Constructing smooth potentials of mean force, radial distribution functions, and probability densities from sampled...

Area of Science:

• Computational Physics
• Statistical Mechanics
• Data Analysis

Background:

• Histograms provide noisy estimates and require arbitrary bin sizes.
• The Berg-Harris method struggles with Jacobian factors and requires many Fourier modes for accurate radial distribution functions and potentials of mean force.

Purpose of the Study:

• To present a general method for obtaining smooth, analytical estimates of probability densities, radial distribution functions, and potentials of mean force from sampled data.
• To overcome limitations of histograms and the standard Berg-Harris method.

Main Methods:

• A biased resampling scheme to resolve issues from Jacobian factors.
• An automated piecewise construction approach to mitigate the need for numerous Fourier modes.
• Extension and refinement of the Berg-Harris method.

Main Results:

• The developed method provides statistically controlled, smooth analytical estimates.
• It successfully analyzes radial distribution functions in an energy-discretized water model.
• Demonstrated superior performance over histograms and the original Berg-Harris method for various complex densities, including those with long tails and discontinuous features.

Conclusions:

• The proposed method offers a robust and accurate alternative for density estimation from sampled data.
• It effectively handles challenging datasets where traditional methods fail.
• This technique enhances the reliability of analyzing radial distribution functions and potentials of mean force in statistical mechanics and computational physics.