Protein Bioinformatics and Mixtures of Bivariate von Mises Distributions for Angular Data

Mardia, Kanti V.; Taylor, Charles; Subramaniam, Ganesh K.

doi:10.1111/j.1541-0420.2006.00682.x

Cited by 146 publications

(181 citation statements)

References 10 publications

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“…Mardia et al 2007Mardia et al , 2008, an iterative approach to find the maximum of the likelihood, applied to a mixture models) used to model rotational phases of all registered photons (column N in the Table A.1) as a mixture of two component von Mises distribution. The results of the fit are presented in the Table A.1, where for the estimation of uncertainties, an additional, bootstrap algorithm was implemented and applied.…”

Section: Appendix A: True Spin-period Of Rx J07204−3125mentioning

confidence: 99%

The compactness of the isolated neutron star RX J0720.4−3125

Hambaryan

Suleimanov

Haberl

et al. 2017

A&A

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Aims. To estimate the compactness of the thermally emitting isolated neutron star RX J0720.4−3125, an X-ray spin phase-resolved spectroscopic study is conducted. In addition, to identify the genuine spin-period, an X-ray timing analysis is performed. Methods. The data from all observations of RX J0720.4−3125 conducted by XMM-Newton EPIC-pn with the same instrumental setup in 2000-2012 were reprocessed to form a homogenous data set of solar barycenter corrected photon arrival times registered from RX J0720.4−3125. A Bayesian method for the search, detection, and estimation of the parameters of an unknown-shaped periodic signal was employed as developed by Gregory & Loredo (1992). A number of complex models (single and double peaked) of light curves from pulsating neutron stars were statistically analyzed. The distribution of phases for the registered photons was calculated by folding the arrival times with the derived spin-period and the resulting distribution of phases -approximated with a mixed von Mises distribution -, and its parameters were estimated by using the Expected Maximization method. Spin phase-resolved spectra were extracted, and a number of highly magnetized atmosphere models of an INS were used to fit simultaneously, the results were verified via an MCMC approach. Results. The phase-folded light curves in different energy bands with high S/N ratio show a high complexity and variations depending on time and energy. They can be parameterized with a mixed von Mises distribution, i.e. with double-peaked light curve profile showing a dependence of the estimated parameters (mean directions, concentrations, and proportion) upon the energy band, indicating that radiation emerges from at least two emitting areas. Conclusions. The genuine spin-period of the isolated neutron star RX J0720−3125 derived as more likely is twice of that reported in the literature (16.78s instead of 8.39s). The gravitational redshift of RX J0720.4−3125 was determined to z = 0.205 +0.006 −0.003 and the compactness was estimated to (M/M )/(R/km) = 0.105 ± 0.002.

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Section: Appendix A: True Spin-period Of Rx J07204−3125mentioning

confidence: 99%

The compactness of the isolated neutron star RX J0720.4−3125

Hambaryan

Suleimanov

Haberl

et al. 2017

A&A

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“…Previous attempts to model such data using a mixture of bivariate von Mises-type distributions (Mardia et al, 2007) have resulted in some success in identifying clusters which are associated with secondary structure. However, the number of components in the mixture model is problematic, and correct convergence of the EM algorithm is not assured.…”

Section: A Real Data Case Studymentioning

confidence: 99%

Kernel density estimation on the torus

Marzio

Panzera

Taylor

2011

Journal of Statistical Planning and Inference

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Kernel density estimation for multivariate, circular data has been formulated only when the sample space is the sphere, but theory for the torus would also be useful. For data lying on a d-dimensional torus (d ≥ 1), we discuss kernel estimation of a density, its mixed partial derivatives, and their squared functionals. We introduce a specific class of product kernels whose order is suitably defined in such a way to obtain L2-risk formulas whose structure can be compared to their euclidean counterparts. Our kernels are based on circular densities, however we also discuss smaller bias estimation involving negative kernels which are functions of circular densities. Practical rules for selecting the smoothing degree, based on cross-validation, bootstrap and plug-in ideas are derived. Moreover, we provide specific results on the use of kernels based on the von Mises density. Finally, real-data examples and simulation studies illustrate the findings.

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“…The computational advantages of the full conditional composite likelihood become even more pronounced in this case. Such models have become important in bioinformatics for the modelling of correlated conformational angles in protein structure prediction (Mardia et al, 2007;Boomsma et al, 2008).…”

Section: The Bivariate Von Mises Distributionmentioning

confidence: 99%

Maximum likelihood estimation using composite likelihoods for closed exponential families

et al. 2009

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SUMMARYIn certain multivariate problems the full probability density has an awkward normalizing constant, but the conditional and/or marginal distributions may be much more tractable. In this paper we investigate the use of composite likelihoods instead of the full likelihood. For closed exponential families, both are shown to be maximized by the same parameter values for any number of observations. Examples include log-linear models and multivariate normal models. In other cases the parameter estimate obtained by maximizing a composite likelihood can be viewed as an approximation to the full maximum likelihood estimate. An application is given to an example in directional data based on a bivariate von Mises distribution.

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Protein Bioinformatics and Mixtures of Bivariate von Mises Distributions for Angular Data

Cited by 146 publications

References 10 publications

The compactness of the isolated neutron star RX J0720.4−3125

The compactness of the isolated neutron star RX J0720.4−3125

Kernel density estimation on the torus

Maximum likelihood estimation using composite likelihoods for closed exponential families

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