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Register a new userSherpa: a Mission-Independent Data Analysis Application
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The ever-increasing quality and complexity of astronomical data underscores the need for new and powerful data analysis applications. This need has led to the development of Sherpa, a modeling and fitting program in the CIAO software package that enables the analysis of multi-dimensional, multi-wavelength data. In this paper, we present an overview of Sherpas features, which include: support for a wide variety of input and output data formats, including the new Model Descriptor List (MDL) format; a model language which permits the construction of arbitrarily complex model expressions, including ones representing instrument characteristics; a wide variety of fit statistics and methods of optimization, model comparison, and parameter estimation; multi-dimensional visualization, provided by ChIPS; and new interactive analysis capabilities provided by embedding the S-Lang interpreted scripting language. We conclude by showing example Sherpa analysis sessions.
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We apply the independent component analysis (ICA) to the real data from a gravitational wave detector for the first time. Specifically we use the iKAGRA data taken in April 2016, and calculate the correlations between the gravitational wave strain channel and 35 physical environmental channels. Using a couple of seismic channels which are found to be strongly correlated with the strain, we perform ICA. Injecting a sinusoidal continuous signal in the strain channel, we find that ICA recovers correct parameters with enhanced signal-to-noise ratio, which demonstrates usefulness of this method. Among the two implementations of ICA used here, we find the correlation method yields the optimal result for the case environmental noises act on the strain channel linearly.
After performing highly sensitive acceleration measurements during two years of drag-free flight around the Earth, MICROSCOPE provided the best constraint on the Weak Equivalence Principle (WEP) to date. Beside being a technological challenge, this experiment required a specialised data analysis pipeline to look for a potential small signal buried in the noise, possibly plagued by instrumental defects, missing data and glitches. This paper describes the frequency-domain iterative least-square technique that we developed for MICROSCOPE. In particular, using numerical simulations, we prove that our estimator is unbiased and provides correct error bars. This paper therefore justifies the robustness of the WEP measurements given by MICROSCOPE.
The analysis of physical measurements often copes with highly correlated noises and interruptions caused by outliers, saturation events or transmission losses. We assess the impact of missing data on the performance of linear regression analysis involving the fit of modeled or measured time series. We show that data gaps can significantly alter the precision of the regression parameter estimation in the presence of colored noise, due to the frequency leakage of the noise power. We present a regression method which cancels this effect and estimates the parameters of interest with a precision comparable to the complete data case, even if the noise power spectral density (PSD) is not known a priori. The method is based on an autoregressive (AR) fit of the noise, which allows us to build an approximate generalized least squares estimator approaching the minimal variance bound. The method, which can be applied to any similar data processing, is tested on simulated measurements of the MICROSCOPE space mission, whose goal is to test the Weak Equivalence Principle (WEP) with a precision of $10^{-15}$. In this particular context the signal of interest is the WEP violation signal expected to be found around a well defined frequency. We test our method with different gap patterns and noise of known PSD and find that the results agree with the mission requirements, decreasing the uncertainty by a factor 60 with respect to ordinary least squares methods. We show that it also provides a test of significance to assess the uncertainty of the measurement.
Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is challenging as the application of standard multivariate analysis tools on the raw observations can lead to spurious results. Hence, it is appropriate to apply certain transformations prior further analysis. One popular multivariate data analysis tool is independent component analysis. Independent component analysis aims to find statistically independent components in the data and as such might be seen as an extension to principal component analysis. In this paper we examine an approach of how to apply independent component analysis on compositional data by respecting the nature of the former and demonstrate the usefulness of this procedure on a metabolomic data set.
In the last two decades, unsupervised latent variable models---blind source separation (BSS) especially---have enjoyed a strong reputation for the interpretable features they produce. Seldom do these models combine the rich diversity of information available in multiple datasets. Multidatasets, on the other hand, yield joint solutions otherwise unavailable in isolation, with a potential for pivotal insights into complex systems. To take advantage of the complex multidimensional subspace structures that capture underlying modes of shared and unique variability across and within datasets, we present a direct, principled approach to multidataset combination. We design a new method called multidataset independent subspace analysis (MISA) that leverages joint information from multiple heterogeneous datasets in a flexible and synergistic fashion. Methodological innovations exploiting the Kotz distribution for subspace modeling in conjunction with a novel combinatorial optimization for evasion of local minima enable MISA to produce a robust generalization of independent component analysis (ICA), independent vector analysis (IVA), and independent subspace analysis (ISA) in a single unified model. We highlight the utility of MISA for multimodal information fusion, including sample-poor regimes and low signal-to-noise ratio scenarios, promoting novel applications in both unimodal and multimodal brain imaging data.
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