Integrated cosmological probes: Concordance quantified

Assessing the consistency of parameter constraints derived from different cosmological probes is an important way to test the validity of the underlying cosmological model. In an earlier work [Nicola et al., 2017], we computed constraints on cosmological parameters for $\Lambda$CDM from an integrated analysis of CMB temperature anisotropies and CMB lensing from Planck, galaxy clustering and weak lensing from SDSS, weak lensing from DES SV as well as Type Ia supernovae and Hubble parameter measurements. In this work, we extend this analysis and quantify the concordance between the derived constraints and those derived by the Planck Collaboration as well as WMAP9, SPT and ACT. As a measure for consistency, we use the Surprise statistic [Seehars et al., 2014], which is based on the relative entropy. In the framework of a flat $\Lambda$CDM cosmological model, we find all data sets to be consistent with one another at a level of less than 1$\sigma$. We highlight that the relative entropy is sensitive to inconsistencies in the models that are used in different parts of the analysis. In particular, inconsistent assumptions for the neutrino mass break its invariance on the parameter choice. When consistent model assumptions are used, the data sets considered in this work all agree with each other and $\Lambda$CDM, without evidence for tensions.Comment: 17 pages, 4 figures, 2 tables, updated following referee's comments, now includes discussion of the Riess et al., 2016 Hubble parameter measurement, matches version accepted by JCA

Non-linear Causal Inference using Gaussianity Measures

We provide theoretical and empirical evidence for a type of asymmetry between causes and effects that is present when these are related via linear models contaminated with additive non-Gaussian noise. Assuming that the causes and the effects have the same distribution, we show that the distribution of the residuals of a linear fit in the anti-causal direction is closer to a Gaussian than the distribution of the residuals in the causal direction. This Gaussianization effect is characterized by reduction of the magnitude of the high-order cumulants and by an increment of the differential entropy of the residuals. The problem of non-linear causal inference is addressed by performing an embedding in an expanded feature space, in which the relation between causes and effects can be assumed to be linear. The effectiveness of a method to discriminate between causes and effects based on this type of asymmetry is illustrated in a variety of experiments using different measures of Gaussianity. The proposed method is shown to be competitive with state-of-the-art techniques for causal inference.Comment: 35 pages, 9 figure

Likelihood Non-Gaussianity in Large-Scale Structure Analyses

Standard present day large-scale structure (LSS) analyses make a major assumption in their Bayesian parameter inference --- that the likelihood has a Gaussian form. For summary statistics currently used in LSS, this assumption, even if the underlying density field is Gaussian, cannot be correct in detail. We investigate the impact of this assumption on two recent LSS analyses: the Beutler et al. (2017) power spectrum multipole ($P_\ell$) analysis and the Sinha et al. (2017) group multiplicity function ($\zeta$) analysis. Using non-parametric divergence estimators on mock catalogs originally constructed for covariance matrix estimation, we identify significant non-Gaussianity in both the $P_\ell$ and $\zeta$ likelihoods. We then use Gaussian mixture density estimation and Independent Component Analysis on the same mocks to construct likelihood estimates that approximate the true likelihood better than the Gaussian $pseudo$-likelihood. Using these likelihood estimates, we accurately estimate the true posterior probability distribution of the Beutler et al. (2017) and Sinha et al. (2017) parameters. Likelihood non-Gaussianity shifts the $f\sigma_8$ constraint by $-0.44\sigma$, but otherwise, does not significantly impact the overall parameter constraints of Beutler et al. (2017). For the $\zeta$ analysis, using the pseudo-likelihood significantly underestimates the uncertainties and biases the constraints of Sinha et al. (2017) halo occupation parameters. For $\log M_1$ and $\alpha$, the posteriors are shifted by $+0.43\sigma$ and $-0.51\sigma$ and broadened by $42\%$ and $66\%$, respectively. The divergence and likelihood estimation methods we present provide a straightforward framework for quantifying the impact of likelihood non-Gaussianity and deriving more accurate parameter constraints.Comment: 33 pages, 7 figure

