35 research outputs found
Maximal compression of the redshift space galaxy power spectrum and bispectrum
We explore two methods of compressing the redshift space galaxy power
spectrum and bispectrum with respect to a chosen set of cosmological
parameters. Both methods involve reducing the dimension of the original
data-vector ( e.g. 1000 elements ) to the number of cosmological parameters
considered ( e.g. seven ) using the Karhunen-Lo\`eve algorithm. In the first
case, we run MCMC sampling on the compressed data-vector in order to recover
the one-dimensional (1D) and two-dimensional (2D) posterior distributions. The
second option, approximately 2000 times faster, works by orthogonalising the
parameter space through diagonalisation of the Fisher information matrix before
the compression, obtaining the posterior distributions without the need of MCMC
sampling. Using these methods for future spectroscopic redshift surveys like
DESI, EUCLID and PFS would drastically reduce the number of simulations needed
to compute accurate covariance matrices with minimal loss of constraining
power. We consider a redshift bin of a DESI-like experiment. Using the power
spectrum combined with the bispectrum as a data-vector, both compression
methods on average recover the 68% credible regions to within 0.7% and 2% of
those resulting from standard MCMC sampling respectively. These confidence
intervals are also smaller than the ones obtained using only the power spectrum
by (81%, 80%, 82%) respectively for the bias parameter b_1, the growth rate f
and the scalar amplitude parameter A_s.Comment: 27 pages, 8 figures, 1 table, Accepted 2018 January 28. Received 2018
January 25; in original form 2017 September 11. Added clarifications in the
text on the bias modelling and compression limits following referee's
comments. Removed tetraspectrum term from the pk-bk cross covariance +
correction in the appendi
Integrated trispectrum detection from BOSS DR12 NGC CMASS
We present the first detection of the integrated trispectrum
(-trispectrum) monopole and quadrupoles signal from BOSS CMASS NGC
DR12. Extending the FKP estimators formalism to the Fourier transform of the
four-point correlation function, we test shot-noise subtraction, Gaussianity of
the i-trispectrum data-vector, significance of the detection and similarity
between the signal from the data and from the galaxy mock catalogues used to
numerically estimate the covariance matrix. Using scales corresponding to modes
from minimum to maximum
, we find a detection in terms of distance
from the null hypothesis of -intervals for the
i-trispectrum monopole and quadrupoles respectively. This quantifies the
presence of the physical signal of the four-points statistics on BOSS data. For
completeness the same analysis is also performed for power spectrum and
bispectrum, both monopoles and quadrupoles.Comment: 17 pages plus appendix, 11 figures, matching published version on
JCA
Cosmology from compressed high-order statistics in galaxy surveys
The work presented in this thesis focuses on developing compression techniques to exploit fully the constraining power of high-order statistics when applied to the cosmological observable of interest. We present four different methods in the three-point (3pt) case. The mathematical theoretical framework is first de- veloped and then followed, for all the methods, by application on real data. In particular we use data from the CMASS sample of the Sloan Digital Sky Survey III BOSS Data Releases 11 and 12. Our compression results are compared to those obtained via standard analysis, for example Markov chain Monte Carlo (MCMC) sampling. First, we consider the three-point auto-correlation function as an integrated compressed version of the standard correlation one. We derive analytic expres- sions including corrections for the Primordial non-Gaussianity. We then test the model on data to constrain cosmological parameters. Secondly, we explore two methods of compressing the redshift-space galaxy power spectrum and bispectrum with respect to a chosen set of cosmological parameters. Both methods transform the original data-vector into a compressed one with dimension equal to the number of model parameters considered using the Multiple Optimised Parameter Estimation and Data compression algorithm (MOPED) algorithm. Analytic expressions for the covariance matrix are derived in order both to compress the data-vector and to test the compression perfor- mance by comparing with standard MCMC sampling on the full data-vector. Finally, we apply our compression methods to the galaxy power spectrum monopole, quadrupole and bispectrum monopole measurements from the BOSS DR12 CMASS sample. We derive an analytic expression for the covariance ma- trix of the new data-vector. We show that compression allows a much longer data-vector to be used, returning tighter constraints on the cosmological param- eters of interest
Current immigration to Europe from North Africa. Health and physical activity
Immigration to Europe - especially from neighbouring North Africa - is a consistent phenomenon with social and health-related implications. Even if in many cases immigrants come from lower-income countries, their health status is better than that of European-born citizens at immigration time, given their younger age. Still, the adoption of a Western life style, with increased caloric intake and reduced physical activity, may soon lead to a deterioration of individual health. European-born individuals engage more often in leisure-time physical activity than immigrants (especially women) and follow a more healthy diet. Thus, obesity, cardiovascular diseases and diabetes may have a higher prevalence in accustomed immigrants
Joint analysis of anisotropic power spectrum, bispectrum and trispectrum: application to N-body simulations
We perform for the first time a joint analysis of the monopole and
quadrupoles for power spectrum, bispectrum and integrated trispectrum
(i-trispectrum) from the redshift space matter field in N-body simulations.
