How will our knowledge of short gamma-ray bursts affect the distance measurement of binary neutron stars?

Gravitational waves from binary neutron stars associated with short gamma-ray bursts have drawn considerable attention due to their prospect in cosmology. For such events, the sky locations of sources can be pinpointed with techniques such as identifying the host galaxies. However, the cosmological applications of these events still suffer from the problem of degeneracy between luminosity distance and inclination angle. To address this issue, a technique was proposed in previous study, i.e., using the collimation property of short gamma-ray bursts. Based on the observations, we assume that the cosine of inclination follows a Gaussian distribution, which may act as a prior in the Bayes analysis to break the degeneracy. This paper investigates the effects of different Gaussian priors and detector configurations on distance measurement and cosmological research. We first derive a simplified Fisher information matrix for demonstration, and then conduct quantitative analyses via simulation. By varying the number of third-generation detectors and the scale of prior, we generate four catalogs of 1000 events. It is shown that, in the same detecting period, a network of detectors can recognize more and farther events than a single detector. Besides, adopting tighter prior and employing multiple detectors both decrease the error of luminosity distance. Also considered is the performance of a widely adopted formula in the error budget, which turns out to be a conservative choice in each case. As for cosmological applications, for the ΛCDM model, 500, 200, 600, and 300 events are required for the four configurations to achieve 1% H0 accuracy. With all 1000 events in each catalog, H0 and Ωm can be constrained to (0.66%, 0.37%, 0.76%, 0.49%), and (0.010, 0.006, 0.013, 0.010), respectively. The results of the Gaussian process also show that the gravitational wave standard siren can serve as a probe of cosmology at high redshifts.

Bayesian regions of evidence (for normal distributions)

Bayesian data analysis allows a researcher to assess whether a claim about an effect (e.g. effect > 0, effect > Δ, |effect| < Δ)) is justified given the data and a prior distribution, expressing her or his personal belief before seeing the data. However, the recipients of the analysis might use different priors, so it remains unclear whether they would share the claim. "Reverse Bayes" analysis and the "sufficiently sceptical prior" address this problem by asking how strongly one may believe in the absence of an effect in order to be convinced otherwise by the data. A method called "Region of Evidence" is presented that takes this idea and extends it for any normal prior (and a normally distributed estimate). It visualises all the priors that, if they had been used, would support the claim, including those that favour a positive or negative effect. Since the method depends only on an estimate and its standard error, it can be easily applied to previously published results. The paper describes the method and its implementation in a new Stata command called arevi, which can be freely used and modified.

Evaluation of the Use of a Road Diet Design: An Urban Corridor Case Study in Washington, DC

A traditional road diet design converts a four-lane two-way road to a three-lane road consisting of two through lanes and a center two-way left turn lane. This paper introduces a new application of the road diet design in an urban corridor. Specifically, the new application converts a four-lane two-way road into a two-lane two-way road with full-time parking lanes in both directions. The paper analyzed the traffic impacts of the road diet application on the corridor of New Jersey Avenue, northwest, in the city of Washington, District of Columbia. The corridor included five signalized and one unsignalized intersections. Before-and-after analyses using Synchro 11 simulation and Site-Specific Empirical Bayes analysis were used to evaluate and compare existing and proposed scenarios. The proposed scenario provided various benefits including offering accessibility to the businesses in the area and acting as a traffic calming strategy. For signalized intersections, the overall performance remained the same for most intersections except for one intersection (on P Street), as it is significantly impacted by the road diet design due to the dramatic increase of traffic volumes in its minor streets as a result of diverting traffic volumes from the unsignalized intersection for left and through movements. Results showed that the use of a road diet design enhanced the unsignalized intersection performance due to the traffic volume divergence from its minor streets and enhanced the safety of the study area by decreasing the annual number of predicted crashes. To achieve better operational benefits and reflect traffic demands, the paper recommends to re-optimize signal timings when a road diet design is adopted.

A Hierarchical Bayes Analysis and Comparison of PH Weibull and PH Exponential Models for One-Shot Device Testing Experiment

The one-shot devices are highly reliable and, therefore, accelerated life tests are often employed to perform the experiments on such devices. Obviously, in the process, some covariates are introduced. This paper considers the proportional hazards model to observe the effect of covariates on the failure rates under the assumption of two commonly used models, namely the exponential and the Weibull for the lifetimes. The Bayes implementation is proposed using the hybridization of Gibbs and Metropolis algorithms that routinely extend to missing data situations as well. The entertained models are compared using the Bayesian and deviance information criteria and the expected posterior predictive loss criterion. Finally, the results based on two real data examples are given as an illustration.