Browsing by Subject "methods: statistical"
Now showing items 1-13 of 13
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(2017)We propose a new mathematical model for n - k-dimensional non-linear correlations with intrinsic scatter in n-dimensional data. The model is based on Riemannian geometry and is naturally symmetric with respect to the measured variables and invariant under coordinate transformations. We combine the model with a Bayesian approach for estimating the parameters of the correlation relation and the intrinsic scatter. A side benefit of the approach is that censored and truncated data sets and independent, arbitrary measurement errors can be incorporated. We also derive analytic likelihoods for the typical astrophysical use case of linear relations in n-dimensional Euclidean space. We pay particular attention to the case of linear regression in two dimensions and compare our results to existing methods. Finally, we apply our methodology to the well-known MBH-s correlation between the mass of a supermassive black hole in the centre of a galactic bulge and the corresponding bulge velocity dispersion. The main result of our analysis is that the most likely slope of this correlation is similar to 6 for the data sets used, rather than the values in the range of similar to 4-5 typically quoted in the literature for these data.
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(2020)Context. We assess statistical inversion of asteroid rotation periods, pole orientations, shapes, and phase curve parameters from photometric lightcurve observations, here sparse data from the ESA Gaia space mission (Data Release 2) or dense and sparse data from ground-based observing programs.Aims. Assuming general convex shapes, we develop inverse methods for characterizing the Bayesian a posteriori probability density of the parameters (unknowns). We consider both random and systematic uncertainties (errors) in the observations, and assign weights to the observations with the help of Bayesian a priori probability densities.Methods. For general convex shapes comprising large numbers of parameters, we developed a Markov-chain Monte Carlo sampler (MCMC) with a novel proposal probability density function based on the simulation of virtual observations giving rise to virtual least-squares solutions. We utilized these least-squares solutions to construct a proposal probability density for MCMC sampling. For inverse methods involving triaxial ellipsoids, we update the uncertainty model for the observations.Results. We demonstrate the utilization of the inverse methods for three asteroids with Gaia photometry from Data Release 2: (21) Lutetia, (26) Proserpina, and (585) Bilkis. First, we validated the convex inverse methods using the combined ground-based and Gaia data for Lutetia, arriving at rotation and shape models in agreement with those derived with the help of Rosetta space mission data. Second, we applied the convex inverse methods to Proserpina and Bilkis, illustrating the potential of the Gaia photometry for setting constraints on asteroid light scattering as a function of the phase angle (the Sun-object-observer angle). Third, with the help of triaxial ellipsoid inversion as applied to Gaia photometry only, we provide additional proof that the absolute Gaia photometry alone can yield meaningful photometric slope parameters. Fourth, for (585) Bilkis, we report, with 1-sigma uncertainties, a refined rotation period of (8.5750559 0.0000026) h, pole longitude of 320.6 degrees +/- 1.2 degrees, pole latitude of - 25.6 degrees +/- 1.7 degrees, and the first shape model and its uncertainties from convex inversion.Conclusions. We conclude that the inverse methods provide realistic uncertainty estimators for the lightcurve inversion problem and that the Gaia photometry can provide an asteroid taxonomy based on the phase curves.
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(2019)Analyses of 15,314 electron velocity distribution functions (VDFs) within +/- 2 hr of 52 interplanetary (IP) shocks observed by the Wind spacecraft near 1 au are introduced. The electron VDFs are fit to the sum of three model functions for the cold dense core, hot tenuous halo, and field-aligned beam/strahl component. The best results were found by modeling the core as either a bi-kappa or a symmetric (or asymmetric) bi-self-similar VDF, while both the halo and beam/strahl components were best fit to bi-kappa VDF. This is the first statistical study to show that the core electron distribution is better fit to a self-similar VDF than a bi-Maxwellian under all conditions. The self-similar distribution deviation from a Maxwellian is a measure of inelasticity in particle scattering from waves and/or turbulence. The ranges of values defined by the lower and upper quartiles for the kappa exponents are k(ec) similar to 5.40-10.2 for the core, k(eh) similar to 3.58-5.34 for the halo, and k(eb) similar to 3.40-5.16 for the beam/strahl. The lower-to-upper quartile range of symmetric bi-self-similar core exponents is s(ec) similar to 2.00-2.04, and those of asymmetric bi-self-similar core exponents are p(ec) similar to 2.20-4.00 for the parallel exponent and q(ec) similar to 2.00-2.46 for the perpendicular exponent. The nuanced details of the fit procedure and description of resulting data product are also presented. The statistics and detailed analysis of the results are presented in Paper II and Paper III of this three-part study.
