KLLR: A Scale-dependent, Multivariate Model Class for Regression Analysis

Farahi, Arya; Anbajagane, Dhayaa; Evrard, A. E.

doi:10.3847/1538-4357/ac6ac7

Cited by 13 publications

(4 citation statements)

References 61 publications

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Section: Analysis Methodsmentioning

confidence: 99%

“…In this work, we employ the KERNEL LOCALIZED LINEAR REGRESSION (KLLR, https://github.com/afarahi/kllr; Farahi et al 2022) method to regress the logarithm of the dark matter, gas, and stellar density profiles as a function of x and for TNG halos in a given mass bin. The KLLR performs a kernelweighted least-squares fitting and reports the average profile and the covariance between profiles at fixed x (see Equations (8)-( 13) in Farahi et al 2022). In empirical settings, where one needs to deal with low signal-to-noise (S/N) measurements, population-based inference methods like the POPULATION PROFILE ESTIMATOR (PoPE, https://github.com/afarahi/ PoPE; Farahi et al 2021) are more suitable.…”

Section: Analysis Methodsmentioning

confidence: 99%

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Correlations of Dark Matter, Gas, and Stellar Profiles in Dark Matter Halos

Farahi

Nagai

Anbajagane

2022

ApJ

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Halos of similar mass and redshift exhibit a large degree of variability in their differential properties, such as dark matter, hot gas, and stellar mass density profiles. This variability is an indicator of diversity in the formation history of these dark matter halos that is reflected in the coupling of scatters about the mean relations. In this work, we show that the strength of this coupling depends on the scale at which halo profiles are measured. By analyzing the outputs of the IllustrisTNG hydrodynamical cosmological simulations, we report the radial- and mass-dependent couplings between the dark matter, hot gas, and stellar mass radial density profiles utilizing the population diversity in dark matter halos. We find that for the same mass halos, the scatters in the density of baryons and dark matter are strongly coupled at large scales (r > R 200), but the coupling between gas and dark matter density profiles fades near the core of halos (r < 0.3R 200). We then show that the correlation between halo profile and integrated quantities induces a radius-dependent additive bias in the profile observables of halos when halos are selected on properties other than their mass. We discuss the impact of this effect on cluster abundance and cross-correlation cosmology with multiwavelength cosmological surveys.

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Section: Analysis Methodsmentioning

confidence: 99%

Section: Analysis Methodsmentioning

confidence: 99%

Correlations of Dark Matter, Gas, and Stellar Profiles in Dark Matter Halos

Farahi

Nagai

Anbajagane

2022

ApJ

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“…Opportunities also exist for studying the correlations between profiles, and these can have strong astrophysical signatures (e.g., Farahi et al 2022b). Techniques have also been developed to extract such profile correlations in a data-driven manner, with minimal assumptions, such as Gaussian processes (Farahi et al 2021) and local linear regression (Farahi et al 2022a). Thus, there are many synergistic opportunities for crosscorrelating the different types of datasets -both ongoing and upcoming -and each combination will allow us to access different science cases regarding the physics of these cluster outskirts.…”

Section: Summary and Discussionmentioning

confidence: 99%

Shocks in the stacked Sunyaev-Zel’dovich profiles of clusters II: Measurements from SPT-SZ + Planck Compton-y map

Anbajagane

Jain

Adhikari

et al. 2022

Monthly Notices of the Royal Astronomical Society

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We search for the signature of cosmological shocks in stacked gas pressure profiles of galaxy clusters using data from the South Pole Telescope (SPT). Specifically, we stack the latest Compton-y maps from the 2500 deg2 SPT-SZ survey on the locations of clusters identified in that same dataset. The sample contains 516 clusters with mean mass 〈M200m〉 = 1014.9 M⊙ and redshift 〈z〉 = 0.55. We analyse in parallel a set of zoom-in hydrodynamical simulations from The Three Hundred project. The SPT-SZ data show two features: (i) a pressure deficit at R/R200m = 1.08 ± 0.09, measured at 3.1σ significance and not observed in the simulations, and; (ii) a sharp decrease in pressure at R/R200m = 4.58 ± 1.24 at 2.0σ significance. The pressure deficit is qualitatively consistent with a shock-induced thermal non-equilibrium between electrons and ions, and the second feature is consistent with accretion shocks seen in previous studies. We split the cluster sample by redshift and mass, and find both features exist in all cases. There are also no significant differences in features along and across the cluster major axis, whose orientation roughly points towards filamentary structure. As a consistency test, we also analyse clusters from the Planck and Atacama Cosmology Telescope Polarimeter surveys and find quantitatively similar features in the pressure profiles. Finally, we compare the accretion shock radius (Rsh, acc) with existing measurements of the splashback radius (Rsp) for SPT-SZ and constrain the lower limit of the ratio, Rsh, acc/Rsp > 2.16 ± 0.59.

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“…To examine this mean relationship, we employ Kernel-Localized Linear Regression 18,19 (KLLR), a method that determines parameters of a locally linear fit (mean, slope, and variance) within a sliding Gaussian window. This approach to population modeling allows for more nuanced analysis than polynomial fitting as it does not enforce a particular global behavior.…”

Section: E Measuring Study Gains With Kllrmentioning

confidence: 99%

Practice Makes Better: Quantifying Grade Benefits of Study

Black¹,

Matz²,

Mills³

et al. 2023

Preprint

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Problem Roulette (PR), an online study service at the University of Michigan, offers point-free practice to students preparing for examinations in introductory STEM courses. Using four years of PR data involving millions of problem attempts by thousands of students, we quantify benefits of increased practice study volume in introductory physics. After conditioning mean final grade on standardized (ACT/SAT) math test score, we analyze deviations based on student study volume. We find a strong effect; mean course grade rises quadratically with the logarithm of the total number of PR questions encountered over the term (N Q,tot ), with an overall gain of 0.78 ± 0.12 grade points between 1 < N Q,tot < 1000. The gains are persistent across the range of math test score represented in our sample. A linear model for final grade using test score and study volume largely accounts for demographic stratification, including by sex, parental education level, number of parents at home, nationality / underrepresented minority status, and regional income level, with two significant exceptions: students whose parents did not earn a college degree, who earn −0.27 ± 0.04 grade points (6.2σ ) below expectations and underrepresented minority students at −0.14±0.04 points (3.7σ ). Residual scatter in final grade remains comparable to the maximum gain from studying more, implying that the model is far from deterministic at the level of an individual. Our findings can help motivate students to study more and help teachers to identify which types of students may especially need such encouragement.

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KLLR: A Scale-dependent, Multivariate Model Class for Regression Analysis

Cited by 13 publications

References 61 publications

Correlations of Dark Matter, Gas, and Stellar Profiles in Dark Matter Halos

Correlations of Dark Matter, Gas, and Stellar Profiles in Dark Matter Halos

Shocks in the stacked Sunyaev-Zel’dovich profiles of clusters II: Measurements from SPT-SZ + Planck Compton-y map

Practice Makes Better: Quantifying Grade Benefits of Study

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