The global shape, or topology, of the universe is not constrained by the equations of General Relativity, which only describe the local universe. As a consequence, the boundaries of space are not fixed and topologies different from the trivial infinite Euclidean space are possible. The cosmic microwave background (CMB) is the most efficient tool to study topology and test alternative models. Multi-connected topologies, such as the 3-torus, are of great interest because they are anisotropic and allow us to test a possible violation of isotropy in CMB data. We show that the correlation function of the coefficients of the expansion of the temperature and polarization anisotropies in spherical harmonics encodes a topological signature. This signature can be used to distinguish an infinite space from a multi-connected space on sizes larger than the diameter of the last scattering surface (DLSS). With the help of the Kullback-Leibler divergence, we set the size of the edge of the biggest distinguishable torus with CMB temperature fluctuations and E-modes of polarization to 1.15 DLSS. CMB temperature fluctuations allow us to detect universes bigger than the observable universe, whereas E-modes are efficient to detect universes smaller than the observable universe.

We present a new photometric typing technique for normal type Ia supernovae (SNe~Ia) and peculiar SNe~Ia such as SN~1991bg-like, type Iax and super-Chandrasekhar SNe~Ia. This photometric classifier allows the identification of exclusively normal SNe~Ia (with a purity above 99% and an efficiency greater than 80%) in current and future large wide field surveys for cosmological studies.

We analyse the correlations between continuum properties and emission line equivalent widths of star-forming and narrow-line active galaxies from SDSS. We show that emission line strengths can be predicted reasonably well from PCA coefficients of the stellar continuum using local multiple linear regression. Since upcoming sky surveys will make broadband observations only, theoretical modelling of spectra will be essential to estimate physical properties of galaxies. Combined with stellar population synthesis models, our technique will help generate more accurate model spectra and mock catalogues of galaxies to be used to fit data from new surveys. We also show that, by combining PCA coefficients from the pure continuum and the emission lines, a plausible distinction can be made between weak AGNs and quiescent star-forming galaxies. Our method uses a support vector machine, and allows a more refined separation of active and star-forming galaxies than the empirical curve of Kauffmann et al. (2003).

Combining datasets from different experiments and probes to constrain cosmological models is an important challenge in observational cosmology. We summarize a framework for measuring the constraining power and the consistency of separately or jointly analyzed data within a given model that we proposed in earlier work (Seehars et al.2014). Applying the Kullback-Leibler divergence to posterior distributions, we can quantify the difference between constraints and distinguish contributions from gains in precision and shifts in parameter space. We show results from applying this technique to a combination of datasets and probes such as the cosmic microwave background or baryon acoustic oscillations.

We study the statistical inference of the cosmological dark matter density field from non-Gaussian, non-linear and non-Poisson biased distributed tracers. We have implemented a Bayesian posterior sampling computer-code solving this problem and tested it with mock data based on N-body simulations.

This work studies the behavior of entropy in recent cosmological models that start with an initial de Sitter expansion phase, go through the conventional radiation and matter dominated eras to be followed by a final de Sitter epoch. In spite of their seemingly similarities (observationally they are close to the Λ-CDM model), different models deeply differ in their physics. The second law of thermodynamics encapsulates the underlying microscopic, statistical description, and hence we investigate it in the present work. Our study reveals that the entropy of the apparent horizon plus that of matter and radiation inside it, increases and is a concave function of the scale factor. Thus thermodynamic equilibrium is approached in the last de Sitter era, and this class of models is thermodynamically correct. Cosmological models that do not approach equilibrium appear in conflict with the second law of thermodynamics. (Based on Mimoso & Pavon 2013)

Given the generic definition of statistics, it is clear that astronomers have engaged in statistical analysis of some variety since astronomy first emerged as a science. However, from the early nineteenth century until the beginning of the twenty-first the two disciplines have been somewhat estranged – there was no formal relationship between the two. This has now changed, as is evidenced by the recent creation of the International Astrostatistics Association (IAA), the ISI astrostatistics committee, astrostatistics working groups authorized by the IAU and AAS, and this Symposium. The challenge for us to come is in establishing how statisticians and astronomers relate in developing the discipline of astrostatistics. I shall propose a direction for how the discipline can progress in both the short term and well as for future generations of astrostatisticians.

