Bayesian coherent analysis of in-spiral gravitational wave signals with a detector network

The present operation of the ground-based network of gravitational-wave laser interferometers in "enhanced" configuration brings the search for gravitational waves into a regime where detection is highly plausible. The development of techniques that allow us to discriminate a signal of astrophysical origin from instrumental artefacts in the interferometer data and to extract the full range of information are some of the primary goals of the current work. Here we report the details of a Bayesian approach to the problem of inference for gravitational wave observations using a network of instruments, for the computation of the Bayes factor between two hypotheses and the evaluation of the marginalised posterior density functions of the unknown model parameters. The numerical algorithm to tackle the notoriously difficult problem of the evaluation of large multi-dimensional integrals is based on a technique known as Nested Sampling, which provides an attractive alternative to more traditional Markov-chain Monte Carlo (MCMC) methods. We discuss the details of the implementation of this algorithm and its performance against a Gaussian model of the background noise, considering the specific case of the signal produced by the in-spiral of binary systems of black holes and/or neutron stars, although the method is completely general and can be applied to other classes of sources. We also demonstrate the utility of this approach by introducing a new coherence test to distinguish between the presence of a coherent signal of astrophysical origin in the data of multiple instruments and the presence of incoherent accidental artefacts, and the effects on the estimation of the source parameters as a function of the number of instruments in the network.Comment: 22 page

A Bayesian approach to the follow-up of candidate gravitational wave signals

Ground-based gravitational wave laser interferometers (LIGO, GEO-600, Virgo and Tama-300) have now reached high sensitivity and duty cycle. We present a Bayesian evidence-based approach to the search for gravitational waves, in particular aimed at the followup of candidate events generated by the analysis pipeline. We introduce and demonstrate an efficient method to compute the evidence and odds ratio between different models, and illustrate this approach using the specific case of the gravitational wave signal generated during the inspiral phase of binary systems, modelled at the leading quadrupole Newtonian order, in synthetic noise. We show that the method is effective in detecting signals at the detection threshold and it is robust against (some types of) instrumental artefacts. The computational efficiency of this method makes it scalable to the analysis of all the triggers generated by the analysis pipelines to search for coalescing binaries in surveys with ground-based interferometers, and to a whole variety of signal waveforms, characterised by a larger number of parameters.Comment: 9 page

Application of Bryan's algorithm to the mobility spectrum analysis of semiconductor devices

A powerful method for mobility spectrum analysis is presented, based on Bryan's maximum entropy algorithm. The Bayesian analysis central to Bryan's algorithm ensures that we avoid overfitting of data, resulting in a physically reasonable solution. The algorithm is fast, and allows the analysis of large quantities of data, removing the bias of data selection inherent in all previous techniques. Existing mobility spectrum analysis systems are reviewed, and the performance of the Bryan's algorithm mobility spectrum (BAMS) approach is demonstrated using synthetic data sets. Analysis of experimental data is briefly discussed. We find that BAMS performs well compared to existing mobility spectrum methods

Fitting the Phenomenological MSSM

We perform a global Bayesian fit of the phenomenological minimal supersymmetric standard model (pMSSM) to current indirect collider and dark matter data. The pMSSM contains the most relevant 25 weak-scale MSSM parameters, which are simultaneously fit using `nested sampling' Monte Carlo techniques in more than 15 years of CPU time. We calculate the Bayesian evidence for the pMSSM and constrain its parameters and observables in the context of two widely different, but reasonable, priors to determine which inferences are robust. We make inferences about sparticle masses, the sign of the $\mu$ parameter, the amount of fine tuning, dark matter properties and the prospects for direct dark matter detection without assuming a restrictive high-scale supersymmetry breaking model. We find the inferred lightest CP-even Higgs boson mass as an example of an approximately prior independent observable. This analysis constitutes the first statistically convergent pMSSM global fit to all current data.Comment: Added references, paragraph on fine-tunin

Fitting in a complex chi^2 landscape using an optimized hypersurface sampling

Fitting a data set with a parametrized model can be seen geometrically as finding the global minimum of the chi^2 hypersurface, depending on a set of parameters {P_i}. This is usually done using the Levenberg-Marquardt algorithm. The main drawback of this algorithm is that despite of its fast convergence, it can get stuck if the parameters are not initialized close to the final solution. We propose a modification of the Metropolis algorithm introducing a parameter step tuning that optimizes the sampling of parameter space. The ability of the parameter tuning algorithm together with simulated annealing to find the global chi^2 hypersurface minimum, jumping across chi^2{P_i} barriers when necessary, is demonstrated with synthetic functions and with real data

A Bayesian Approach to the Detection Problem in Gravitational Wave Astronomy

The analysis of data from gravitational wave detectors can be divided into three phases: search, characterization, and evaluation. The evaluation of the detection - determining whether a candidate event is astrophysical in origin or some artifact created by instrument noise - is a crucial step in the analysis. The on-going analyses of data from ground based detectors employ a frequentist approach to the detection problem. A detection statistic is chosen, for which background levels and detection efficiencies are estimated from Monte Carlo studies. This approach frames the detection problem in terms of an infinite collection of trials, with the actual measurement corresponding to some realization of this hypothetical set. Here we explore an alternative, Bayesian approach to the detection problem, that considers prior information and the actual data in hand. Our particular focus is on the computational techniques used to implement the Bayesian analysis. We find that the Parallel Tempered Markov Chain Monte Carlo (PTMCMC) algorithm is able to address all three phases of the anaylsis in a coherent framework. The signals are found by locating the posterior modes, the model parameters are characterized by mapping out the joint posterior distribution, and finally, the model evidence is computed by thermodynamic integration. As a demonstration, we consider the detection problem of selecting between models describing the data as instrument noise, or instrument noise plus the signal from a single compact galactic binary. The evidence ratios, or Bayes factors, computed by the PTMCMC algorithm are found to be in close agreement with those computed using a Reversible Jump Markov Chain Monte Carlo algorithm.Comment: 19 pages, 12 figures, revised to address referee's comment

