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In this paper a method of obtaining smooth analytical estimates ofprobability densities, radial distribution functions and potentials of meanforce from sampled data in a statistically controlled fashion is presented. Theapproach is general and can be applied to any density of a single randomvariable. The method outlined here avoids the use of histograms, which requirethe specification of a physical parameter (bin size) and tend to give noisyresults. The technique is an extension of the Berg-Harris method [B.A. Berg andR.C. Harris, Comp. Phys. Comm. 179, 443 (2008)], which is typically inaccuratefor radial distribution functions and potentials of mean force due to anon-uniform Jacobian factor. In addition, the standard method often requires alarge number of Fourier modes to represent radial distribution functions, whichtends to lead to oscillatory fits. It is shown that the issues of poor samplingdue to a Jacobian factor can be resolved using a biased resampling scheme,while the requirement of a large number of Fourier modes is mitigated throughan automated piecewise construction approach. The method is demonstrated byanalyzing the radial distribution functions in an energy-discretized watermodel. In addition, the fitting procedure is illustrated on three moreapplications for which the original Berg-Harris method is not suitable, namely,a random variable with a discontinuous probability density, a density with longtails, and the distribution of the first arrival times of a diffusing particleto a sphere, which has both long tails and short-time structure. In all cases,the resampled, piecewise analytical fit outperforms the histogram and theoriginal Berg-Harris method.

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