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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Full forward model of galaxy clustering statistics with AbacusSummit light cones

ABSTRACT Novel summary statistics beyond the standard 2-point correlation function (2PCF) are necessary to capture the full astrophysical and cosmological information from the small-scale (r < 30h−1Mpc) galaxy clustering. However, the analysis of beyond-2PCF statistics on small scales is challenging because we lack the appropriate treatment of observational systematics for arbitrary summary statistics of the galaxy field. In this paper, we develop a full forward modelling pipeline for a wide range of summary statistics using the large high-fidelity AbacusSummit light cones that account for many systematic effects as well as remain flexible and computationally efficient to enable posterior sampling. We apply our forward model approach to a fully realistic mock galaxy catalog and demonstrate that we can recover unbiased constraints on the underlying galaxy–halo connection model using two separate summary statistics: the standard 2PCF and the novel k-th nearest neighbour (kNN) statistics, which are sensitive to correlation functions of all orders. We will demonstrate its strong constraining power on extended galaxy–halo connection models and cosmology in follow up papers. We expect this to become a powerful approach when applying to upcoming surveys such as DESI where we can leverage a multitude of summary statistics across a wide redshift range to maximally extract information from the non-linear scales.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

{chi}{sup 2} versus median statistics in supernova type Ia data analysis

In this paper we compare the performances of the {chi}{sup 2} and median likelihood analysis in the determination of cosmological constraints using type Ia supernovae data. We perform a statistical analysis using the 307 supernovae of the Union 2 compilation of the Supernova Cosmology Project and find that the {chi}{sup 2} statistical analysis yields tighter cosmological constraints than the median statistic if only supernovae data is taken into account. We also show that when additional measurements from the cosmic microwave background and baryonic acoustic oscillations are considered, the combined cosmological constraints are not strongly dependent on whether one applies the {chi}{sup 2} statistic or the median statistic to the supernovae data. This indicates that, when complementary information from other cosmological probes is taken into account, the performances of the {chi}{sup 2} and median statistics are very similar, demonstrating the robustness of the statistical analysis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

ON MORE SENSITIVE PERIODOGRAM STATISTICS

Period searches in event data have traditionally used the Rayleigh statistic, R {sup 2}. For X-ray pulsars, the standard has been the Z {sup 2} statistic, which sums over more than one harmonic. For γ-rays, the H-test, which optimizes the number of harmonics to sum, is often used. These periodograms all suffer from the same problem, namely artifacts caused by correlations in the Fourier components that arise from testing frequencies with a non-integer number of cycles. This article addresses this problem. The modified Rayleigh statistic is discussed, its generalization to any harmonic, R{sub k}{sup 2}, is formulated, and from the latter, the modified Z {sup 2} statistic, Z{sup 2}, is constructed. Versions of these statistics for binned data and point measurements are derived, and it is shown that the variance in the uncertainties can have an important influence on the periodogram. It is shown how to combine the information about the signal frequency from the different harmonics to estimate its value with maximum accuracy. The methods are applied to an XMM-Newton observation of the Crab pulsar for which a decomposition of the pulse profile is presented, and shows that most of the power is in the second, third, and fifth harmonics. Statistical detection power of the R{sub k}{sup 2} statistic is superior to the FFT and equivalent to the Lomb--Scargle (LS). Response to gaps in the data is assessed, and it is shown that the LS does not protect against the distortions they cause. The main conclusion of this work is that the classical R {sup 2} and Z {sup 2} should be replaced by R{sub k}{sup 2} and Z{sup 2} in all applications with event data, and the LS should be replaced by the R{sub k}{sup 2} when the uncertainty varies from one point measurement to another.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Experimental sloshing pressure impacts in ensemble domain: Transient and stationary statistical characteristics

The present paper focuses on the analysis of impact pressure registrations from repeated model scale sloshing experiments under harmonic rotational excitation. A series of more than 100 experiments, each one encompassing more than 100 impact events, has been conducted seeking the highest feasible repeatability. Different excitation periods, that cover the main features of the impact dynamics, have been considered in a preliminary screening, describing the main features of the impact dynamics. Since, even under a nominally deterministic excitation, the pressure at each impact is characterized by a high variability, a statistical approach is used treating the impact pressure as a stochastic process. For one selected excitation period, the statistical analysis focuses on the ensemble distribution of the maximum pressure during each impact event. Particular attention is given to the evolution of such distributions, in order to detect the variations in the statistical characteristics of the process. This is achieved by, first, identifying the presence and the length of the transient phase and, second, by characterizing the process at stationary state. The statistics of impact pressure for different peaks are discussed mostly in the ensemble domain. Linking the latter with the time domain analysis is made by checking that the problem can be considered “practically ergodic.” The “practical ergodicity” of the process is dealt with by checking to what extent steady state ensemble statistical information can be obtained from a single long run experiment. Statistical checks for correlation and independence of maximum impact pressures are also carried out to test the hypothesis of independent identically distributed random variables. The method of analysis presented in this paper through the considered example case is general in nature and is considered to be highly portable. In particular, it is considered to allow for a more thorough understanding of non-deterministic events such as those considered herein, by looking at them from a sound statistical perspective. The thorough description of the whole experimental setup makes the presented data suitable for comparison purposes and for validation of theoretical/numerical approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

