The Impact of Peculiar Velocities on the Estimation of the Hubble Constant from Gravitational Wave Standard Sirens

In this work we investigate the systematic uncertainties that arise from the calculation of the peculiar velocity when estimating the Hubble constant ($H_0$) from gravitational wave standard sirens. We study the GW170817 event and the estimation of the peculiar velocity of its host galaxy, NGC 4993, when using Gaussian smoothing over nearby galaxies. NGC 4993 being a relatively nearby galaxy, at $\sim 40 \ {\rm Mpc}$ away, is subject to a significant effect of peculiar velocities. We demonstrate a direct dependence of the estimated peculiar velocity value on the choice of smoothing scale. We show that when not accounting for this systematic, a bias of $\sim 200 \ {\rm km \ s ^{-1}}$ in the peculiar velocity incurs a bias of $\sim 4 \ {\rm km \ s ^{-1} \ Mpc^{-1}}$on the Hubble constant. We formulate a Bayesian model that accounts for the dependence of the peculiar velocity on the smoothing scale and by marginalising over this parameter we remove the need for a choice of smoothing scale. The proposed model yields$H_0 = 68.6 ^{+14.0}_{-8.5}~{\rm km\ s^{-1}\ Mpc^{-1}}$. We demonstrate that under this model a more robust unbiased estimate of the Hubble constant from nearby GW sources is obtained.Comment: 9 pages, 5 figure

Large Deviations and Sum Rules for Spectral Theory - A Pedagogical Approach

This is a pedagogical exposition of the large deviation approach to sum rules pioneered by Gamboa, Nagel and Rouault. We’ll explain how to use their ideas to recover the Szegő and Killip–Simon Theorems. The primary audience is spectral theorists and people working on orthogonal polynomials who have limited familiarity with the theory of large deviations

Large Deviations and the Lukic Conjecture

We use the large deviation approach to sum rules pioneered by Gamboa, Nagel, and Rouault to prove higher-order sum rules for orthogonal polynomials on the unit circle. In particular, we prove one half of a conjectured sum rule of Lukic in the case of two singular points, one simple and one double. This is important because it is known that the conjecture of Simon fails in exactly this case, so this article provides support for the idea that Lukic’s replacement for Simon’s conjecture might be true

Finding the Beat: From Socially Coordinated Vocalizations in Songbirds to Rhythmic Entrainment in Humans

Humans and oscine songbirds share the rare capacity for vocal learning. Songbirds have the ability to acquire songs and calls of various rhythms through imitation. In several species, birds can even coordinate the timing of their vocalizations with other individuals in duets that are synchronized with millisecond-accuracy. It is not known, however, if songbirds can perceive rhythms holistically nor if they are capable of spontaneous entrainment to complex rhythms, in a manner similar to humans. Here we review emerging evidence from studies of rhythm generation and vocal coordination across songbirds and humans. In particular, recently developed experimental methods have revealed neural mechanisms underlying the temporal structure of song and have allowed us to test birds\u27 abilities to predict the timing of rhythmic social signals. Surprisingly, zebra finches can readily learn to anticipate the calls of a “vocal robot” partner and alter the timing of their answers to avoid jamming, even in reference to complex rhythmic patterns. This capacity resembles, to some extent, human predictive motor response to an external beat. In songbirds, this is driven, at least in part, by the forebrain song system, which controls song timing and is essential for vocal learning. Building upon previous evidence for spontaneous entrainment in human and non-human vocal learners, we propose a comparative framework for future studies aimed at identifying shared mechanism of rhythm production and perception across songbirds and humans

Asymptotically Unbiased Estimation of Exposure Odds Ratios in Complete Records Logistic Regression.

Missing data are a commonly occurring threat to the validity and efficiency of epidemiologic studies. Perhaps the most common approach to handling missing data is to simply drop those records with 1 or more missing values, in so-called "complete records" or "complete case" analysis. In this paper, we bring together earlier-derived yet perhaps now somewhat neglected results which show that a logistic regression complete records analysis can provide asymptotically unbiased estimates of the association of an exposure of interest with an outcome, adjusted for a number of confounders, under a surprisingly wide range of missing-data assumptions. We give detailed guidance describing how the observed data can be used to judge the plausibility of these assumptions. The results mean that in large epidemiologic studies which are affected by missing data and analyzed by logistic regression, exposure associations may be estimated without bias in a number of settings where researchers might otherwise assume that bias would occur