New method to compute Rcomplete enables maximum likelihood refinement for small datasets.

Area of Science:

• Crystallography
• Structural Biology
• Materials Science

Background:

• The crystallographic reliability index (R) is an established metric for assessing structural model quality.
• Its computational expense has limited its widespread adoption compared to cross-validation (CV) methods like k-fold CV.
• R's utility is expanding beyond validation, but its application traditionally requires large datasets.

Purpose of the Study:

• To evaluate the reliability of the R index.
• To compare R with other statistical validation techniques: k-fold cross-validation, bootstrapping, and jackknifing.
• To investigate methods for reducing model bias and assess their impact on R's performance.

Main Methods:

• Comparison of R with k-fold cross-validation, bootstrapping, and jackknifing.
• Assessment of two distinct model bias reduction techniques.
• Evaluation of R's statistical bias and variance against CV methods.
• Analysis of R's capability for estimating maximum likelihood parameters with varying dataset sizes.

Main Results:

• The R index demonstrates statistical bias comparable to k-fold cross-validation.
• R exhibits significantly lower variance compared to cross-validation methods.
• R allows for accurate maximum likelihood parameter estimation even with small crystallographic datasets.
• The study questions the necessity of random parameter shifts for bias reduction in R calculations.

Conclusions:

• The R index is a reliable and statistically sound method for crystallographic structure determination.
• R offers advantages over traditional cross-validation, particularly in terms of variance and applicability to smaller datasets.
• Its ability to perform maximum likelihood refinement extends its utility to diverse crystallographic applications, including high-pressure, neutron diffraction, and free electron laser studies.