Malmquist Bias Research Articles

Solving the inverse cosmological calibration problem of gamma-ray bursts

ABSTRACT We have received a new physical characteristics fitting based on actual observational data from the Swift mission’s long-duration gamma-ray bursts (LGRBs). We considered such characteristics as the Amati parameters for linear correlation (Eiso–Ep,i) and the k-correction for gravitational lensing and Malmquist bias (GLMB) effect. We used the Pantheon SN Ia catalogue and the standard Lambda cold dark matter model with a fixed Hubble constant of H0 = 70 km s−1 Mpc−1 as the baseline for the Hubble function μ(z). In our paper, we formulated the inverse cosmological calibration problem (ICCP) in the non-parametric statistics framework. The ICCP involves fitting non-observable physical characteristics while assuming a fixed cosmological model. To solve this problem, we developed a new method that is resistant to non-Gaussian processes. This method is based on error propagation through the Monte Carlo method and the Theil–Sen method for linear regression estimate. We have demonstrated the stability and robustness of this assessment method. The parameter estimates are as follows: $a=0.92^{+0.12}_{-0.12}$, $b=50.32^{+0.33}_{-0.32}$ without considering the GLMB effect, and $a=0.63^{+0.13}_{-0.14}$, $b=50.12^{+0.33}_{-0.31}$, and $k=1.98^{+0.25}_{-0.24}$ with the effect included. The proposed method can be applied to any other calibration sample of known standard candles, a calibrated sample of LGRBs, and the Hubble function μ(z). In the future, the ICCP idea can be used as an alternative cosmological test for estimating cosmological parameters, including the GLMB effect, or even for the selection of models, providing new information about the Universe. This can be done by analysing the residual values of observational data within the Bayesian statistics paradigm.

Statistically bias-minimized peculiar velocity catalogs from Gibbs point processes and Bayesian inference

The peculiar velocities of galaxies can serve as excellent cosmological probes provided that the biases inherent to their measurements are contained prior to the start of any study. This paper proposes a new algorithm based on an object point process model whose probability density is built to statistically reduce the effects of Malmquist biases and uncertainties due to lognormal errors in radial peculiar velocity catalogs. More precisely, a simulated annealing algorithm allows for the probability density describing the point process model to be maximized. The resulting configurations are bias-minimized catalogs. We conducted tests on synthetic catalogs mimicking the second and third distance modulus catalogs of the Cosmicflows project from which peculiar velocity catalogs are derived. By reducing the local peculiar velocity variance in catalogs by an order of magnitude, the algorithm permits the recovery of the expected one, while preserving the small-scale velocity correlation. It also allows for the expected clustering to be retrieved. The algorithm was then applied to the observational catalogs. The large-scale structure reconstructed with the Wiener-filter technique applied to the bias-minimized observational catalogs matches that of the local cosmic web well, as supported by redshift surveys of local galaxies. These new bias-minimized versions of peculiar velocity catalogs can be used as a starting point for several studies, from plausible estimations of the most probable value for the Hubble constant, H0, to the production of simulations constrained to reproduce the local Universe.

A population of Type Ibc supernovae with massive progenitors

If high-mass stars (≳20 − 25 M⊙) are the progenitors of stripped-envelope (SE) supernovae (SNe), their massive ejecta should lead to broad, long-duration lightcurves. Instead, literature samples of SE SNe have reported relatively narrow lightcurves corresponding to ejecta masses between 1 − 4 M⊙ that favor intermediate-mass progenitors (≲20 − 25 M⊙). Working with an untargeted sample from a single telescope to better constrain their rates, we searched the Palomar Transient Factory (PTF) and intermediate-PTF (iPTF) sample of SNe for SE SNe with broad lightcurves. Using a simple observational marker of g- or r-band lightcurve stretch compared to a template to measure broadness, we identified eight significantly broader Type Ibc SNe after applying quantitative sample selection criteria. The lightcurves, broad-band colors, and spectra of these SNe are found to evolve more slowly relative to typical Type Ibc SNe, proportional with the stretch parameter. Bolometric lightcurve modeling and their nebular spectra indicate high ejecta masses and nickel masses, assuming radioactive decay powering. Additionally, these objects are preferentially located in low-metallicity host galaxies with high star formation rates, which may account for their massive progenitors, as well as their relative absence from the literature. Our study thus supports the link between broad lightcurves (as measured by stretch) and high-mass progenitor stars in SE SNe with independent evidence from bolometric lightcurve modeling, nebular spectra, host environment properties, and photometric evolution. In the first systematic search of its kind using an untargeted sample, we used the stretch distribution to identify a higher than previously appreciated fraction of SE SNe with broad lightcurves (∼13%). Correcting for Malmquist and lightcurve duration observational biases, we conservatively estimate that a minimum of ∼6% of SE SNe are consistent with high-mass progenitors. This result has implications for the progenitor channels of SE SNe, including late stages of massive stellar evolution, the origin of the observed oxygen fraction in the universe, and formation channels for stellar-mass black holes.

