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Register a new userOptimized Clustering Estimators for BAO Measurements Accounting for Significant Redshift Uncertainty
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We determine an optimized clustering statistic to be used for galaxy samples with significant redshift uncertainty, such as those that rely on photometric redshifts. To do so, we study the baryon acoustic oscillation (BAO) information content as a function of the orientation of galaxy clustering modes with respect to their angle to the line-of-sight (LOS). The clustering along the LOS, as observed in a redshift-space with significant redshift uncertainty, has contributions from clustering modes with a range of orientations with respect to the true LOS. For redshift uncertainty $sigma_z geq 0.02(1+z)$ we find that while the BAO information is confined to transverse clustering modes in the true space, it is spread nearly evenly in the observed space. Thus, measuring clustering in terms of the projected separation (regardless of the LOS) is an efficient and nearly lossless compression of the signal for $sigma_z geq 0.02(1+z)$. For reduced redshift uncertainty, a more careful consideration is required. We then use more than 1700 realizations (combining two separate sets) of galaxy simulations mimicking the Dark Energy Survey Year 1 sample to validate our analytic results and optimized analysis procedure. We find that using the correlation function binned in projected separation, we can achieve uncertainties that are within 10 per cent of those predicted by Fisher matrix forecasts. We predict that DES Y1 should achieve a 5 per cent distance measurement using our optimized methods. We expect the results presented here to be important for any future BAO measurements made using photometric redshift data.
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In this contribution we present the preliminary results regarding the non-linear BAO signal in higher-order statistics of the cosmic density field. We use ensembles of N-body simulations to show that the non-linear evolution changes the amplitudes of the BAO signal, but has a negligible effect on the scale of the BAO feature. The latter observation accompanied by the fact that the BAO feature amplitude roughly doubles as one moves to higher orders, suggests that the higher-order correlation amplitudes can be used as probe of the BAO signal.
Traditional approaches to ensure group fairness in algorithmic decision making aim to equalize ``total error rates for different subgroups in the population. In contrast, we argue that the fairness approaches should instead focus only on equalizing errors arising due to model uncertainty (a.k.a epistemic uncertainty), caused due to lack of knowledge about the best model or due to lack of data. In other words, our proposal calls for ignoring the errors that occur due to uncertainty inherent in the data, i.e., aleatoric uncertainty. We draw a connection between predictive multiplicity and model uncertainty and argue that the techniques from predictive multiplicity could be used to identify errors made due to model uncertainty. We propose scalable convex proxies to come up with classifiers that exhibit predictive multiplicity and empirically show that our methods are comparable in performance and up to four orders of magnitude faster than the current state-of-the-art. We further propose methods to achieve our goal of equalizing group error rates arising due to model uncertainty in algorithmic decision making and demonstrate the effectiveness of these methods using synthetic and real-world datasets.
Our goals are (i) to search for BAO and large-scale structure in current QSO survey data and (ii) to use these and simulation/forecast results to assess the science case for a new, >10x larger, QSO survey. We first combine the SDSS, 2QZ and 2SLAQ surveys to form a survey of ~60000 QSOs. We find a hint of a peak in the QSO 2-point correlation function, xi(s), at the same scale (~105h^-1 Mpc) as detected by Eisenstein et al (2005) in their sample of DR5 LRGs but only at low statistical significance. We then compare these data with QSO mock catalogues from the Hubble Volume simulation used by Hoyle et al (2002) and find that both routes give statistical error estimates that are consistent at ~100h^-1 Mpc scales. Mock catalogues are then used to estimate the nominal survey size needed for a 3-4 sigma detection of the BAO peak. We find that a redshift survey of ~250000 z<2.2 QSOs is required over ~3000 deg^2. This is further confirmed by static log-normal simulations where the BAO are clearly detectable in the QSO power spectrum and correlation function. The nominal survey would on its own produce the first detection of, for example, discontinuous dark energy evolution in the so far uncharted 1<z<2.2 redshift range. A survey with ~50% higher QSO sky densities and 50% bigger area will give an ~6sigma BAO detection, leading to an error ~60% of the size of the BOSS error on the dark energy evolution parameter, w_a. Another important aim for a QSO survey is to place new limits on primordial non-Gaussianity at large scales, testing tentative evidence we have found for the evolution of the linear form of the combined QSO xi(s) at z~1.6. Such a QSO survey will also determine the gravitational growth rate at z~1.6 via z-space distortions, allow lensing tomography via QSO magnification bias while also measuring the exact luminosity dependence of small-scale QSO clustering.
As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality measures rely on the assumption that the graph is perfectly known -- a premise not necessarily fulfilled for large, uncertain networks. Accordingly, centrality measures may fail to faithfully extract the importance of nodes in the presence of uncertainty. To mitigate these problems, we suggest a statistical approach based on graphon theory: we introduce formal definitions of centrality measures for graphons and establish their connections to classical graph centrality measures. A key advantage of this approach is that centrality measures defined at the modeling level of graphons are inherently robust to stochastic variations of specific graph realizations. Using the theory of linear integral operators, we define degree, eigenvector, Katz and PageRank centrality functions for graphons and establish concentration inequalities demonstrating that graphon centrality functions arise naturally as limits of their counterparts defined on sequences of graphs of increasing size. The same concentration inequalities also provide high-probability bounds between the graphon centrality functions and the centrality measures on any sampled graph, thereby establishing a measure of uncertainty of the measured centrality score. The same concentration inequalities also provide high-probability bounds between the graphon centrality functions and the centrality measures on any sampled graph, thereby establishing a measure of uncertainty of the measured centrality score.
Small fractions of isocurvature perturbations correlated with the dominant adiabatic mode are shown to be a significant primordial systematic for future Baryon Acoustic Oscillation (BAO) surveys, distorting the standard ruler distance by broadening and shifting the peak in the galaxy correlation function. Untreated this systematic leads to biases that can exceed $10sigma$ in the dark energy parameters even for Planck-level isocurvature constraints. Accounting for the isocurvature modes corrects for this bias but degrades the dark energy figure of merit by at least 50%. The BAO data in turn provides extremely powerful new constraints on the nature of the primordial perturbations. Future large galaxy surveys will thus be powerful probes of the earliest phase of the universe in addition to helping pin down the nature of dark energy.
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