scholarly journals Comparing approximate methods for mock catalogues and covariance matrices II: power spectrum multipoles

2019 ◽  
Vol 485 (2) ◽  
pp. 2806-2824 ◽  
Author(s):  
Linda Blot ◽  
Martin Crocce ◽  
Emiliano Sefusatti ◽  
Martha Lippich ◽  
Ariel G Sánchez ◽  
...  

ABSTRACT We study the accuracy of several approximate methods for gravitational dynamics in terms of halo power spectrum multipoles and their estimated covariance matrix. We propagate the differences in covariances into parameter constraints related to growth rate of structure, Alcock–Paczynski distortions, and biasing. We consider seven methods in three broad categories: algorithms that solve for halo density evolution deterministically using Lagrangian trajectories (ICE–COLA, pinocchio, and peakpatch), methods that rely on halo assignment schemes on to dark matter overdensities calibrated with a target N-body run (halogen, patchy), and two standard assumptions about the full density probability distribution function (Gaussian and lognormal). We benchmark their performance against a set of three hundred N-body simulations, running similar sets of approximate simulations with matched initial conditions, for each method. We find that most methods reproduce the monopole to within $5{{\ \rm per\ cent}}$, while residuals for the quadrupole are sometimes larger and scale dependent. The variance of the multipoles is typically reproduced within $10{{\ \rm per\ cent}}$. Overall, we find that covariances built from approximate simulations yield errors on model parameters within $10{{\ \rm per\ cent}}$ of those from the N-body-based covariance.

Author(s):  
Ahmad Bani Younes ◽  
James Turner

In general, the behavior of science and engineering is predicted based on nonlinear math models. Imprecise knowledge of the model parameters alters the system response from the assumed nominal model data. We propose an algorithm for generating insights into the range of variability that can be the expected due to model uncertainty. An Automatic differentiation tool builds exact partial derivative models to develop State Transition Tensor Series-based (STTS) solution for mapping initial uncertainty models into instantaneous uncertainty models. Development of nonlinear transformations for mapping an initial probability distribution function into a current probability distribution function for computing fully nonlinear statistical system properties. This also demands the inverse mapping of the series. The resulting nonlinear probability distribution function (pdf) represents a Liouiville approximation for the stochastic Fokker Planck equation. Numerical examples are presented that demonstrate the effectiveness of the proposed methodology.


2020 ◽  
Vol 496 (3) ◽  
pp. 3862-3869 ◽  
Author(s):  
Anatoly Klypin ◽  
Francisco Prada ◽  
Joyce Byun

ABSTRACT Making cosmological inferences from the observed galaxy clustering requires accurate predictions for the mean clustering statistics and their covariances. Those are affected by cosmic variance – the statistical noise due to the finite number of harmonics. The cosmic variance can be suppressed by fixing the amplitudes of the harmonics instead of drawing them from a Gaussian distribution predicted by the inflation models. Initial realizations also can be generated in pairs with 180○ flipped phases to further reduce the variance. Here, we compare the consequences of using paired-and-fixed versus Gaussian initial conditions on the average dark matter clustering and covariance matrices predicted from N-body simulations. As in previous studies, we find no measurable differences between paired-and-fixed and Gaussian simulations for the average density distribution function, power spectrum, and bispectrum. Yet, the covariances from paired-and-fixed simulations are suppressed in a complicated scale- and redshift-dependent way. The situation is particularly problematic on the scales of Baryon acoustic oscillations where the covariance matrix of the power spectrum is lower by only $\sim 20{{\ \rm per\ cent}}$ compared to the Gaussian realizations, implying that there is not much of a reduction of the cosmic variance. The non-trivial suppression, combined with the fact that paired-and-fixed covariances are noisier than from Gaussian simulations, suggests that there is no path towards obtaining accurate covariance matrices from paired-and-fixed simulations – result, that is theoretically expected and accepted in the field. Because the covariances are crucial for the observational estimates of galaxy clustering statistics and cosmological parameters, paired-and-fixed simulations, though useful for some applications, cannot be used for the production of mock galaxy catalogues.


2000 ◽  
Vol 543 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Patrick McDonald ◽  
Jordi Miralda‐Escude ◽  
Michael Rauch ◽  
Wallace L. W. Sargent ◽  
Tom A. Barlow ◽  
...  

1998 ◽  
Vol 37 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Hany Hassan ◽  
Keisuke Hanaki ◽  
Tomonori Matsuo

Global climate change induced by increased concentrations of greenhouse gases (especially CO2) is expected to include changes in precipitation, wind speed, incoming solar radiation, and air temperature. These major climate variables directly influence water quality in lakes by altering changes in flow and water temperature balance. High concentration of nutrient enrichment and expected variability of climate can lead to periodic phytoplankton blooms and an alteration of the neutral trophic balance. As a result, dissolved oxygen levels, with low concentrations, can fluctuate widely and algal productivity may reach critical levels. In this work, we will present: 1) recent results of GCMs climate scenarios downscaling project that was held at the University of Derby, UK.; 2) current/future comparative results of a new mathematical lake eutrophication model (LEM) in which output of phytoplankton growth rate and dissolved oxygen will be presented for Suwa lake in Japan as a case study. The model parameters were calibrated for the period of 1973–1983 and validated for the period of 1983–1993. Meterologic, hydrologic, and lake water quality data of 1990 were selected for the assessment analysis. Statistical relationships between seven daily meteorological time series and three airflow indices were used as a means for downscaling daily outputs of Hadley Centre Climate Model (HadCM2SUL) to the station sub-grid scale.


2021 ◽  
Vol 504 (1) ◽  
pp. 33-52
Author(s):  
Gong-Bo Zhao ◽  
Yuting Wang ◽  
Atsushi Taruya ◽  
Weibing Zhang ◽  
Héctor Gil-Marín ◽  
...  

ABSTRACT We perform a joint BAO and RSD analysis using the eBOSS DR16 LRG and ELG samples in the redshift range of z ∈ [0.6, 1.1], and detect an RSD signal from the cross-power spectrum at a ∼4σ confidence level, i.e., fσ8 = 0.317 ± 0.080 at zeff = 0.77. Based on the chained power spectrum, which is a new development in this work to mitigate the angular systematics, we measure the BAO distances and growth rate simultaneously at two effective redshifts, namely, DM/rd (z = 0.70) = 17.96 ± 0.51, DH/rd (z = 0.70) = 21.22 ± 1.20, fσ8 (z = 0.70) = 0.43 ± 0.05, and DM/rd (z = 0.845) = 18.90 ± 0.78, DH/rd (z = 0.845) = 20.91 ± 2.86, fσ8 (z = 0.845) = 0.30 ± 0.08. Combined with BAO measurements including those from the eBOSS DR16 QSO and Lyman-α sample, our measurement has raised the significance level of a non-zero ΩΛ to ∼11σ. The data product of this work is publicly available at https://github.com/icosmology/eBOSS_DR16_LRGxELG and https://www.sdss.org/science/final-bao-and-rsd-measurements/.


Sign in / Sign up

Export Citation Format

Share Document