Bayesian tests of symmetry for the generalized Von Mises distribution

Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka in Stat Methodol 4(3):341–353, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric, unimodal or bimodal. A characterization of axial symmetry is provided and taken as null hypothesis for one of the proposed Bayesian tests. The Bayesian tests are obtained by the technique of probability perturbation. The prior probability measure is perturbed so to give a positive prior probability to the null hypothesis, which would be null otherwise. This allows for the derivation of simple computational formulae for the Bayes factors. Numerical results reveal that, whenever the simulation scheme of the samples supports the null hypothesis, the null posterior probabilities appear systematically larger than their prior counterpart.

Understanding the Behaviour of Wind Direction in Malaysia during Monsoon Seasons using Replicated Functional Relationship in von Mises Distribution

In studies of potential wind energy, knowing statistical distribution of wind direction provides useful information in making predictions and gives a better understanding of the behavior of the wind direction. Malaysia experiences two monsoon seasons per year, namely Southwest Monsoon and Northeast Monsoon and in this paper, our interest is to investigate whether the direction of wind data in monsoon seasons can be modelled using replicated LFRM with von Mises distribution. The beauty of this model is that it considers the error terms in both x and y variables. This study considers the bivariate relationship of directional wind data where errors are present in both. Here, we propose a replicated functional relationship model, with the von Mises distribution to describe the relationship of the wind direction data. In the parameter estimation, maximum likelihood method is considered with pseudo-replicated group of the replicated form of the functional relationship. The novelty of this approach is that assumption on the ratio of concentration parameters is no longer deemed necessary. Also, we derive the covariance matrix of the parameters based on Fisher Information. From the Monte Carlo simulation study, small bias measures were obtained, suggesting the viability of the model. Based on the simulation study, it can be concluded that the wind direction of the two monsoons in Malaysia can be modelled using replicated linear functional relationship model.

Adaptive Cartesian and torsional restraints for interactive model rebuilding

When building atomic models into weak and/or low-resolution density, a common strategy is to restrain their conformation to that of a higher resolution model of the same or similar sequence. When doing so, it is important to avoid over-restraining to the reference model in the face of disagreement with the experimental data. The most common strategy for this is the use of `top-out' potentials. These act like simple harmonic restraints within a defined range, but gradually weaken when the deviation between the model and reference grows beyond that range. In each current implementation the rate at which the potential flattens at large deviations follows a fixed form, although the form chosen varies among implementations. A restraint potential with a tuneable rate of flattening would provide greater flexibility to encode the confidence in any given restraint. Here, two new such potentials are described: a Cartesian distance restraint derived from a recent generalization of common loss functions and a periodic torsion restraint based on a renormalization of the von Mises distribution. Further, their implementation as user-adjustable/switchable restraints in ISOLDE is described and their use in some real-world examples is demonstrated.