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(2020)Context. In metric theories of gravity with photon number conservation, the luminosity and angular diameter distances are related via the Etherington relation, also known as the distance duality relation (DDR). A violation of this relation would rule out the standard cosmological paradigm and point to the presence of new physics.Aims. We quantify the ability of Euclid, in combination with contemporary surveys, to improve the current constraints on deviations from the DDR in the redshift range 0<z<1.6.Methods. We start with an analysis of the latest available data, improving previously reported constraints by a factor of 2.5. We then present a detailed analysis of simulated Euclid and external data products, using both standard parametric methods (relying on phenomenological descriptions of possible DDR violations) and a machine learning reconstruction using genetic algorithms.Results. We find that for parametric methods Euclid can (in combination with external probes) improve current constraints by approximately a factor of six, while for non-parametric methods Euclid can improve current constraints by a factor of three.Conclusions. Our results highlight the importance of surveys like Euclid in accurately testing the pillars of the current cosmological paradigm and constraining physics beyond the standard cosmological model.
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(2019)We present a new power spectrum emulator named EuclidEmulator that estimates the nonlinear correction to the linear dark matter power spectrum depending on the six cosmological parameters ωb, ωm, ns, h, w0, and σ8. It is constructed using the uncertainty quantification software UQLab using a spectral decomposition method called polynomial chaos expansion. All steps in its construction have been tested and optimized: the large highresolution N-body simulations carried out with PKDGRAV3 were validated using a simulation from the Euclid Flagship campaign and demonstrated to have converged up to wavenumbers k ≈ 5 h Mpc−1 for redshifts z ≤ 5. The emulator is based on 100 input cosmologies simulated in boxes of (1250 Mpc/h)3 using 20483 particles. We show that by creating mock emulators it is possible to successfully predict and optimize the performance of the final emulator prior to performing any N-body simulations. The absolute accuracy of the final nonlinear power spectrum is as good as one obtained with N-body simulations, conservatively, ∼1 per cent for k 1 h Mpc−1 and z 1. This enables efficient forward modelling in the nonlinear regime, allowing for estimation of cosmological parameters using Markov ChainMonteCarlo methods. EuclidEmulator has been compared to HALOFIT, CosmicEmu, and NGenHalofit, and shown to be more accurate than these other approaches. This work paves a new way for optimal construction of future emulators that also consider other cosmological observables, use higher resolution input simulations, and investigate higher dimensional cosmological parameter spaces.
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(2021)We present a new, updated version of the EuclidEmulator (called EuclidEmulator2), a fast and accurate predictor for the nonlinear correction of the matter power spectrum. 2 per cent level accurate emulation is now supported in the eight-dimensional parameter space of w(0)w(a)CDM+Sigma m(nu) models between redshift z = 0 and z = 3 for spatial scales within the range . In order to achieve this level of accuracy, we have had to improve the quality of the underlying N-body simulations used as training data: (i) we use self-consistent linear evolution of non-dark matter species such as massive neutrinos, photons, dark energy, and the metric field, (ii) we perform the simulations in the so-called N-body gauge, which allows one to interpret the results in the framework of general relativity, (iii) we run over 250 high-resolution simulations with 3000(3) particles in boxes of 1(h(-1)Gpc)(3) volumes based on paired-and-fixed initial conditions, and (iv) we provide a resolution correction that can be applied to emulated results as a post-processing step in order to drastically reduce systematic biases on small scales due to residual resolution effects in the simulations. We find that the inclusion of the dynamical dark energy parameter w(a) significantly increases the complexity and expense of creating the emulator. The high fidelity of EuclidEmulator2 is tested in various comparisons against N-body simulations as well as alternative fast predictors such as HALOFIT, HMCode, and CosmicEmu. A blind test is successfully performed against the Euclid Flagship v2.0 simulation. Nonlinear correction factors emulated with EuclidEmulator2 are accurate at the level of or better for and z
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(2021)The analysis of weak gravitational lensing in wide-field imaging surveys is considered to be a major cosmological probe of dark energy. Our capacity to constrain the dark energy equation of state relies on an accurate knowledge of the galaxy mean redshift z. We investigate the possibility of measuring z with an accuracy better than 0.002 (1+z) in ten tomographic bins spanning the redshift interval 0.2 99.8%. The zPDF approach can also be successful if the zPDF is de-biased using a spectroscopic training sample. This approach requires deep imaging data but is weakly sensitive to spectroscopic redshift failures in the training sample. We improve the de-biasing method and confirm our finding by applying it to real-world weak-lensing datasets (COSMOS and KiDS+VIKING-450).
