Inferences based on a bivariate distribution with von Mises marginals

Tractable circula densities from Fourier series

This article proposes an approach, based on infinite Fourier series, to constructing tractable densities for the bivariate circular analogues of copulas recently coined ‘circulas’. As examples of the general approach, we consider circula densities generated by various patterns of nonzero Fourier coefficients. The shape and sparsity of such arrangements are found to play a key role in determining the properties of the resultant models. The special cases of the circula densities we consider all have simple closed-form expressions involving no computationally demanding normalizing constants and display wide-ranging distributional shapes. A highly successful model identification tool and methods for parameter estimation and goodness-of-fit testing are provided for the circula densities themselves and the bivariate circular densities obtained from them using a marginal specification construction. The modelling capabilities of such bivariate circular densities are compared with those of five existing models in a numerical experiment, and their application illustrated in an analysis of wind directions.

Theory and Statistical Description of the Enhanced Multi-Temporal InSAR (E-MTInSAR) Noise-Filtering Algorithm

In this work, the statistical fundaments of the recently proposed enhanced, multi-temporal interferometric synthetic aperture radar (InSAR) noise-filtering (E-MTInSAR) technique is addressed. The adopted noise-filtering algorithm is incorporated into the improved extended Minimum Cost Flow (EMCF) Small Baseline Subset (SBAS) differential interferometric SAR (InSAR) processing chain, which has extensively been used for the generation of Earth’s surface displacement time-series in several different contexts. Originally, the input of the InSAR EMCF-SBAS processing toolbox consisted of a sequence of multi-looked, small baseline interferograms, which were unwrapped using the space-time EMCF phase unwrapping algorithm. Subsequently, the unwrapped interferograms were inverted through the SBAS algorithm to retrieve the expected InSAR deformation products. The improved processing chain complemented the original codes with two additional steps. In particular, a new multi-temporal noise-filtering algorithm for sequences of time-redundant multi-looked DInSAR interferograms, followed by a proper interferogram selection step, has been proposed. This research study is aimed at primarily assessing the performance of the E-MTInSAR noise-filtering algorithm from a theoretical perspective. To this aim, the principles of directional statistics and errors propagation are exploited. Experimental results, carried out by applying the E-MTInSAR algorithm to a sequence of SAR data collected over the Los Angeles bay area, have been used to corroborate the academic outcome of this research.

Modeling and comparing the organization of circular genomes

Motivation: Most prokaryotic genomes are circular with a single chromosome (called circular genomes), which consist of bacteria and archaea. Orthologous genes (abbreviated as orthologs) are genes directly evolved from an ancestor gene, and can be traced through different species in evolution. Shared orthologs between bacterial genomes have been used to measure their genome evolution. Here, organization of circular genomes is analyzed via distributions of shared orthologs between genomes. However, these distributions are often asymmetric and bimodal; to date, there is no joint distribution to model such data. This motivated us to develop a family of bivariate distributions with generalized von Mises marginals (BGVM) and its statistical inference.

Results: A new measure based on circular grade correlation and the fraction of shared orthologs is proposed for association between circular genomes, and a visualization tool developed to depict genome structure similarity. The proposed procedures are applied to eight pairs of prokaryotes separated from domain down to species, and 13 mycoplasma bacteria that are mammalian pathogens belonging to the same genus. We close with remarks on further applications to many features of genomic organization, e.g. shared transcription factor binding sites, between any pair of circular genomes. Thus, the proposed procedures may be applied to identifying conserved chromosome backbones, among others, for genome construction in synthetic biology.

Availability: All codes of the BGVM procedures and 1000+ prokaryotic genomes are available at http://www.stat.sinica.edu.tw/∼gshieh/bgvm.htm.

Contact:gshieh@stat.sinica.edu.tw

Supplementary information:Supplementary data are available at Bioinformatics online.