number of modes hidden in the datasets, and also eliminates the difficulty in specifying criteria for acceptable values of the fitting errors. The advantages and disadvantages of the new method are also discussed.