Measuring Directed Functional Connectivity Using Non-Parametric Directionality Analysis : Validation and Comparison with Non-Parametric Granger Causality

BACKGROUND: 'Non-parametric directionality' (NPD) is a novel method for estimation of directed functional connectivity (dFC) in neural data. The method has previously been verified in its ability to recover causal interactions in simulated spiking networks in Halliday et al. (2015). METHODS: This work presents a validation of NPD in continuous neural recordings (e.g. local field potentials). Specifically, we use autoregressive models to simulate time delayed correlations between neural signals. We then test for the accurate recovery of networks in the face of several confounds typically encountered in empirical data. We examine the effects of NPD under varying: a) signal-to-noise ratios, b) asymmetries in signal strength, c) instantaneous mixing, d) common drive, e) data length, and f) parallel/convergent signal routing. We also apply NPD to data from a patient who underwent simultaneous magnetoencephalography and deep brain recording. RESULTS: We demonstrate that NPD can accurately recover directed functional connectivity from simulations with known patterns of connectivity. The performance of the NPD measure is compared with non-parametric estimators of Granger causality (NPG), a well-established methodology for model-free estimation of dFC. A series of simulations investigating synthetically imposed confounds demonstrate that NPD provides estimates of connectivity that are equivalent to NPG, albeit with an increased sensitivity to data length. However, we provide evidence that: i) NPD is less sensitive than NPG to degradation by noise; ii) NPD is more robust to the generation of false positive identification of connectivity resulting from SNR asymmetries; iii) NPD is more robust to corruption via moderate amounts of instantaneous signal mixing. CONCLUSIONS: The results in this paper highlight that to be practically applied to neural data, connectivity metrics should not only be accurate in their recovery of causal networks but also resistant to the confounding effects often encountered in experimental recordings of multimodal data. Taken together, these findings position NPD at the state-of-the-art with respect to the estimation of directed functional connectivity in neuroimaging

Nonparametric estimation of the dynamic range of music signals

The dynamic range is an important parameter which measures the spread of sound power, and for music signals it is a measure of recording quality. There are various descriptive measures of sound power, none of which has strong statistical foundations. We start from a nonparametric model for sound waves where an additive stochastic term has the role to catch transient energy. This component is recovered by a simple rate-optimal kernel estimator that requires a single data-driven tuning. The distribution of its variance is approximated by a consistent random subsampling method that is able to cope with the massive size of the typical dataset. Based on the latter, we propose a statistic, and an estimation method that is able to represent the dynamic range concept consistently. The behavior of the statistic is assessed based on a large numerical experiment where we simulate dynamic compression on a selection of real music signals. Application of the method to real data also shows how the proposed method can predict subjective experts' opinions about the hifi quality of a recording

Time-Delay Interferometry

Equal-arm interferometric detectors of gravitational radiation allow phase measurements many orders of magnitude below the intrinsic phase stability of the laser injecting light into their arms. This is because the noise in the laser light is common to both arms, experiencing exactly the same delay, and thus cancels when it is differenced at the photo detector. In this situation, much lower level secondary noises then set overall performance. If, however, the two arms have different lengths (as will necessarily be the case with space-borne interferometers), the laser noise experiences different delays in the two arms and will hence not directly cancel at the detector. In order to solve this problem, a technique involving heterodyne interferometry with unequal arm lengths and independent phase-difference readouts has been proposed. It relies on properly time-shifting and linearly combining independent Doppler measurements, and for this reason it has been called Time-Delay Interferometry (or TDI). This article provides an overview of the theory and mathematical foundations of TDI as it will be implemented by the forthcoming space-based interferometers such as the Laser Interferometer Space Antenna (LISA) mission. We have purposely left out from this first version of our ``Living Review'' article on TDI all the results of more practical and experimental nature, as well as all the aspects of TDI that the data analysts will need to account for when analyzing the LISA TDI data combinations. Our forthcoming ``second edition'' of this review paper will include these topics.Comment: 51 pages, 11 figures. To appear in: Living Reviews. Added conten

Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. We present a simple nonparametric modeling technique and an algorithm implementing it - an improved and generalized version of Bayesian Blocks (Scargle 1998) - that finds the optimal segmentation of the data in the observation interval. The structure of the algorithm allows it to be used in either a real-time trigger mode, or a retrospective mode. Maximum likelihood or marginal posterior functions to measure model fitness are presented for events, binned counts, and measurements at arbitrary times with known error distributions. Problems addressed include those connected with data gaps, variable exposure, extension to piecewise linear and piecewise exponential representations, multi-variate time series data, analysis of variance, data on the circle, other data modes, and dispersed data. Simulations provide evidence that the detection efficiency for weak signals is close to a theoretical asymptotic limit derived by (Arias-Castro, Donoho and Huo 2003). In the spirit of Reproducible Research (Donoho et al. 2008) all of the code and data necessary to reproduce all of the figures in this paper are included as auxiliary material.Comment: Added some missing script files and updated other ancillary data (code and data files). To be submitted to the Astophysical Journa