Current and forthcoming cosmological data analyses share the challenge of huge datasets alongside increasingly tight requirements on the precision and accuracy of extracted cosmological parameters. The community is becoming increasingly aware that these requirements not only apply to the central values of parameters but, equally important, also to the error bars. Due to non-linear effects in the astrophysics, the instrument, and the analysis pipeline, data covariance matrices are usually not well known a priori and need to be estimated from the data itself, or from suites of large simulations. In either case, the finite number of realisations available to determine data covariances introduces significant biases and additional variance in the errors on cosmological parameters in a standard likelihood analysis. Here, we review recent work on quantifying these biases and additional variances and discuss approaches to remedy these effects.

In astronomical and cosmological studies one often wishes to infer some properties of an infinite-dimensional field indexed within a finite-dimensional metric space given only a finite collection of noisy observational data. Bayesian inference offers an increasingly-popular strategy to overcome the inherent ill-posedness of this signal reconstruction challenge. However, there remains a great deal of confusion within the astronomical community regarding the appropriate mathematical devices for framing such analyses and the diversity of available computational procedures for recovering posterior functionals. In this brief research note I will attempt to clarify both these issues from an “applied statistics” perpective, with insights garnered from my post-astronomy experiences as a computational Bayesian / epidemiological geostatistician.

A new non-parametric method based on Gaussian Processes (GP) was proposed recently to measure the Hubble constant H0. The freedom in this approach comes in the chosen covariance function, which determines how smooth the process is and how nearby points are correlated. We perform coverage tests with a thousand mock samples within the ΛCDM model in order to determine what covariance function provides the least biased results. The function Matérn(5/2) is the best with sligthly higher errors than other covariance functions, although much more stable when compared to standard parametric analyses.

I present first results from the algorithm we developed to photometrically classify the Supernovae discovered by the Supernova Diversity and Rate Evolution (SUDARE). The classification outcome is compared with that of the public available code SNANA.

Present and future large scale surveys offer promising probes of cosmology. For example the Dark Energy Survey (DES) is forecast to detect ~300 millions galaxies and thousands clusters up to redshift ~1.3. I here show ongoing work to combine two probes of large scale structure : cluster number counts and galaxy 2-point function (in real or harmonic space). The halo model (coupled to a Halo Occupation Distribution) can be used to model the cross-covariance between these probes, and I introduce a diagrammatic method to compute easily the different terms involved. Furthermore, I compute the joint non-Gaussian likelihood, using the Gram-Charlier series. Then I show how to extend the methods of Bayesian hyperparameters to Poissonian distributions, in a first step to include them in this joint likelihood.

I conclude the SCCC21 conference highlighting some of the contrasts we heard about, some specific topics (the statistics of random fields), and discuss how some of these play out in the analysis of cosmic microwave background data. I conclude with a hopeful look at the efficacy of blind analyses in the CMB and elsewhere in cosmology.

We present new measurements of Cosmic Infrared Background (CIB) anisotropies using Planck. Combining HFI data with IRAS, the angular auto- and cross-frequency power spectrum is measured from 143 to 3000 GHz. After careful removal of the contaminants (cosmic microwave background anisotropies, Galactic dust and Sunyaev-Zeldovich emission), and a complete study of systematics, the CIB power spectrum is measured with unprecedented signal to noise ratio from angular multipoles ℓ ~ 150 to 2500. The interpretation based on the halo model is able to associate star-forming galaxies with dark matter halos and their subhalos, using a parametrized relation between the dust-processed infrared luminosity and (sub-)halo mass, and it allows to simultaneously fit all auto- and cross- power spectra very well. We find that the star formation history is well constrained up to redshifts around 2, and agrees with recent estimates of the obscured star-formation density using Spitzer and Herschel. However, at higher redshift, the accuracy of the star formation history measurement is strongly degraded by the uncertainty in the spectral energy distribution of CIB galaxies. We also find that the mean halo mass which is most efficient at hosting star formation is log(Meff/M⊙) = 12.6 and that CIB galaxies have warmer temperatures as redshift increases.

