A Precessing Numerical Relativity Waveform Surrogate Model for Binary Black Holes: A Gaussian Process Regression Approach

Gravitational wave astrophysics relies heavily on the use of matched filtering both to detect signals in noisy data from detectors, and to perform parameter estimation on those signals. Matched filtering relies upon prior knowledge of the signals expected to be produced by a range of astrophysical systems, such as binary black holes. These waveform signals can be computed using numerical relativity techniques, where the Einstein field equations are solved numerically, and the signal is extracted from the simulation. Numerical relativity simulations are, however, computationally expensive, leading to the need for a surrogate model which can predict waveform signals in regions of the physical parameter space which have not been probed directly by simulation. We present a method for producing such a surrogate using Gaussian process regression which is trained directly on waveforms generated by numerical relativity. This model returns not just a single interpolated value for the waveform at a new point, but a full posterior probability distribution on the predicted value. This model is therefore an ideal component in a Bayesian analysis framework, through which the uncertainty in the interpolation can be taken into account when performing parameter estimation of signals.Comment: 13 pages, with 7 figures. Accepted by Physical Review

Statistical Gravitational Waveform Models: What to Simulate Next?

Models of gravitational waveforms play a critical role in detecting and characterizing the gravitational waves (GWs) from compact binary coalescences. Waveforms from numerical relativity (NR), while highly accurate, are too computationally expensive to produce to be directly used with Bayesian parameter estimation tools like Markov-chain-Monte-Carlo and nested sampling. We propose a Gaussian process regression (GPR) method to generate accurate reduced-order-model waveforms based only on existing accurate (e.g. NR) simulations. Using a training set of simulated waveforms, our GPR approach produces interpolated waveforms along with uncertainties across the parameter space. As a proof of concept, we use a training set of IMRPhenomD waveforms to build a GPR model in the 2-d parameter space of mass ratio $q$ and equal-and-aligned spin $\chi_1=\chi_2$. Using a regular, equally-spaced grid of 120 IMRPhenomD training waveforms in $q\in[1,3]$ and $\chi_1 \in [-0.5,0.5]$, the GPR mean approximates IMRPhenomD in this space to mismatches below $4.3\times 10^{-5}$. Our approach can alternatively use training waveforms directly from numerical relativity. Beyond interpolation of waveforms, we also present a greedy algorithm that utilizes the errors provided by our GPR model to optimize the placement of future simulations. In a fiducial test case we find that using the greedy algorithm to iteratively add simulations achieves GPR errors that are $\sim 1$ order of magnitude lower than the errors from using Latin-hypercube or square training grids

Educational mismatches in the EU: immigrants vs native

The purpose of this paper is to analyse and explain the factors contributing to the observed differences in skill mismatches (vertical and horizontal) between natives and immigrants in EU countries. Using microdata from the 2007 wave of the Adult Education Survey (AES), different probit models are specified and estimated to analyse differences in the probability of each type of skill mismatch between natives and immigrants. Yun's decomposition method is used to identify the relative contribution of characteristics and returns to explain the differences between the two groups. Findings: Immigrants are more likely to be skill mismatched than natives. The difference is much larger for vertical mismatch, wherein the difference is higher for immigrants coming from non-EU countries than for those coming from other EU countries. We find that immigrants from non-EU countries are less valued in EU labour markets than natives with similar characteristics -a result that is not observed for immigrants from EU countries. These results could be related to the limited transferability of human capital acquired in non-EU countries. Social implications: The findings suggest that specific programs to adapt immigrants' human capital acquired in the home country are required to reduce differences in the incidence of skill mismatch and better integration into EU labour markets. Originality: This research is original, because it distinguishes between horizontal and vertical mismatch -an issue that has not been considered in the literature on differences between native and immigrant workers- and due to the wide geographical scope of our analysis, which considers EU and non EU-countries

Computational inference in systems biology

Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem. The computational costs associated with repeatedly solving the ODEs are often high. Aimed at reducing this cost, new concepts using gradient matching have been proposed. This paper combines current adaptive gradient matching approaches, using Gaussian processes, with a parallel tempering scheme, and conducts a comparative evaluation with current methods used for parameter inference in ODEs

