Analysis of Partially Observed Networks via Exponential-family Random Network Models

Exponential-family random network (ERN) models specify a joint representation of both the dyads of a network and nodal characteristics. This class of models allow the nodal characteristics to be modelled as stochastic processes, expanding the range and realism of exponential-family approaches to network modelling. In this paper we develop a theory of inference for ERN models when only part of the network is observed, as well as specific methodology for missing data, including non-ignorable mechanisms for network-based sampling designs and for latent class models. In particular, we consider data collected via contact tracing, of considerable importance to infectious disease epidemiology and public health

Efficient Probabilistic Group Testing Based on Traitor Tracing

Inspired by recent results from collusion-resistant traitor tracing, we provide a framework for constructing efficient probabilistic group testing schemes. In the traditional group testing model, our scheme asymptotically requires T ~ 2 K ln N tests to find (with high probability) the correct set of K defectives out of N items. The framework is also applied to several noisy group testing and threshold group testing models, often leading to improvements over previously known results, but we emphasize that this framework can be applied to other variants of the classical model as well, both in adaptive and in non-adaptive settings.Comment: 8 pages, 3 figures, 1 tabl

Shape, shear and flexion II - Quantifying the flexion formalism for extended sources with the ray-bundle method

Flexion-based weak gravitational lensing analysis is proving to be a useful adjunct to traditional shear-based techniques. As flexion arises from gradients across an image, analytic and numerical techniques are required to investigate flexion predictions for extended image/source pairs. Using the Schwarzschild lens model, we demonstrate that the ray-bundle method for gravitational lensing can be used to accurately recover second flexion, and is consistent with recovery of zero first flexion. Using lens plane to source plane bundle propagation, we find that second flexion can be recovered with an error no worse than 1% for bundle radii smaller than {\Delta}{\theta} = 0.01 {\theta}_E and lens plane impact pararameters greater than {\theta}_E + {\Delta}{\theta}, where {\theta}_E is the angular Einstein radius. Using source plane to lens plane bundle propagation, we demonstrate the existence of a preferred flexion zone. For images at radii closer to the lens than the inner boundary of this zone, indicative of the true strong lensing regime, the flexion formalism should be used with caution (errors greater than 5% for extended image/source pairs). We also define a shear zone boundary, beyond which image shapes are essentially indistinguishable from ellipses (1% error in ellipticity). While suggestive that a traditional weak lensing analysis is satisfactory beyond this boundary, a potentially detectable non-zero flexion signal remains.Comment: 14 pages, 13 figures, accepted for publication in Monthly Notices of the Royal Astronomical Societ

The non-Gaussianity of the cosmic shear likelihood - or: How odd is the Chandra Deep Field South?

(abridged) We study the validity of the approximation of a Gaussian cosmic shear likelihood. We estimate the true likelihood for a fiducial cosmological model from a large set of ray-tracing simulations and investigate the impact of non-Gaussianity on cosmological parameter estimation. We investigate how odd the recently reported very low value of $\sigma_8$ really is as derived from the \textit{Chandra} Deep Field South (CDFS) using cosmic shear by taking the non-Gaussianity of the likelihood into account as well as the possibility of biases coming from the way the CDFS was selected. We find that the cosmic shear likelihood is significantly non-Gaussian. This leads to both a shift of the maximum of the posterior distribution and a significantly smaller credible region compared to the Gaussian case. We re-analyse the CDFS cosmic shear data using the non-Gaussian likelihood. Assuming that the CDFS is a random pointing, we find $\sigma_8=0.68_{-0.16}^{+0.09}$ for fixed $\Omega_{\rm m}=0.25$. In a WMAP5-like cosmology, a value equal to or lower than this would be expected in $\approx 5$ of the times. Taking biases into account arising from the way the CDFS was selected, which we model as being dependent on the number of haloes in the CDFS, we obtain $\sigma_8 = 0.71^{+0.10}_{-0.15}$. Combining the CDFS data with the parameter constraints from WMAP5 yields $\Omega_{\rm m} = 0.26^{+0.03}_{-0.02}$ and $\sigma_8 = 0.79^{+0.04}_{-0.03}$ for a flat universe.Comment: 18 pages, 16 figures, accepted for publication in A&A; New Bayesian treatment of field selection bia

Oceanographic Weather Maps: Using Oceanographic Models to Improve Seabed Mapping Planning and Acquisition

In a world of high precision sensors, one of the few remaining challenges in multibeam echosounding is that of refraction based uncertainty. A poor understanding of oceanographic variability can lead to inadequate sampling of the water mass and the uncertainties that result from this can dominate the uncertainty budget of even state-of-the-art echosounding systems. Though dramatic improvements have been made in sensor accuracies over the past few decades, survey accuracy and efficiency is still potentially limited by a poor understanding of the “underwater weather”. Advances in the sophistication of numerical oceanographic forecast modeling, combined with ever increasing computing power, allow for the timely operation and dissemination of oceanographic nowcast and forecast model systems on regional and global scales. These sources of information, when examined using sound speed uncertainty analysis techniques, have the potential to change the way hydrographers work by increasing our understanding of what to expect from the ocean and when to expect it. Sound speed analyses derived from ocean modeling system’s three-dimensional predictions could provide guidance for hydrographers during survey planning, acquisition and post-processing of hydrographic data. In this work, we examine techniques for processing and visualizing of predictions from global and regional operational oceanographic forecast models and climatological analyses from an ocean atlas to better understand how these data could best be put to use to in the field of hydrograph