With a full Markov Chain Monte Carlo exploration of the posterior distribution,
we quantify the constraints on cosmological parameters for an object density of
, redshift , and
a covariance corresponding to a survey volume of , a set up which is representative of forthcoming
galaxy redshift surveys. We demonstrate the complementarity of the bispectrum
and i-trispectrum in constraining key cosmological parameters. In particular,
compared to the state-of-the-art power spectrum (monopole plus quadrupole) and
bispectrum (monopole) analyses, we find 1D credible regions smaller by a
factor of for the parameters
respectively. This
work motivates the additional effort necessary to include the redshift-space
anisotropic signal of higher-order statistics in the analysis and
interpretation of ongoing and future galaxy surveys.Comment: 42 pages (21 + appendixes and references), 12 figures, 3 tables,
matching accepted version after minor revisio
Matter trispectrum: theoretical modelling and comparison to N-body simulations
The power spectrum has long been the workhorse summary statistics for
large-scale structure cosmological analyses. However, gravitational non-linear
evolution moves precious cosmological information from the two-point statistics
(such as the power spectrum) to higher-order correlations. Moreover,
information about the primordial non-Gaussian signal lies also in higher-order
correlations. Without tapping into these, that information remains hidden.
While the three-point function (or the bispectrum), even if not extensively,
has been studied and applied to data, there has been only limited discussion
about the four point/trispectrum. This is because the high-dimensionality of
the statistics (in real space a skew-quadrilateral has 6 degrees of freedom),
and the high number of skew-quadrilaterals, make the trispectrum numerically
and algorithmically very challenging. Here we address this challenge by
introducing the i-trispectrum, an integrated trispectrum that only depends on
four -modes moduli. We model and measure the matter i-trispectrum from a set
of 5000 \textsc{Quijote} N-body simulations both in real and redshift space,
finding good agreement between simulations outputs and model up to mildly
non-linear scales. Using the power spectrum, bispectrum and i-trispectrum joint
data-vector covariance matrix estimated from the simulations, we begin to
quantify the added-value provided by the i-trispectrum. In particular, we
forecast the i-trispectrum improvements on constraints on the local primordial
non-Gaussianity amplitude parameters and . For
example, using the full joint data-vector, we forecast
constraints up to two times () smaller in real (redshift) space than
those obtained without i-trispectrum.Comment: accepted: 6th of November 2020, published: 11th of January 2021 , 64
pages (35 pages for the main text), 15 figure
GEO-FPT: a model of the galaxy bispectrum at mildly non-linear scales
We present GEO-FPT (Geometric Fitted Perturbation Theory), a new model for
the galaxy bispectrum anisotropic signal in redshift space, with functional
form rooted in perturbation theory. It also models the dependence of the
bispectrum with the geometric properties of the triangles in Fourier space, and
has a broader regime of validity than state-of-the-art theoretical models based
on perturbation theory. We calibrate the free parameters of this model using
high-resolution dark matter simulations and perform stringent tests to show
that GEO-FPT describes the galaxy bispectrum accurately up to scales of
for different cosmological models, as well as for
biased tracers of the dark matter field, considering a survey volume of
(Gpc . In particular, a joint analysis of the power spectrum and
bispectrum anisotropic signals, taking into account their full covariance
matrix, reveals that the relevant physical quantities -- the BAO peak position
(along and across the line-of-sight), and the growth of structure parameters
times the amplitude of dark matter fluctuations, -- are recovered in
an unbiased way, with an accuracy better than and respectively
(which is our statistical limit of the systematic error estimate). In
addition, the bispectrum signal breaks the degeneracy without
detectable bias: and are recovered with better than and
accuracy respectively (which is our statistical limit of the
systematic error estimate).