The crossing statistic: dealing with unknown errors in the dispersion of Type Ia supernovae

We propose a new statistic that has been designed to be used in situations where the intrinsic dispersion of a data set is not well known: The Crossing Statistic. This statistic is in general less sensitive than χ{sup 2} to the intrinsic dispersion of the data, and hence allows us to make progress in distinguishing between different models using goodness of fit to the data even when the errors involved are poorly understood. The proposed statistic makes use of the shape and trends of a model's predictions in a quantifiable manner. It is applicable to a variety of circumstances, although we consider it to be especially well suited to the task of distinguishing between different cosmological models using type Ia supernovae. We show that this statistic can easily distinguish between different models in cases where the χ{sup 2} statistic fails. We also show that the last mode of the Crossing Statistic is identical to χ{sup 2}, so that it can be considered as a generalization of χ{sup 2}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Propagation of statistical uncertainties in covariant density functional theory: Ground state observables and single-particle properties

Statistical errors in ground state observables and single-particle properties of spherical even-even nuclei and their propagation to the limits of nuclear landscape have been investigated in covariant density functional theory (CDFT) for the first time. Here, we consider only covariant energy density functionals with non-linear density dependency. Statistical errors for binding energies and neutron skins significantly increase on approaching two-neutron drip line. On the contrary, such a trend does not exist for statistical errors in charge radii and two-neutron separation energies. The absolute and relative energies of the single-particle states in the vicinity of the Fermi level are characterized by low statistical errors ($\sigma(e_i)\sim 0.1$ MeV). Statistical errors in the predictions of spin-orbit splittings are rather small. Statistical errors in physical observables are substantially smaller than related systematic uncertainties. As a result, at the present level of the development of theory, theoretical uncertainties at nuclear limits are dominated by systematic ones. Statistical errors in the description of physical observables related to the ground state and single-particle degrees of freedom are typically substantially lower in CDFT as compared with Skyrme density functional theory. The correlations between the model parameters are studied in detail. The parametric correlations are especially pronounced for the $g_2$ and $g_3$ parameters which are responsible for the density dependence of the model. The accounting of this fact potentially allows to reduce the number of free parameters of non-linear meson coupling model from six to five.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Impact of baryonic feedback on HSC-Y1 weak lensing non-Gaussian statistics

Baryonic feedback is a major systematic in weak lensing cosmology. Its most studied effect is the suppression of the lensing power spectrum, a second-order statistic, on small scales. Motivated by the growing interest in statistics beyond the second order, we investigate the effect of baryons on lensing non-Gaussian statistics and the resulting biases in the matter clustering amplitude S 8 = σ 8 Ω m / 0.3 . We focus on the Subaru Hyper Suprime-Cam Year 1 (HSC-Y1) data which, with its high source number density, closely resembles those expected from the upcoming Euclid and Rubin Legacy Survey of Space and Time. We study four non-Gaussian statistics of convergence maps—peak counts, minimum counts, the probability distribution function, and the scattering transform coefficients—in addition to the usual power spectrum. We first estimate the biases in S 8 using mock observations built from the IllustrisTNG and BAHAMAS hydrodynamical simulations and theoretical models built from dark-matter-only simulations. We find up to 1 σ bias in S 8 when the smallest scales (2 arcmin) and the highest feedback level are considered. We then analyze the HSC-Y1 data and compare the S 8 obtained for each statistic with different smoothing scales or scale cuts. As we expect that baryons mostly affect the small scales, comparing the results obtained from including and excluding small scales can indicate the level of impact from baryons. With HSC data, we find only minor ( ≤ 0.5 σ ) differences in S 8 for all statistics, even when considering very small scales (2 arcmin). Our results suggest that the effect of baryons is insignificant at the level of HSC-Y1 down to 2 arcmin for all statistics examined here, or it is canceled by other scale-dependent systematics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking

Open quantum systems have complex energy eigenvalues which are expected to follow non-Hermitian random matrix statistics, when chaotic, or two-dimensional (2d) Poisson statistics, when integrable. We investigate the spectral properties of a many-body quantum spin chain, i.e., the Hermitian Heisenberg model with imaginary disorder. Its rich complex eigenvalue statistics is found to separately break both Hermiticity and integrability at different scales of the disorder strength. With no disorder, the system is integrable and Hermitian, with spectral statistics corresponding to the 1d Poisson point process. At very small disorder, we find a transition from 1d Poisson statistics to an effective D -dimensional Poisson point process, showing Hermiticity breaking. At intermediate disorder, we find integrability breaking, as inferred from the statistics matching that of non-Hermitian complex symmetric random matrices in class AI † . For large disorder, as the spins align, we recover the expected integrability (now in the non-Hermitian setup), indicated by 2d Poisson statistics. These conclusions are based on fitting the spin-chain data of numerically generated nearest- and next-to-nearest-neighbor spacing distributions to an effective 2d Coulomb gas description at inverse temperature β . We confirm that such an effective description of random matrices also applies in classes AI † and AII † up to next-to-nearest-neighbor spacings. Published by the American Physical Society 2025

Akemann, Gernot (ORCID:0000000217104258)↗
DOE OSTI2022

Streaming Statistics

In the context of a larger effort for in situ data analytics, there is a need to calculate basic statistics metrics (e.g., count, mean, median) online as new data points become available. Originally, the code for such online, or in other words streaming, statistics was part of the TALASS (Topological Analysis of Large- Scale Simulations) library. We isolated the relevant code and created a standalone library from it called Streaming Statistics. We also added an ability to serialize and deserialize the statistics objects so that the library can be used in distributed, task-based processing. To use the Streaming Statistics library, the user chooses a statistic, constructs an object for it, and then "adds" values to it, which means the statistic is augmented.

Shudler, Sergei↗
DOE OSTI2013

Topology for Statistical Modeling of Petascale Data

Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, the approach of the entire team involving all three institutions is based on the complementary techniques of combinatorial topology and statistical modelling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modelling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. The overall technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modelling, and (3) new integrated topological and statistical methods. Roughly speaking, the division of labor between our 3 groups (Sandia Labs in Livermore, Texas A&M in College Station, and U Utah in Salt Lake City) is as follows: the Sandia group focuses on statistical methods and their formulation in algebraic terms, and finds the application problems (and data sets) most relevant to this project, the Texas A&M Group develops new algebraic geometry algorithms, in particular with fewnomial theory, and the Utah group develops new algorithms in computational topology via Discrete Morse Theory. However, we hasten to point out that our three groups stay in tight contact via videconference every 2 weeks, so there is much synergy of ideas between the groups. The following of this document is focused on the contributions that had grater direct involvement from the team at the University of Utah in Salt Lake City.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1998

Statistical Treatment of Earth Observing System Pyroshock Separation Test Data

The Earth Observing System (EOS) AM-1 spacecraft for NASA's Mission to Planet Earth is scheduled to be launched on an Atlas IIAS vehicle in June of 1998. One concern is that the instruments on the EOS spacecraft are sensitive to the shock-induced vibration produced when the spacecraft separates from the launch vehicle. By employing unique statistical analysis to the available ground test shock data, the NASA Lewis Research Center found that shock-induced vibrations would not be as great as the previously specified levels of Lockheed Martin. The EOS pyroshock separation testing, which was completed in 1997, produced a large quantity of accelerometer data to characterize the shock response levels at the launch vehicle/spacecraft interface. Thirteen pyroshock separation firings of the EOS and payload adapter configuration yielded 78 total measurements at the interface. The multiple firings were necessary to qualify the newly developed Lockheed Martin six-hardpoint separation system. Because of the unusually large amount of data acquired, Lewis developed a statistical methodology to predict the maximum expected shock levels at the interface between the EOS spacecraft and the launch vehicle. Then, this methodology, which is based on six shear plate accelerometer measurements per test firing at the spacecraft/launch vehicle interface, was used to determine the shock endurance specification for EOS. Each pyroshock separation test of the EOS spacecraft simulator produced its own set of interface accelerometer data. Probability distributions, histograms, the median, and higher order moments (skew and kurtosis) were analyzed. The data were found to be lognormally distributed, which is consistent with NASA pyroshock standards. Each set of lognormally transformed test data produced was analyzed to determine if the data should be combined statistically. Statistical testing of the data's standard deviations and means (F and t testing, respectively) determined if data sets were significantly different at a 95-percent confidence level. If two data sets were found to be significantly different, these families of data were not combined for statistical purposes. This methodology produced three separate statistical data families of shear plate data. For each population, a P99.1/50 (probability/confidence) per-separation-nut firing level was calculated. By using the binomial distribution, Lewis researchers determined that this pernut firing level was equivalent to a P95/50 per-flight confidence level. The overall envelope of the per-flight P95/50 levels led to Lewis' recommended EOS interface shock endurance specification. A similar methodology was used to develop Lewis' recommended EOS mission assurance levels. The available test data for the EOS mission are significantly larger than for a normal mission, thus increasing the confidence level in the calculated expected shock environment. Lewis significantly affected the EOS mission by properly employing statistical analysis to the data. This analysis prevented a costly requalification of the spacecraft's instruments, which otherwise would have been exposed to significantly higher test levels.