Photo-zSNthesis: Converting Type Ia Supernova Lightcurves to Redshift Estimates via Deep Learning

Upcoming photometric surveys will discover tens of thousands of Type Ia supernovae (SNe Ia), vastly outpacing the capacity of our spectroscopic resources. In order to maximize the scientific return of these observations in the absence of spectroscopic information, we must accurately extract key parameters, such as SN redshifts, with photometric information alone. We present Photo-zSNthesis, a convolutional neural network-based method for predicting full redshift probability distributions from multi-band supernova lightcurves, tested on both simulated Sloan Digital Sky Survey (SDSS) and Vera C. Rubin Legacy Survey of Space and Time data as well as observed SDSS SNe. We show major improvements over predictions from existing methods on both simulations and real observations as well as minimal redshift-dependent bias, which is a challenge due to selection effects, e.g., Malmquist bias. Specifically, we show a 61× improvement in prediction bias 〈Δz〉 on PLAsTiCC simulations and 5× improvement on real SDSS data compared to results from a widely used photometric redshift estimator, LCFIT+Z. The PDFs produced by this method are well constrained and will maximize the cosmological constraining power of photometric SNe Ia samples.

NICMOS Kernel-phase Interferometry. II. Demographics of Nearby Brown Dwarfs

Star formation theories have struggled to reproduce binary brown dwarf population demographics (e.g., frequency, separation, and mass ratio). Kernel-phase interferometry is sensitive to companions at separations inaccessible to classical imaging, enabling tests of these theories at new physical scales below the hydrogen burning limit. We analyze the detections and sensitivity limits from our previous kernel-phase analysis of archival HST/NICMOS surveys of field brown dwarfs. After estimating physical properties of the 105 late-M to T dwarfs using Gaia distances and evolutionary models, we use a Bayesian framework to compare these results to a model companion population defined by log-normal separation and power-law mass-ratio distributions. When correcting for Malmquist bias, we find a companion fraction of and a separation distribution centered at au, smaller and tighter than seen in previous studies. We also find a mass-ratio power-law index that strongly favors equal-mass systems: depending on the assumed age of the field population (0.9–3.1 Gyr). We attribute the change in values to our use of kernel-phase interferometry, which enables us to resolve the peak of the semimajor axis distribution with significant sensitivity to low-mass companions. We confirm the previously seen trends of decreasing binary fraction with decreasing mass and a strong preference for tight and equal-mass systems in the field-age substellar regime; only % of systems are wider than 20 au and % of systems have a mass ratio q < 0.6. We attribute this to turbulent fragmentation setting the initial conditions followed by a brief period of dynamical evolution, removing the widest and lowest-mass companions, before the birth cluster dissolves.

Redshift–luminosity characterization of active galactic nucleus galaxies having obscuring dusty material using the spectral energy distribution from the X-ray to far-infrared

ABSTRACT The spectral energy distribution (SED) from the X-ray to far-IR is used to characterize active galactic nuclei (AGNs) having obscuring dusty material. A sample of 73 AGNs, with redshifts of z &amp;lt; 2.5, is subdivided based on the optical spectra into subgroups of type 1 and 2 AGNs and no-AGN. The x-cigale code is used to produce the SEDs of these galaxies, fitting them with their observed flux densities. Accordingly, this code provides estimates of the physical properties, including the stellar mass, dust-to-gas mass ratio, far-UV attenuation, star-formation rate, and luminosity. All these properties and luminosity components, namely stellar, AGN, X-ray, and dust luminosities, are characterized versus the redshift. With the caveat that the sample is flux-limited and thus is affected by Malmquist bias, the results show that these properties increase as a function of redshift with various variation rates for each galaxy group, except for the far-UV attenuation of type 1 AGNs, which shows a slight reduction with redshift. The stellar, AGN, and X-ray luminosities show tight correlations with the intrinsic AGN luminosity, which is, in principle, attributed to the intrinsic AGN accretion power acting as a fuelling source. This power has an impact on most other correlations versus the redshift when the intrinsic AGN luminosity increases with redshift. Owing to their different emission sources, these luminosities make different fractional contributions to the total luminosity. The stellar luminosity, where the dust luminosity is the most effective, has the highest contribution of all galaxy groups, while the AGN luminosity has the lowest.

