A new unified approach for the simulation of a wide class of directional distributions

<p>The need for effective simulation methods for directional distributions has grown as they have become components in more sophisticated statistical models. A new acceptance-rejection method is proposed and investigated for the Bingham distribution on the sphere using the angular central Gaussian distribution as an envelope. It is shown that the proposed method has high efficiency and is also straightforward to use. Next, the simulation method is extended to the Fisher and Fisher-Bingham distributions on spheres and related manifolds. Together, these results provide a widely applicable and efficient methodology to simulate many of the standard models in directional data analysis. An R package simdd, available in the online supplementary material, implements these simulation methods.</p

Synthetic datasets used in this study.

<p>First colum: C atoms involved in the pairwise distance. Second and last columns: averaged and power-averaged pairwise distances, respectively.</p

A directed graphical model of the ensemble model (on the left) and its interplay with a fine-grained conformational prior distribution (top right) through the reference ratio method, (bottom right).

<p>In the graphical model, the black circles are random variables, and the arrows determine their conditional independencies. The parameter , marked in grey on the left, is fixed and given, and denotes the experimental error in this particular example. denotes the reference distribution.</p

The influence of and on the ensembles.

<p>The figure shows histograms, , of a representative pairwise distance (between C-C, in Å ) in the ensembles obtained without the reference distribution or the scale vector . The black line denotes the PROFASI target ensemble; the red and green lines denote the ensembles obtained using the linearly and the power averaged data, respectively. The blue line denotes the case of the power averaged data without , but with .</p

Histograms, , of a representative pairwise distance (between C-C, in ) in the ensembles.

<p>The black and blue lines are obtained from the PROFASI and ISD ensembles respectively, while the cyan line represent the prior . Finally, the green and red lines respectively represent ensembles obtained from the power-averaged and linearly averaged data.</p