Copula-Based Dependence Characterizations and Modeling for Time Series

This paper develops a new unified approach to copula-based modeling and characterizations for time series and stochastic processes. We obtain complete characterizations of many time series dependence structures in terms of copulas corresponding to their finite-dimensional distributions. In particular, we focus on copula- based representations for Markov chains of arbitrary order, m-dependent and r-independent time series as well as martingales and conditionally symmetric processes. Our results provide new methods for modeling time series that have prescribed dependence structures such as, for instance, higher order Markov processes as well as non-Markovian processes that nevertheless satisfy Chapman-Kolmogorov stochastic equations. We also focus on the construction and analysis of new classes of copulas that have flexibility to combine many different dependence properties for time series. Among other results, we present a study of new classes of cop- ulas based on expansions by linear functions (Eyraud-Farlie-Gumbel-Mongenstern copulas), power functions (power copulas) and Fourier polynomials (Fourier copulas) and introduce methods for modeling time series using these classes of dependence functions. We also focus on the study of weak convergence of empirical copula processes in the time series context and obtain new results on asymptotic gaussianity of such processes for a wide class of beta mixing sequences.

Hyperspectral colon tissue cell classification

A novel algorithm to discriminate between normal and malignant tissue cells of the human colon is presented. The microscopic level images of human colon tissue cells were acquired using hyperspectral imaging technology at contiguous wavelength intervals of visible light. While hyperspectral imagery data provides a wealth of information, its large size normally means high computational processing complexity. Several methods exist to avoid the so-called curse of dimensionality and hence reduce the computational complexity. In this study, we experimented with Principal Component Analysis (PCA) and two modifications of Independent Component Analysis (ICA). In the first stage of the algorithm, the extracted components are used to separate four constituent parts of the colon tissue: nuclei, cytoplasm, lamina propria, and lumen. The segmentation is performed in an unsupervised fashion using the nearest centroid clustering algorithm. The segmented image is further used, in the second stage of the classification algorithm, to exploit the spatial relationship between the labeled constituent parts. Experimental results using supervised Support Vector Machines (SVM) classification based on multiscale morphological features reveal the discrimination between normal and malignant tissue cells with a reasonable degree of accuracy

The non-Gaussianity of the cosmic shear likelihood - or: How odd is the Chandra Deep Field South?

(abridged) We study the validity of the approximation of a Gaussian cosmic shear likelihood. We estimate the true likelihood for a fiducial cosmological model from a large set of ray-tracing simulations and investigate the impact of non-Gaussianity on cosmological parameter estimation. We investigate how odd the recently reported very low value of $\sigma_8$ really is as derived from the \textit{Chandra} Deep Field South (CDFS) using cosmic shear by taking the non-Gaussianity of the likelihood into account as well as the possibility of biases coming from the way the CDFS was selected. We find that the cosmic shear likelihood is significantly non-Gaussian. This leads to both a shift of the maximum of the posterior distribution and a significantly smaller credible region compared to the Gaussian case. We re-analyse the CDFS cosmic shear data using the non-Gaussian likelihood. Assuming that the CDFS is a random pointing, we find $\sigma_8=0.68_{-0.16}^{+0.09}$ for fixed $\Omega_{\rm m}=0.25$. In a WMAP5-like cosmology, a value equal to or lower than this would be expected in $\approx 5$ of the times. Taking biases into account arising from the way the CDFS was selected, which we model as being dependent on the number of haloes in the CDFS, we obtain $\sigma_8 = 0.71^{+0.10}_{-0.15}$. Combining the CDFS data with the parameter constraints from WMAP5 yields $\Omega_{\rm m} = 0.26^{+0.03}_{-0.02}$ and $\sigma_8 = 0.79^{+0.04}_{-0.03}$ for a flat universe.Comment: 18 pages, 16 figures, accepted for publication in A&A; New Bayesian treatment of field selection bia