Inference of population splits and mixtures from genome-wide allele frequency data

Many aspects of the historical relationships between populations in a species are reflected in genetic data. Inferring these relationships from genetic data, however, remains a challenging task. In this paper, we present a statistical model for inferring the patterns of population splits and mixtures in multiple populations. In this model, the sampled populations in a species are related to their common ancestor through a graph of ancestral populations. Using genome-wide allele frequency data and a Gaussian approximation to genetic drift, we infer the structure of this graph. We applied this method to a set of 55 human populations and a set of 82 dog breeds and wild canids. In both species, we show that a simple bifurcating tree does not fully describe the data; in contrast, we infer many migration events. While some of the migration events that we find have been detected previously, many have not. For example, in the human data we infer that Cambodians trace approximately 16% of their ancestry to a population ancestral to other extant East Asian populations. In the dog data, we infer that both the boxer and basenji trace a considerable fraction of their ancestry (9% and 25%, respectively) to wolves subsequent to domestication, and that East Asian toy breeds (the Shih Tzu and the Pekingese) result from admixture between modern toy breeds and "ancient" Asian breeds. Software implementing the model described here, called TreeMix, is available at http://treemix.googlecode.comComment: 28 pages, 6 figures in main text. Attached supplement is 22 pages, 15 figures. This is an updated version of the preprint available at http://precedings.nature.com/documents/6956/version/

Penalized Regression Splines-Based Tests for Comparing Two Time Series with Unequal Lengths

The Spline-based modeling has been an established tool for parametric and nonparametricregression modeling because of its continuous progress on theoretical and computational fronts over the last three decades. This thesis explores the idea of penalized spline modeling and goodness of fit testing in the context of time series testing in the frequency domain approach. The comparison of different time series is an important topic in statistical data analysis and has various applications in scientific research. One approach to identifying similarities or dissimilarities between two stationary processes is to compare the spectral densities of both time series. This thesis examines whether two stationary and independent time series with unequal lengths have the same spectral density. A new test statistic is proposed based on penalized splines regression. It relies on penalized splines estimator of an unspecified smooth function for the log-ratio of two spectral estimates, which are obtained from averaging out of the blocked periodograms for corresponding time series. Under the null hypothesis that two spectral densities are the same, the theoretical asymptotic distribution of the test statistic is derived. Several tests have been proposed in recent years: some of them are computationally intensive, and some lack stable size. Also, some current tests have low powers. So, we examined a relatively computationally fast and consistent test using penalized splines regression which reveals stable empirical type I error and good power properties. Simulation studies show that our proposed test is very comparable to the current test statistics in almost every case. Another advantage of our proposed test statistic is that it is very simple to construct and computationally fast based on a low-rank estimation technique

SARAS 2: A Spectral Radiometer for probing Cosmic Dawn and the Epoch of Reionization through detection of the global 21 cm signal

The global 21 cm signal from Cosmic Dawn (CD) and the Epoch of Reionization (EoR), at redshifts $z \sim 6-30$, probes the nature of first sources of radiation as well as physics of the Inter-Galactic Medium (IGM). Given that the signal is predicted to be extremely weak, of wide fractional bandwidth, and lies in a frequency range that is dominated by Galactic and Extragalactic foregrounds as well as Radio Frequency Interference, detection of the signal is a daunting task. Critical to the experiment is the manner in which the sky signal is represented through the instrument. It is of utmost importance to design a system whose spectral bandpass and additive spurious can be well calibrated and any calibration residual does not mimic the signal. SARAS is an ongoing experiment that aims to detect the global 21 cm signal. Here we present the design philosophy of the SARAS 2 system and discuss its performance and limitations based on laboratory and field measurements. Laboratory tests with the antenna replaced with a variety of terminations, including a network model for the antenna impedance, show that the gain calibration and modeling of internal additives leave no residuals with Fourier amplitudes exceeding 2~mK, or residual Gaussians of 25 MHz width with amplitudes exceeding 2~mK. Thus, even accounting for reflection and radiation efficiency losses in the antenna, the SARAS~2 system is capable of detection of complex 21-cm profiles at the level predicted by currently favoured models for thermal baryon evolution.Comment: 44 pages, 17 figures; comments and suggestions are welcom