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(2022)Context. Gaia Data Release 2 (DR2) includes milliarcsecond-accuracy astrometry for 14 099 asteroids. One of the main expected scientific applications of these data is asteroid mass estimation via the modeling of perturbations during asteroid-asteroid encounters. Aims. We explore the practical impact of the Gaia astrometry of asteroids for the purpose of asteroid mass and orbit estimation by estimating the masses individually for four large asteroids. We use various combinations of Gaia astrometry and/or Earth-based astrometry so as to determine the impact of Gaia on the estimated masses. By utilizing published information about estimated volumes and meteorite analogs, we also derive estimates for bulk densities and macroporosities. Methods. We apply a Markov chain Monte Carlo (MCMC) algorithm for asteroid mass and orbit estimation by modeling asteroidasteroid close encounters to four separate large asteroids in an attempt to estimate their masses based on multiple simultaneously studied close encounters with multiple test asteroids. In order to validate our algorithm and data treatment, we apply the MCMC algorithm to pure orbit determination for the main-belt asteroid (367) Amicitia and compare the residuals to previously published ones. In addition, we attempt to estimate a mass for (445) Edna with Gaia astrometry alone based on its close encounter with (1764) Cogshall. Results. In the case of the orbit of (367) Amicitia, we find a solution that improves on the previously published solution. The study of (445) Edna reveals that mass estimation with DR2 astrometry alone is unfeasible and that it must be combined with astrometry from other sources to achieve meaningful results. We find that a combination of DR2 and Earth-based astrometry results in dramatically reduced uncertainties and, by extension, significantly improved results in comparison to those computed based on less accurate Earth-based astrometry alone. Conclusions. Our mass estimation algorithm works well with a combination of Gaia DR2 and Earth-based astrometry and provides very impressive results with significantly reduced uncertainties. We note that the DR2 has a caveat in that many asteroids suitable for mass-estimation purposes are not included in the relatively small sample. This limits the number of asteroids to which mass estimation can be applied. However, this issue will largely be corrected with the forthcoming third Gaia data release, which is expected to allow for a wave of numerous accurate mass estimates for a wide range of asteroids.
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(2018)Aims. We present an automated system called neoranger that regularly computes asteroid-Earth impact probabilities for objects on the Minor Planet Center's (MPC) Near-Earth-Object Confirmation Page (NEOCP) and sends out alerts of imminent impactors to registered users. In addition to potential Earth-impacting objects, neoranger also monitors for other types of interesting objects such as Earth's natural temporarily-captured satellites. Methods. The system monitors the NEOCP for objects with new data and solves, for each object, the orbital inverse problem, which results in a sample of orbits that describes the, typically highly-nonlinear, orbital-element probability density function (PDF). The PDF is propagated forward in time for seven days and the impact probability is computed as the weighted fraction of the sample orbits that impact the Earth. Results. The system correctly predicts the then-imminent impacts of 2008 TC3 and 2014 Lambda Lambda based on the first data sets available. Using the same code and configuration we find that the impact probabilities for objects typically on the NEOCP, based on eight weeks of continuous operations, are always less than one in ten million, whereas simulated and real Earth-impacting asteroids always have an impact probability greater than 10% based on the first two tracklets available.
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(2020)Analysis of the Planck 2018 data set indicates that the statistical properties of the cosmic microwave background (CMB) temperature anisotropies are in excellent agreement with previous studies using the 2013 and 2015 data releases. In particular, they are consistent with the Gaussian predictions of the Lambda CDM cosmological model, yet also confirm the presence of several so-called "anomalies" on large angular scales. The novelty of the current study, however, lies in being a first attempt at a comprehensive analysis of the statistics of the polarization signal over all angular scales, using either maps of the Stokes parameters, Q and U, or the E-mode signal derived from these using a new methodology (which we describe in an appendix). Although remarkable progress has been made in reducing the systematic effects that contaminated the 2015 polarization maps on large angular scales, it is still the case that residual systematics (and our ability to simulate them) can limit some tests of non-Gaussianity and isotropy. However, a detailed set of null tests applied to the maps indicates that these issues do not dominate the analysis on intermediate and large angular scales (i.e., l less than or similar to 400). In this regime, no unambiguous detections of cosmological non-Gaussianity, or of anomalies corresponding to those seen in temperature, are claimed. Notably, the stacking of CMB polarization signals centred on the positions of temperature hot and cold spots exhibits excellent agreement with the Lambda CDM cosmological model, and also gives a clear indication of how Planck provides state-of-the-art measurements of CMB temperature and polarization on degree scales.
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(2019)We present a statistical study of the relative orientation in the plane of the sky between interstellar magnetic fields and filaments hosting cold clumps. For the first time, we consider both the density of the environment and the density contrast between the filaments and their environment. Moreover, we geometrically distinguish between the clumps and the remaining portions of the filaments. We infer the magnetic field orientations in the filaments and in their environment from the Stokes parameters, 1 assuming optically thin conditions. Thus, we analyse the relative orientations between filaments, embedded clumps, internal and background magnetic fields, depending on their environment and evolutionary stages. We recover the previously observed trend for filaments in low column density environments to be aligned parallel to the background magnetic field; however, we find that this trend is significant only for low-contrast filaments, whereas high-contrast filaments tend to be randomly orientated with respect to the background magnetic field. Filaments in high column density environments do not globally show any preferential orientation, although low-contrast filaments alone tend to have perpendicular relative orientation with respect to the background magnetic field. For a subsample of nearby filaments, for which volume densities can be derived, we find a clear transition in the relative orientation with increasing density, at n(H) similar to 10(3) cm(-3), changing from mostly parallel to mostly perpendicular in the off-clump portions of filaments and from even to bimodal in clumps. Our results confirm a strong interplay between interstellar magnetic fields and filaments during their formation and evolution.