GEO-FPT boosts the applicability of the bispectrum signal of galaxy surveys
beyond the current limitation of Mpc % and makes the
bispectrum a key statistic to unlock the information content from the mildly
non-linear regime in the on-going and forthcoming galaxy redshift surveys.Comment: 37 pages, 14 figures. To be submitted to JCAP, comments welcom
GEOMAX: beyond linear compression for 3pt galaxy clustering statistics
We present the GEOMAX algorithm and its Python implementation for a two-step
compression of bispectrum measurements. The first step groups bispectra by the
geometric properties of their arguments; the second step then maximises the
Fisher information with respect to a chosen set of model parameters in each
group. The algorithm only requires the derivatives of the data vector with
respect to the parameters and a small number of mock data, producing an
effective, non-linear compression. By applying GEOMAX to bispectrum monopole
measurements from BOSS DR12 CMASS redshift-space galaxy clustering data, we
reduce the credible intervals for the inferred parameters
by
with respect to standard MCMC on the full data vector. We run the analysis and
comparison between compression methods over one hundred galaxy mocks to test
the statistical significance of the improvements. On average GEOMAX performs
better than geometrical or maximal linear compression alone and is
consistent with being lossless. Given its flexibility, the GEOMAX approach has
the potential to optimally exploit three-point statistics of various
cosmological probes like weak lensing or line-intensity maps from current and
future cosmological data-sets such as DESI, Euclid, PFS and SKA.Comment: 17 pages, 9 figures, accepted version by MNRA
Beyond two-point statistics: using the minimum spanning tree as a tool for cosmology
Cosmological studies of large-scale structure have relied on two-point statistics, not fully exploiting the rich structure of the cosmic web. In this paper we show how to capture some of this cosmic web information by using the minimum spanning tree (MST), for the first time using it to estimate cosmological parameters in simulations. Discrete tracers of dark matter such as galaxies, N-body particles or haloes are used as nodes to construct a unique graph, the MST, that traces skeletal structure. We study the dependence of the MST on cosmological parameters using haloes from a suite of COmoving Lagrangian Acceleration (COLA) simulations with a box size of 250 h(-1) Mpc, varying the amplitude of scalar fluctuations (A(s)), matter density (Omega(m)), and neutrino mass (Sigma m(nu)). The power spectrum P and bispectrum B are measured for wavenumbers between 0.125 and 0.5 h Mpc(-1), while a corresponding lower cut of similar to 12.6 h(-1) Mpc is applied to the MST. The constraints from the individual methods are fairly similar but when combined we see improved 1 sigma constraints of similar to 17 per cent (similar to 12 per cent) on Omega(m) and similar to 12 per cent (similar to 10 per cent) on A(s) with respect to P (P + B) thus showing the MST is providing additional information. The MST can be applied to current and future spectroscopic surveys (BOSS, DESI, Euclid, PSF, WFIRST, and 4MOST) in 3D and photometric surveys (DES and LSST) in tomographic shells to constrain parameters and/or test systematics
Height and body-mass index trajectories of school-aged children and adolescents from 1985 to 2019 in 200 countries and territories: a pooled analysis of 2181 population-based studies with 65 million participants
Summary Background Comparable global data on health and nutrition of school-aged children and adolescents are scarce. We aimed to estimate age trajectories and time trends in mean height and mean body-mass index (BMI), which measures weight gain beyond what is expected from height gain, for school-aged children and adolescents. Methods For this pooled analysis, we used a database of cardiometabolic risk factors collated by the Non-Communicable Disease Risk Factor Collaboration. We applied a Bayesian hierarchical model to estimate trends from 1985 to 2019 in mean height and mean BMI in 1-year age groups for ages 5–19 years. The model allowed for non-linear changes over time in mean height and mean BMI and for non-linear changes with age of children and adolescents, including periods of rapid growth during adolescence. Findings We pooled data from 2181 population-based studies, with measurements of height and weight in 65 million participants in 200 countries and territories. In 2019, we estimated a difference of 20 cm or higher in mean height of 19-year-old adolescents between countries with the tallest populations (the Netherlands, Montenegro, Estonia, and Bosnia and Herzegovina for boys; and the Netherlands, Montenegro, Denmark, and Iceland for girls) and those with the shortest populations (Timor-Leste, Laos, Solomon Islands, and Papua New Guinea for boys; and Guatemala, Bangladesh, Nepal, and Timor-Leste for girls). In the same year, the difference between the highest mean BMI (in Pacific island countries, Kuwait, Bahrain, The Bahamas, Chile, the USA, and New Zealand for both boys and girls and in South Africa for girls) and lowest mean BMI (in India, Bangladesh, Timor-Leste, Ethiopia, and Chad for boys and girls; and in Japan and Romania for girls) was approximately 9–10 kg/m2. In some countries, children aged 5 years started with healthier height or BMI than the global median and, in some cases, as healthy as the best performing countries, but they became progressively less healthy compared with their comparators as they grew older by not growing as tall (eg, boys in Austria and Barbados, and girls in Belgium and Puerto Rico) or gaining too much weight for their height (eg, girls and boys in Kuwait, Bahrain, Fiji, Jamaica, and Mexico; and girls in South Africa and New Zealand). In other countries, growing children overtook the height of their comparators (eg, Latvia, Czech Republic, Morocco, and Iran) or curbed their weight gain (eg, Italy, France, and Croatia) in late childhood and adolescence. When changes in both height and BMI were considered, girls in South Korea, Vietnam, Saudi Arabia, Turkey, and some central Asian countries (eg, Armenia and Azerbaijan), and boys in central and western Europe (eg, Portugal, Denmark, Poland, and Montenegro) had the healthiest changes in anthropometric status over the past 3·5 decades because, compared with children and adolescents in other countries, they had a much larger gain in height than they did in BMI. The unhealthiest changes—gaining too little height, too much weight for their height compared with children in other countries, or both—occurred in many countries in sub-Saharan Africa, New Zealand, and the USA for boys and girls; in Malaysia and some Pacific island nations for boys; and in Mexico for girls. Interpretation The height and BMI trajectories over age and time of school-aged children and adolescents are highly variable across countries, which indicates heterogeneous nutritional quality and lifelong health advantages and risks