Comparison of statistical sampling methods with ScannerBit, the GAMBIT scanning module [CL]

We introduce ScannerBit, the statistics and sampling module of the public, open-source global fitting framework Gambit. ScannerBit provides a standardised interface to different sampling algorithms, enabling the use and comparison of multiple computational methods for inferring profile likelihoods, Bayesian posteriors, and other statistical quantities. The current version offers random, grid, raster, nested sampling, differential evolution, Markov Chain Monte Carlo (MCMC) and ensemble Monte Carlo samplers. We also announce the release of a new standalone differential evolution sampler, Diver, and describe its design, usage and interface to ScannerBit. We subject Diver and three other samplers (the nested sampler MultiNest, the MCMC GreAT, and the native ScannerBit implementation of the ensemble Monte Carlo algorithm TWalk) to a battery of statistical tests. For this we use a realistic physical likelihood function, based on the scalar singlet model of dark matter. We examine the performance of each sampler as a function of its adjustable settings, and the dimensionality of the sampling problem. We evaluate performance on four metrics: optimality of the best fit found, completeness in exploring the best-fit region, number of likelihood evaluations, and total runtime. For Bayesian posterior estimation at high resolution, TWalk provides the most accurate and timely mapping of the full parameter space. For profile likelihood analysis in less than about ten dimensions, we find that Diver and MultiNest score similarly in terms of best fit and speed, outperforming GreAT and TWalk; in ten or more dimensions, Diver substantially outperforms the other three samplers on all metrics.

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G. Workgroup, G. Martinez, J. McKay, et. al.
Wed, 24 May 17

Comments: 46 pages, 18 figures, 2 tables, submitted to EPJC

Noisy independent component analysis of auto-correlated components [CL]

We present a new method for the separation of superimposed, independent, auto-correlated com- ponents from noisy multi-channel measurement. The presented method simultaneously reconstructs and separates the components, taking all channels into account and thereby increases the effective signal-to-noise ratio considerably, allowing separations even in the high noise regime. Characteristics of the measurement instruments can be included, allowing for application in complex measurement situations. Independent posterior samples can be provided, permitting error estimates on all de- sired quantities. Using the concept of information field theory, the algorithm is not restricted to any dimensionality of the underlying space or discretization scheme thereof.

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J. Knollmuller and T. Ensslin
Tue, 9 May 17

Comments: N/A

Recurrence network measures for hypothesis testing using surrogate data: application to black hole light curves [CL]

Recurrence networks and the associated statistical measures have become important tools in the analysis of time series data. In this work, we test how effective the recurrence network measures are in analyzing real world data involving two main types of noise, white noise and colored noise. We use two prominent network measures as discriminating statistic for hypothesis testing using surrogate data for a specific null hypothesis that the data is derived from a linear stochastic process. We show that the characteristic path length is especially efficient as a discriminating measure with the conclusions reasonably accurate even with limited number of data points in the time series. We also highlight an additional advantage of the network approach in identifying the dimensionality of the system underlying the time series through a convergence measure derived from the probability distribution of the local clustering coefficients. As examples of real world data, we use the light curves from a prominent black hole system and show that a combined analysis using three primary network measures can provide vital information regarding the nature of temporal variability of light curves from different spectroscopic classes.

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R. Jacob, K. Harikrishnan, R. Misra, et. al.
Fri, 28 Apr 17

Comments: 29 pages, 15 figures, submitted to . Communications in Nonlinear Science and Numerical Simulation

Multifractal Analysis of Pulsar Timing Residuals: Assessment of Gravitational Waves Detection [SSA]

Relying on multifractal behavior of pulsar timing residuals ({\it PTR}s), we examine the capability of Multifractal Detrended Fluctuation Analysis (MF-DFA) and Multifractal Detrending Moving Average Analysis (MF-DMA) modified by Singular Value Decomposition (SVD) and Adaptive Detrending (AD), to detect footprint of gravitational waves (GWs) superimposed on {\it PTR}s. Mentioned methods enable us to clarify the type of GWs which is related to the value of Hurst exponent. We introduce three strategies based on generalized Hurst exponent and width of singularity spectrum, to determine the dimensionless amplitude of GWs. For a stochastic gravitational wave background with characteristic strain spectrum as $\mathcal{H}c(f)\sim \mathcal{A}f^{\zeta}$, the dimensionless amplitude greater than $\mathcal{A}\gtrsim 10^{-17}$ can be recognized irrespective to value of $\zeta$. We also utilize MF-DFA and MF-DMA to explore 20 millisecond pulsars observed by Parkes Pulsar Timing Array (PPTA). Our analysis demonstrates that there exists a cross-over in fluctuation function versus time scale for observed timing residuals representing a universal property and equates to $s{\times}\sim60$ days. To asses multifractal nature of observed timing residuals, we apply AD and SVD algorithms on time series as pre-processes to remove superimposed trends as much as possible. The scaling exponents determined by MF-DFA and MF-DMA confirm that, all data are classified in non-stationary class elucidating second universality feature. The value of corresponding Hurst exponent is in interval $H \in [0.35,0.85]$. The $q$-dependency of generalized Hurst exponent demonstrates observed {\it PTR}s have multifractal behavior and the source of this multifractality is mainly devoted to correlation of data which is another universality of observed data sets.

