Correlated Weibull regression model for multivariate binary data

The correlated Weibull regression model for the analysis of correlated binary data is presented. This regression model is based on Bonney’s disposition model for the regression analysis of correlated binary outcomes. Parameter estimation was done through the maximum likelihood method. The correlated Weibull regression model was contrasted with the correlated logistic regression model. The results showed that both regression models were useful in explaining the familial aggregation of oesophageal cancer. The correlated logistic regression model fitted the oesophageal cancer data better than the correlated Weibull regression model for both the non-nested and nested cases. Furthermore, the correlated logistic regression model was computationally more attractive than the correlated Weibull regression model

Semi-nonparametric count data estimation with an endogenous binary variable

This paper proposes a semi-nonparametric Poisson model with an endogenous binary variable, which generalizes bivariate correlated unobserved heterogeneity using Hermite polynomials, and compares this model with a parametric one. The National Health Interview Survey (NHIS) data from 1990 shows the difference between the endogenous binary variable's coefficients of the semi-nonparametric and parametric models.Endogenous switching

Data processing large quantities of multispectral information

Method is combination of digital and optical techniques. Multispectral data is coded into binary matrix format and then encoded onto photographic film. Film is holographically correlated with spectral signature to generate single-class classification map. Number of maps are optically superimposed to produce full-color, multiclass classification map

Analysis of binary spatial data by quasi-likelihood estimating equations

The goal of this paper is to describe the application of quasi-likelihood estimating equations for spatially correlated binary data. In this paper, a logistic function is used to model the marginal probability of binary responses in terms of parameters of interest. With mild assumptions on the correlations, the Leonov-Shiryaev formula combined with a comparison of characteristic functions can be used to establish asymptotic normality for linear combinations of the binary responses. The consistency and asymptotic normality for quasi-likelihood estimates can then be derived. By modeling spatial correlation with a variogram, we apply these asymptotic results to test independence of two spatially correlated binary outcomes and illustrate the concepts with a well-known example based on data from Lansing Woods. The comparison of generalized estimating equations and the proposed approach is also discussed.Comment: Published at http://dx.doi.org/10.1214/009053605000000057 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A generalized linear mixed model for longitudinal binary data with a marginal logit link function

Longitudinal studies of a binary outcome are common in the health, social, and behavioral sciences. In general, a feature of random effects logistic regression models for longitudinal binary data is that the marginal functional form, when integrated over the distribution of the random effects, is no longer of logistic form. Recently, Wang and Louis [Biometrika 90 (2003) 765--775] proposed a random intercept model in the clustered binary data setting where the marginal model has a logistic form. An acknowledged limitation of their model is that it allows only a single random effect that varies from cluster to cluster. In this paper we propose a modification of their model to handle longitudinal data, allowing separate, but correlated, random intercepts at each measurement occasion. The proposed model allows for a flexible correlation structure among the random intercepts, where the correlations can be interpreted in terms of Kendall's $\tau$. For example, the marginal correlations among the repeated binary outcomes can decline with increasing time separation, while the model retains the property of having matching conditional and marginal logit link functions. Finally, the proposed method is used to analyze data from a longitudinal study designed to monitor cardiac abnormalities in children born to HIV-infected women.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS390 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fast Spectral Variability from Cygnus X-1

We have developed an algorithm that, starting from the observed properties of the X-ray spectrum and fast variability of an X-ray binary allows the production of synthetic data reproducing observables such as power density spectra and time lags, as well as their energy dependence. This allows to reconstruct the variability of parameters of the energy spectrum and to reduce substantially the effects of Poisson noise, allowing to study fast spectral variations. We have applied the algorithm to Rossi X-ray Timing Explorer data of the black-hole binary Cygnus X-1, fitting the energy spectrum with a simplified power law model. We recovered the distribution of the power law spectral indices on time-scales as low as 62 ms as being limited between 1.6 and 1.8. The index is positively correlated with the flux even on such time-scales.Comment: 14 pages, 19 figures, accepted by MNRA

A Radio Census of Binary Supermassive Black Holes

Using archival VLBI data for 3114 radio-luminous active galactic nuclei, we searched for binary supermassive black holes using a radio spectral index mapping technique which targets spatially resolved, double radio-emitting nuclei. Only one source was detected as a double nucleus. This result is compared with a cosmological merger rate model and interpreted in terms of (1) implications for post-merger timescales for centralisation of the two black holes, (2) implications for the possibility of "stalled" systems, and (3) the relationship of radio activity in nuclei to mergers. Our analysis suggests that the binary evolution of paired supermassive black holes (both of masses >= 1e8 Msun) spends less than 500 Myr in progression from the merging of galactic stellar cores to within the purported stalling radius for supermassive black hole pairs. The data show no evidence for an excess of stalled binary systems at small separations. We see circumstantial evidence that the relative state of radio emission between paired supermassive black holes is correlated within orbital separations of 2.5 kpc.Comment: 11 Pages, 7 figures, accepted for publication in MNRA

Phase-Transition in Binary Sequences with Long-Range Correlations

Motivated by novel results in the theory of correlated sequences, we analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations). In our model, the probability for a unit bit in a binary string depends on the fraction of unities preceding it. We show that the system undergoes a dynamical phase-transition from normal diffusion, in which the variance D_L scales as the string's length L, into a super-diffusion phase (D_L ~ L^{1+|alpha|}), when the correlation strength exceeds a critical value. We demonstrate the generality of our results with respect to alternative models, and discuss their applicability to various data, such as coarse-grained DNA sequences, written texts, and financial data.Comment: 4 pages, 4 figure

Viewing angle of binary neutron star mergers

The joint detection of the gravitational wave (GW) GW170817 and its electromagnetic (EM) counterparts GRB170817A and kilonova AT 2017gfo has triggered extensive study of the EM emission of binary neutron star mergers. A parameter which is common to and plays a key role in both the GW and the EM analyses is the viewing angle of the binary's orbit. If a binary is viewed from different angles, the amount of GW energy changes (implying that orientation and distance are correlated) and the EM signatures can vary, depending on the structure of the emission. Information about the viewing angle of the binary orbital plane is therefore crucial to the interpretation of both the GW and the EM data, and can potentially be extracted from either side. In the first part of this study, we present a systematic analysis of how well the viewing angle of binary neutron stars can be measured from the GW data. We show that if the sky position and the redshift of the binary can be identified via the EM counterpart and an associated host galaxy, then for 50$\%$ of the systems the viewing angle can be constrained to $\leq 7^{\circ}$ uncertainty from the GW data, independent of electromagnetic emission models. On the other hand, if no redshift measurement is available, the measurement of the viewing angle with GW alone is not informative, unless the true viewing angle is close to $90^{\circ}$. This holds true even if the sky position is measured independently. Then, we consider the case where some constraints on the viewing angle can be placed from the EM data itself. We show that the EM measurements can then be used in the analysis of GW data to improve the precision of the luminosity distance, and hence of the Hubble constant, by a factor of 2 to 3.Comment: Accepted by Physical Review