McNelis, Anne M.↗
NASA NTRS2020

Antarctic Meteorites: A Statistical Look at a Uniquely Valuable Resource

As of the end of the 2018-19 field season, the U.S. Antarctic meteorite program has surpassed 23,000 meteorites collected. The U.S. collection is valuable in that it is classified in its entirety. The systematic methods employed to collect the meteorites have provided meteorites of more than 40 types, many of which are the first of their type ever recognized. One of the early drivers for consistent and methodical characterization of the entire U.S. Antarctic collection was to allow statistical comparisons. Early statistical assessments of the U.S. Antarctic collection examined mass distributions and the relative frequency of meteorite types as well as comparisons to a defined set of modern falls. Using these statistics argued that the flux of H chondrites changed over time used model size distributions to deconstruct the contribution of wind movement, meteorite supply and search losses to the Antarctic collection. Mass-based statistics and size distribution comparisons were examined by investigated various aspects of the statistics, including comparison with modern falls/Saharan finds. Also discuss geospatial statistics provides a comprehensive overview of the statistics of the Antarctic collections for the first 35 seasons of U.S. collection by ANSMET. Here we build upon that assessment and that from.

Corrigan, C. M.↗
NASA NTRSDate not supplied

Statistical Engineering

This webinar provides an overview of the International Statistical Engineering Association (ISEA), and it illustrates the practice of statistical engineering at NASA. ISEA was formed to promote the study of how successful data-based problem-solving methods are leveraged to realize innovative opportunities and solve problems sustainably. ISEA is comprised of statisticians, engineers, scientists, and other professionals that exchange ideas and experiences in the development and application of statistical engineering theories. ISEA is building the body of knowledge of the statistical engineering discipline with a particular focus on improving academic preparation for tackling complex problems. Over the past 15 years, the practice of statistical engineering has gained recognition within NASA by spurring innovation and efficiency, and it has demonstrated significant impact. Aerospace research and development benefits from an application-focused statistical engineering perspective to accelerate learning, maximize knowledge, ensure strategic resource investment, and inform data-driven decisions. The second portion of this presentation provides an overview of infusing statistical engineering at NASA through pioneering case studies in aeronautics, space exploration, and atmospheric science.

Peter A Parker↗
DOE OSTI2015

Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence

One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ{sub 1} : λ{sub 2} : λ{sub 3} is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume deformations. The results serve to characterize the fundamental statistical and geometric structure of turbulence at small scales including cumulative, time integrated effects. These are important for deformable particles such as droplets and polymers advected by turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Hierarchical reconstruction of 3D well-connected porous media from 2D exemplars using statistics-informed neural network

The relationships between porous microstructures and transport properties are of fundamental importance in various scientific and engineering applications. Due to the intricacy, stochasticity and heterogeneity of porous media, reliable characterization and modeling of transport properties often require a complete dataset of internal microstructure samples. However, it is often an unbearable cost to acquire sufficient 3D digital microstructures by purely using microscopic imaging systems. Herein this paper presents a machine learning-based technique to hierarchically reconstruct 3D well-connected porous microstructures from one isotropic or several anisotropic low-cost 2D exemplar(s). To compactly characterize the large-scale microstructural features, a Gaussian image pyramid is built for each 2D exemplar. Local morphology patterns are collected from the Gaussian image pyramids, and then they serve as the training data to embed the 2D morphological statistics into feed-forward neural networks at multiple length levels. By using a specially-developed morphology integration scheme, the 3D morphological statistics at different levels can be inferred from the statistics-informed neural networks. Gibbs sampling is adopted to hierarchically reconstruct 3D microstructures by using multi-level 3D morphological statistics, where the large-scale, regional and local morphological patterns are statistically generated and successively added to the same 3D random field. The proposed method is tested on a series of porous media with distinct morphologies, and the statistical equivalence between the reconstructed and the real microstructures is systematically evaluated by comparing morphological descriptors and transport properties. The results demonstrate that the proposed 2D-to-3D microstructure reconstruction method is a universal and efficient approach to generating morphologically and physically realistic samples of porous media.