We use a WISE-2MASS-Pan-STARRS1 galaxy catalog to search for a supervoid in the direction of the Cosmic Microwave Background Cold Spot. We obtain photometric redshifts using our multicolor data set to create a tomographic map of the galaxy distribution. The radial density profile centred on the Cold Spot shows a large low density region, extending over 10's of degrees. Motivated by previous Cosmic Microwave Background results, we test for underdensities within two angular radii, 5°, and 15°. Our data, combined with an earlier measurement by Granett et al. 2010, are consistent with a large Rvoid=(192 ± 15)h−1 Mpc (2σ) supervoid with δ ≃ −0.13 ± 0.03 centered at z=0.22 ± 0.01. Such a supervoid, constituting a ∼3.5 σ fluctuation in the ΛCDM model, is a plausible cause for the Cold Spot.

We investigate how galaxies in VIPERS (the VIMOS Public Extragalactic Redshift Survey) inhabit the cosmological density field by examining the correlations across the observable parameter space of galaxy properties and clustering strength. The high-dimensional analysis is made manageable by the use of group-finding and regression tools. We find that the major trends in galaxy properties can be explained by a single parameter related to stellar mass. After subtracting this trend, residual correlations remain between galaxy properties and the local environment pointing to complex formation dependencies. As a specific application of this work we build subsamples of galaxies with specific clustering properties for use in cosmological tests.

A new spin wavelet transform on the sphere is proposed to analyse the polarisation of the cosmic microwave background (CMB), a spin ± 2 signal observed on the celestial sphere. The scalar directional scale-discretised wavelet transform on the sphere is extended to analyse signals of arbitrary spin. The resulting spin scale-discretised wavelet transform probes the directional intensity of spin signals. A procedure is presented using this new spin wavelet transform to recover E- and B-mode signals from partial-sky observations of CMB polarisation.

Machine-learning methods may be used to perform many tasks required in the analysis of astronomical data, including: data description and interpretation, pattern recognition, prediction, classification, compression, inference and many more. An intuitive and well-established approach to machine learning is the use of artificial neural networks (NNs), which consist of a group of interconnected nodes, each of which processes information that it receives and then passes this product on to other nodes via weighted connections. In particular, I discuss the first public release of the generic neural network training algorithm, called SkyNet, and demonstrate its application to astronomical problems focusing on its use in the BAMBI package for accelerated Bayesian inference in cosmology, and the identification of gamma-ray bursters. The SkyNet and BAMBI packages, which are fully parallelised using MPI, are available at http://www.mrao.cam.ac.uk/software/.

Does photometric and spectroscopic survey benefit from overlapping areas? The photometric survey measures 2D Weak Lensing (WL) information from galaxy shape distortions. On the other hand, the higher redshift precision of an spectroscopic survey allows measurements of redshift space distortions (RSD) and baryonic accustic oscillations (BAO) from 3D galaxy counts.

The two surveys are combined using 2D-correlations, using sufficiently narrow bins to capture the radial information. This poster present effects of RSD and intrinsic correlations between narrow redshift bins. In understanding how the effects affects cosmological constrains, we first define two stage-IV and then present forecast for various configurations. When surveys overlap, they benefit from additional cross-correlations and sample variance cancellations from overlapping volumes. For a combined dark energy and growth history figure of merit, the result increase 50% for overlapping surveys, corresponding to 30% larger area.

We propose a computationally feasible estimator for the needlet trispectrum, which develops earlier work on the bispectrum by Donzelli et al. (2012). Our proposal seems to enjoy a number of useful properties, in particular a) the construction exploits the localization properties of the needlet system, and hence it automatically handles masked regions; b) the procedure incorporates a quadratic correction term to correct for the presence of instrumental noise and sky-cuts; c) it is possible to provide analytic results on its statistical properties, which can serve as a guidance for simulations. The needlet trispectrum we present here provides the natural building blocks for the efficient estimation of nonlinearity parameters on CMB data, and in particular for the third order constants gNL and τNL.