Gradient matching methods for computational inference in mechanistic models for systems biology: a review and comparative analysis

Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem in contemporary systems biology. Conventional methods involve repeatedly solving the ODEs by numerical integration, which is computationally onerous and does not scale up to complex systems. Aimed at reducing the computational costs, new concepts based on gradient matching have recently been proposed in the computational statistics and machine learning literature. In a preliminary smoothing step, the time series data are interpolated; then, in a second step, the parameters of the ODEs are optimised so as to minimise some metric measuring the difference between the slopes of the tangents to the interpolants, and the time derivatives from the ODEs. In this way, the ODEs never have to be solved explicitly. This review provides a concise methodological overview of the current state-of-the-art methods for gradient matching in ODEs, followed by an empirical comparative evaluation based on a set of widely used and representative benchmark data

Approximate parameter inference in systems biology using gradient matching: a comparative evaluation

Background: A challenging problem in current systems biology is that of parameter inference in biological pathways expressed as coupled ordinary differential equations (ODEs). Conventional methods that repeatedly numerically solve the ODEs have large associated computational costs. Aimed at reducing this cost, new concepts using gradient matching have been proposed, which bypass the need for numerical integration. This paper presents a recently established adaptive gradient matching approach, using Gaussian processes, combined with a parallel tempering scheme, and conducts a comparative evaluation with current state of the art methods used for parameter inference in ODEs. Among these contemporary methods is a technique based on reproducing kernel Hilbert spaces (RKHS). This has previously shown promising results for parameter estimation, but under lax experimental settings. We look at a range of scenarios to test the robustness of this method. We also change the approach of inferring the penalty parameter from AIC to cross validation to improve the stability of the method. Methodology: Methodology for the recently proposed adaptive gradient matching method using Gaussian processes, upon which we build our new method, is provided. Details of a competing method using reproducing kernel Hilbert spaces are also described here. Results: We conduct a comparative analysis for the methods described in this paper, using two benchmark ODE systems. The analyses are repeated under different experimental settings, to observe the sensitivity of the techniques. Conclusions: Our study reveals that for known noise variance, our proposed method based on Gaussian processes and parallel tempering achieves overall the best performance. When the noise variance is unknown, the RKHS method proves to be more robust

Cognitive processes in categorical and associative priming: a diffusion model analysis

Cognitive processes and mechanisms underlying different forms of priming were investigated using a diffusion model approach. In a series of 6 experiments, effects of prime-target associations and of a semantic and affective categorical match of prime and target were analyzed for different tasks. Significant associative and categorical priming effects were found in standard analyses of response times (RTs) and error frequencies. Results of diffusion model analyses revealed that priming effects of associated primes were mapped on the drift rate parameter (v), while priming effects of a categorical match on a task-relevant dimension were mapped on the extradecisional parameters (t(0) and d). These results support a spreading activation account of associative priming and an explanation of categorical priming in terms of response competition. Implications for the interpretation of priming effects and the use of priming paradigms in cognitive psychology and social cognition are discussed

Improving elevation perception with a tool for image-guided head-related transfer function selection

This paper proposes an image-guided HRTF selection procedure that exploits the relation between features of the pinna shape and HRTF notches. Using a 2D image of a subject's pinna, the procedure selects from a database the HRTF set that best fits the anthropometry of that subject. The proposed procedure is designed to be quickly applied and easy to use for a user without previous knowledge on binaural audio technologies. The entire process is evaluated by means of an auditory model for sound localization in the mid-sagittal plane available from previous literature. Using virtual subjects from a HRTF database, a virtual experiment is implemented to assess the vertical localization performance of the database subjects when they are provided with HRTF sets selected by the proposed procedure. Results report a statistically significant improvement in predictions of localization performance for selected HRTFs compared to KEMAR HRTF which is a commercial standard in many binaural audio solutions; moreover, the proposed analysis provides useful indications to refine the perceptually-motivated metrics that guides the selection