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I. Eghdami, H. Panahi and S. Movahed
Fri, 28 Apr 17

Comments: 17 pages, 13 figures and 2 tables

A Fresh Approach to Forecasting in Astroparticle Physics and Dark Matter Searches [IMA]

We present a toolbox of new techniques and concepts for the efficient forecasting of experimental sensitivities. These are applicable to a large range of scenarios in (astro-)particle physics, and based on the Fisher information formalism. Fisher information provides an answer to the question what is the maximum extractable information from a given observation?. It is a common tool for the forecasting of experimental sensitivities in many branches of science, but rarely used in astroparticle physics or searches for particle dark matter. After briefly reviewing the Fisher information matrix of general Poisson likelihoods, we propose very compact expressions for estimating expected exclusion and discovery limits (equivalent counts method). We demonstrate by comparison with Monte Carlo results that they remain surprisingly accurate even deep in the Poisson regime. We show how correlated background systematics can be efficiently accounted for by a treatment based on Gaussian random fields. Finally, we introduce the novel concept of Fisher information flux. It can be thought of as a generalization of the commonly used signal-to-noise ratio, while accounting for the non-local properties and saturation effects of background and instrumental uncertainties. It is a powerful and flexible tool ready to be used as core concept for informed strategy development in astroparticle physics and searches for particle dark matter.

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T. Edwards and C. Weniger
Thu, 20 Apr 17

Comments: 19 pages, 12 figures

Dynamic nested sampling: an improved algorithm for parameter estimation and evidence calculation [CL]

We introduce dynamic nested sampling: a generalisation of the nested sampling algorithm in which the number of “live points” varies to allocate samples more efficiently. In empirical tests the new method increases accuracy by up to a factor of ~8 for parameter estimation and ~3 for evidence calculation compared to standard nested sampling with the same number of samples – equivalent to speeding up the computation by factors of ~64 and ~9 respectively. In addition unlike in standard nested sampling more accurate results can be obtained by continuing the calculation for longer. Dynamic nested sampling can be easily included in existing nested sampling software such as MultiNest and PolyChord.

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E. Higson, W. Handley, M. Hobson, et. al.
Thu, 13 Apr 17

Comments: 16 pages + appendix, 8 figures, submitted to Bayesian Analysis. arXiv admin note: text overlap with arXiv:1703.09701

Periodic behaviour of coronal mass ejections, eruptive events, and solar activity proxies during solar cycles 23 and 24 [SSA]

We report on the parallel analysis of the periodic behaviour of coronal mass ejections (CMEs) based on 21 years [1996-2016] of observations with the SOHO/LASCO-C2 coronagraph, solar flares, prominences, and several proxies of solar activity. We consider values of the rates globally and whenever possible, distinguish solar hemispheres and solar cycles 23 and 24. Periodicities are investigated using both frequency (periodogram) and time-frequency (wavelet) analysis. We find that these different processes, in addition to following the ~11-year Solar Cycle, exhibit diverse statistically significant oscillations with properties common to all solar, coronal, and heliospheric processes: variable periodicity, intermittency, asymmetric development in the northern and southern solar hemispheres, and largest amplitudes during the maximum phase of solar cycles, being more pronounced during solar cycle 23 than the weaker cycle 24. However, our analysis reveals an extremely complex and diverse situation. For instance, there exists very limited commonality for periods of less than one year. The few exceptions are the periods of 3.1-3.2 months found in the global occurrence rates of CMEs and in the sunspot area (SSA) and those of 5.9-6.1 months found in the northern hemisphere. Mid-range periods of ~1 and ~2 years are more wide spread among the studied processes, but exhibit a very distinct behaviour with the first one being present only in the northern hemisphere and the second one only in the southern hemisphere. These periodic behaviours likely results from the complexity of the underlying physical processes, prominently the emergence of magnetic flux.

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T. Barlyaeva, J. Wojak, P. Lamy, et. al.
Tue, 11 Apr 17

Comments: 32 pages, 15 figures, 2 tables