Peaks In Parameter Space Research Articles

Deep Follow-up for Gravitational-wave Inference: A Case Study with GW151226

New analyses of gravitational-wave events raise questions about the nature of some events. For example, LIGO–Virgo–KAGRA initially determined GW151226 to be a merger with a mass ratio q ≈ 0.5 and effective inspiral spin χ eff ≈ 0.2. However, recent works offer an alternative picture: GW151226 is a lower mass ratio event q ≈ 0.3 with slightly higher spin χ eff ≈ 0.3. This discrepancy has been challenging to resolve, as a wide range of differences are employed for each analysis. This work introduces a “deep follow-up” framework to efficiently compute the posterior odds between two different peaks in parameter space. In doing so, we aim to help resolve disputes about the true nature of gravitational-wave events associated with conflicting astrophysical interpretations. Our proposal is not a replacement for standard inference techniques; instead, our method provides a diagnostic tool to understand discrepancies between conflicting results. We demonstrate this method by studying three q–χ eff peaks proposed for GW151226. We find that the (q ∼ 0.5, χ eff ∼ 0.2) interpretation is only slightly preferred over the (q ∼ 0.3, χ eff ∼ 0.3) hypothesis with posterior odds of ∼1.7 ± 0.4, suggesting that neither of the two peaks can be ruled out. We discuss strategies to produce more reliable parameter estimation studies in gravitational-wave astronomy.

Galaxy concentrations are trimodal

We have analysed the distribution of inclination-corrected galaxy concentrations in the Sloan Digital Sky Survey. We find that unlike most galaxy properties, which are distributed bimodally, the distribution of concentrations is trimodal: it exhibits three distinct peaks. The newly discovered intermediate peak, which consists of early-type spirals and lenticulars, may contain ∼60 per cent of the number density and ∼50 per cent of the luminosity density of 0.1 M r < - 17 galaxies in the local universe. These galaxies are generally red and quiescent, although the distribution contains a tail of blue star-forming galaxies and also shows evidence of dust. The intermediate-type galaxies have higher apparent ellipticities than either disc or elliptical galaxies, most likely because some of the face-on intermediate types are misidentified as ellipticals. Their physical half-light radii are smaller than the radii of either the disc or elliptical galaxies, which may be evidence that they form from disc fading. The existence of a distinct peak in parameter space associated with early-type spiral galaxies and lenticulars implies that they have a distinct formation mechanism and are not simply the smooth transition between disc-dominated and spheroid-dominated galaxies.

Mapping the Cosmological Confidence Ball Surface

We present a new technique to compute simultaneously valid confidence intervals for a set of model parameters. We apply our method to the Wilkinson Microwave Anisotropy Probe's cosmic microwave background data, exploring a seven-dimensional space (τ,ΩDE,ΩM,ωDM,ωB,fν,ns). We find two distinct regions of interest: the standard concordance model and a region with large values of ωDM, ωB, and H0. This second peak in parameter space can be rejected by applying a constraint (or a prior) on the allowable values of the Hubble constant. Our new technique uses a nonparametric fit to the data, along with a frequentist approach and a smart search algorithm to map out a statistical confidence surface. The result is a confidence ball, a set of parameter values that contains the true value with probability at least 1 - α. Our algorithm performs a role similar to the often-used Markov Chain Monte Carlo (MCMC), which samples from the posterior probability function in order to provide Bayesian credible intervals on the parameters. While the MCMC approach samples densely around a peak in the posterior, our new technique allows cosmologists to perform efficient analyses around any regions of interest, e.g., the peak itself or, possibly more importantly, the 1 - α confidence surface.

The efficient sampling interval of the scanning parameter in the Hough transform

It is well known that in the Hough transform, the sampling interval of the scanning parameter influences the vote distribution around the peak in parameter space. Decreasing the sampling interval to improve the precision of parameters increases the computation cost, and this often becomes a major problem in applications using Hough transform. A standard that guarantees the practical precision of parameters is required for the sampling interval. In this paper, we first define two types of noise: the transformation noise, caused by the Hough transform, and the quantization noise, caused by the quantization of the image. We investigate their distribution. A condition is derived that the transformation noise must satisfy under the assumption that sufficient image resolution must be retained, and we introduce a method for deriving the upper bound of the sampling interval. © 1998 Scripta Technica, Syst Comp Jpn, 29(11): 9–19, 1998

Minimising the search space for polygon detection using the generalised Hough transform

This paper studies the application of the generalised Hough transform to the detection of polygons. When polygonal objects are randomly orientated, the dimensionality of the parameter space must in principle be augmented, and search time is increased. A method is devised for minimising this problem without introducing unnecessary peaks in parameter space. Symmetry is found to permit the removal of a large proportion of the planes in parameter space.