42 ENGINEERING↗
DOE OSTI2017

Tests for, origins of, and corrections to non-Gaussian statistics. The dipole-flip model

Linear response approximations are central to our understanding and simulations of nonequilibrium statistical mechanics. Despite the success of these approaches in predicting nonequilibrium dynamics, open questions remain. Laird and Thompson [J. Chem. Phys. 126, 211104 (2007)] previously formalized, in the context of solvation dynamics, the connection between the static linear-response approximation and the assumption of Gaussian statistics. The Gaussian statistics perspective is useful in understanding why linear response approximations are still accurate for perturbations much larger than thermal energies. In this study, we use this approach to address three outstanding issues in the context of the “dipole-flip” model, which is known to exhibit nonlinear response. First, we demonstrate how non-Gaussian statistics can be predicted from purely equilibrium molecular dynamics (MD) simulations (i.e., without resort to a full nonequilibrium MD as is the current practice). Second, we show that the Gaussian statistics approximation may also be used to identify the physical origins of nonlinear response residing in a small number of coordinates. Third, we explore an approach for correcting the Gaussian statistics approximation for nonlinear response effects using the same equilibrium simulation. Finally, the results are discussed in the context of several other examples of nonlinear responses throughout the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

A NEW METHOD TO CORRECT FOR FIBER COLLISIONS IN GALAXY TWO-POINT STATISTICS

In fiber-fed galaxy redshift surveys, the finite size of the fiber plugs prevents two fibers from being placed too close to one another, limiting the ability to study galaxy clustering on all scales. We present a new method for correcting such fiber collision effects in galaxy clustering statistics based on spectroscopic observations. The target galaxy sample is divided into two distinct populations according to the targeting algorithm of fiber placement, one free of fiber collisions and the other consisting of collided galaxies. The clustering statistics are a combination of the contributions from these two populations. Our method makes use of observations in tile overlap regions to measure the contributions from the collided population, and to therefore recover the full clustering statistics. The method is rooted in solid theoretical ground and is tested extensively on mock galaxy catalogs. We demonstrate that our method can well recover the projected and the full three-dimensional (3D) redshift-space two-point correlation functions (2PCFs) on scales both below and above the fiber collision scale, superior to the commonly used nearest neighbor and angular correction methods. We discuss potential systematic effects in our method. The statistical correction accuracy of our method is only limited by sample variance, which scales down with (the square root of) the volume probed. For a sample similar to the final SDSS-III BOSS galaxy sample, the statistical correction error is expected to be at the level of 1% on scales {approx}0.1-30 h {sup -1} Mpc for the 2PCFs. The systematic error only occurs on small scales, caused by imperfect correction of collision multiplets, and its magnitude is expected to be smaller than 5%. Our correction method, which can be generalized to other clustering statistics as well, enables more accurate measurements of full 3D galaxy clustering on all scales with galaxy redshift surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

2D k -th nearest neighbour statistics: a highly informative probe of galaxy clustering

ABSTRACT Beyond standard summary statistics are necessary to summarize the rich information on non-linear scales in the era of precision galaxy clustering measurements. For the first time, we introduce the 2D k-th nearest neighbour (kNN) statistics as a summary statistic for discrete galaxy fields. This is a direct generalization of the standard 1D kNN by disentangling the projected galaxy distribution from the redshift-space distortion signature along the line-of-sight. We further introduce two different flavours of 2D kNNs that trace different aspects of the galaxy field: the standard flavour which tabulates the distances between galaxies and random query points, and a ‘DD’ flavour that tabulates the distances between galaxies and galaxies. We showcase the 2D kNNs’ strong constraining power both through theoretical arguments and by testing on realistic galaxy mocks. Theoretically, we show that 2D kNNs are computationally efficient and directly generate other statistics such as the popular two-point correlation function (2PCF), voids probability function, and counts-in-cell statistics. In a more practical test, we apply the 2D kNN statistics to simulated galaxy mocks that fold in a large range of observational realism and recover parameters of the underlying extended halo occupation distribution (HOD) model that includes velocity bias and galaxy assembly bias. We find unbiased and significantly tighter constraints on all aspects of the HOD model with the 2D kNNs, both compared to the standard 1D kNN, and the classical redshift-space 2PCF.

79 ASTRONOMY AND ASTROPHYSICS↗