A Bayesian Approach to Inverse Quantum Statistics

A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over potentials implemented in form of stochastic processes. Its specific advantages are the possibilities to deal with heterogeneous data and to express a priori information explicitly, i.e., directly in terms of the potential of interest. A numerical solution in maximum a posteriori approximation was feasible for one--dimensional problems. Using correct a priori information turned out to be essential.Comment: 4 pages, 6 figures, revte

Inferring Core-Collapse Supernova Physics with Gravitational Waves

Stellar collapse and the subsequent development of a core-collapse supernova explosion emit bursts of gravitational waves (GWs) that might be detected by the advanced generation of laser interferometer gravitational-wave observatories such as Advanced LIGO, Advanced Virgo, and LCGT. GW bursts from core-collapse supernovae encode information on the intricate multi-dimensional dynamics at work at the core of a dying massive star and may provide direct evidence for the yet uncertain mechanism driving supernovae in massive stars. Recent multi-dimensional simulations of core-collapse supernovae exploding via the neutrino, magnetorotational, and acoustic explosion mechanisms have predicted GW signals which have distinct structure in both the time and frequency domains. Motivated by this, we describe a promising method for determining the most likely explosion mechanism underlying a hypothetical GW signal, based on Principal Component Analysis and Bayesian model selection. Using simulated Advanced LIGO noise and assuming a single detector and linear waveform polarization for simplicity, we demonstrate that our method can distinguish magnetorotational explosions throughout the Milky Way (D <~ 10kpc) and explosions driven by the neutrino and acoustic mechanisms to D <~ 2kpc. Furthermore, we show that we can differentiate between models for rotating accretion-induced collapse of massive white dwarfs and models of rotating iron core collapse with high reliability out to several kpc.Comment: 22 pages, 9 figure

Multisite Weather Generators Using Bayesian Networks: An Illustrative Case Study for Precipitation Occurrence

ABSTRACT: Many existing approaches for multisite weather generation try to capture several statistics of the observed data (e.g. pairwise correlations) in order to generate spatially and temporarily consistent series. In this work we analyse the application of Bayesian networks to this problem, focusing on precipitation occurrence and considering a simple case study to illustrate the potential of this new approach. We use Bayesian networks to approximate the multi-variate (-site) probability distribution of observed gauge data, which is factorized according to the relevant (marginal and conditional) dependencies. This factorization allows the simulation of synthetic samples from the multivariate distribution, thus providing a sound and promising methodology for multisite precipitation series generation.We acknowledge funding provided by the project MULTI‐SDM (CGL2015‐ 66583‐R, MINECO/FEDER)

Light pseudoscalar decay constants, quark masses, and low energy constants from three-flavor lattice QCD

As part of our program of lattice simulations of three flavor QCD with improved staggered quarks, we have calculated pseudoscalar meson masses and decay constants for a range of valence quark masses and sea quark masses on lattices with lattice spacings of about 0.125 fm and 0.09 fm. We fit the lattice data to forms computed with staggered chiral perturbation theory. Our results provide a sensitive test of the lattice simulations, and especially of the chiral behavior, including the effects of chiral logarithms. We find: f_\pi=129.5(0.9)(3.5)MeV, f_K=156.6(1.0)(3.6)MeV, and f_K/f_\pi=1.210(4)(13), where the errors are statistical and systematic. Following a recent paper by Marciano, our value of f_K/f_\pi implies |V_{us}|=0.2219(26). Further, we obtain m_u/m_d= 0.43(0)(1)(8), where the errors are from statistics, simulation systematics, and electromagnetic effects, respectively. The data can also be used to determine several of the constants of the low energy effective Lagrangian: in particular we find 2L_8-L_5=-0.2(1)(2) 10^{-3} at chiral scale m_\eta. This provides an alternative (though not independent) way of estimating m_u; 2L_8-L_5 is far outside the range that would allow m_u=0. Results for m_s^\msbar, \hat m^\msbar, and m_s/\hat m can be obtained from the same lattice data and chiral fits, and have been presented previously in joint work with the HPQCD and UKQCD collaborations. Using the perturbative mass renormalization reported in that work, we obtain m_u^\msbar=1.7(0)(1)(2)(2)MeV and m_d^\msbar=3.9(0)(1)(4)(2)MeV at scale 2 GeV, with errors from statistics, simulation, perturbation theory, and electromagnetic effects, respectively.Comment: 86 pages, 22 figures. v3: Remarks about m_u=0 and the strong CP problem modified; reference added. Figs 5--8 modified for clarity. Version to be published in Phys. Rev. D. v2: Expanded discussion of finite volume effects, normalization in Table I fixed, typos and minor errors correcte