Bayesian reconstruction of dark matter distribution from peculiar velocities: accounting for inhomogeneous Malmquist bias

ABSTRACT We present a Bayesian velocity field reconstruction algorithm that performs the reconstruction of the mass density field using only peculiar velocity data. Our method consistently accounts for the inhomogeneous Malmquist (IHM) bias using analytical integration along the line of sight. By testing our method on a simulation, we show that our method gives an unbiased reconstruction of the velocity field. We show that not accounting for the IHM bias can lead to significant biases in the Bayesian reconstructions. We applied our method to a peculiar velocity data set consisting of the SFI++ and 2MTF Tully–Fisher catalogues and the A2 supernovae compilation, thus obtaining a novel velocity reconstruction in the local Universe. Our velocity reconstructions have a cosmological power spectrum consistent with the theoretical expectation. Furthermore, we obtain a full description of the uncertainties on reconstruction through samples of the posterior distribution. We validate our velocity reconstruction of the local Universe by comparing it to an independent reconstruction using the 2M++ galaxy catalogue, obtaining good agreement between the two reconstructions. Using Bayesian model comparison, we find that our velocity model performs better than the adaptive kernel smoothed velocity with the same peculiar velocity data. However, our velocity model does not perform as well as the velocity reconstruction from the 2M++ galaxy catalogue, due to the sparse and noisy nature of the peculiar velocity tracer samples. The method presented here provides a way to include peculiar velocity data in initial condition reconstruction frameworks.

Flexible and Accurate Evaluation of Gravitational-wave Malmquist Bias with Machine Learning

Abstract Many astronomical surveys are limited by the brightness of the sources, and gravitational-wave searches are no exception. The detectability of gravitational waves from merging binaries is affected by the mass and spin of the constituent compact objects. To perform unbiased inference on the distribution of compact binaries, it is necessary to account for this selection effect, which is known as Malmquist bias. Since systematic error from selection effects grows with the number of events, it will be increasingly important over the coming years to accurately estimate the observational selection function for gravitational-wave astronomy. We employ density estimation methods to accurately and efficiently compute the compact binary coalescence selection function. We introduce a simple pre-processing method, which significantly reduces the complexity of the required machine-learning models. We demonstrate that our method has smaller statistical errors at comparable computational cost than the method currently most widely used allowing us to probe narrower distributions of spin magnitudes. The currently used method leaves 10%–50% of the interesting black hole spin models inaccessible; our new method can probe &gt;99% of the models and has a lower uncertainty for &gt;80% of the models.

Characterizing the Observation Bias in Gravitational-wave Detections and Finding Structured Population Properties

Abstract The observed distributions of the source properties from gravitational-wave (GW) detections are biased due to the selection effects and detection criteria in the detections, analogous to the Malmquist bias. In this work, this observation bias is investigated through its fundamental statistical and physical origins. An efficient semi-analytical formulation for its estimation is derived, which is as accurate as the standard method of numerical simulations, with only a millionth of the computational cost. Then, the estimated bias is used for unmodeled inferences on the binary black hole population. These inferences show additional structures, specifically two peaks in the joint mass distribution around binary masses ∼10 M ⊙ and ∼30 M ⊙. Example ready-to-use scripts and some produced data sets for this method are shared in an online repository.

Unbiased likelihood-free inference of the Hubble constant from light standard sirens

Multi-messenger observations of binary neutron star mergers offer a promising path towards resolution of the Hubble constant ($H_0$) tension, provided their constraints are shown to be free from systematics such as the Malmquist bias. In the traditional Bayesian framework, accounting for selection effects in the likelihood requires calculation of the expected number (or fraction) of detections as a function of the parameters describing the population and cosmology; a potentially costly and/or inaccurate process. This calculation can, however, be bypassed completely by performing the inference in a framework in which the likelihood is never explicitly calculated, but instead fit using forward simulations of the data, which naturally include the selection. This is Likelihood-Free Inference (LFI). Here, we use density-estimation LFI, coupled to neural-network-based data compression, to infer $H_0$ from mock catalogues of binary neutron star mergers, given noisy redshift, distance and peculiar velocity estimates for each object. We demonstrate that LFI yields statistically unbiased estimates of $H_0$ in the presence of selection effects, with precision matching that of sampling the full Bayesian hierarchical model. Marginalizing over the bias increases the $H_0$ uncertainty by only $6\%$ for training sets consisting of $O(10^4)$ populations. The resulting LFI framework is applicable to population-level inference problems with selection effects across astrophysics.

Two c’s in a pod: cosmology-independent measurement of the Type Ia supernova colour–luminosity relation with a sibling pair

ABSTRACT Using Zwicky Transient Facility (ZTF) observations, we identify a pair of ‘sibling’ Type Ia supernovae (SNe Ia), i.e. hosted by the same galaxy at z = 0.0541. They exploded within 200 d from each other at a separation of $0.6\,\mathrm{ arcsec}$ corresponding to a projected distance of only 0.6 kpc. Performing salt2 light-curve fits to the gri ZTF photometry, we show that for these equally distant ‘standardizable candles’, there is a difference of 2 mag in their rest-frame B-band peaks, and the fainter supernova (SN) has a significantly red salt2 colour c = 0.57 ± 0.04, while the stretch values x1 of the two SNe are similar, suggesting that the fainter SN is attenuated by dust in the interstellar medium of the host galaxy. We use these measurements to infer the salt2 colour standardization parameter, β = 3.5 ± 0.3, independent of the underlying cosmology and Malmquist bias. Assuming the colour excess is entirely due to dust, the result differs by 2σ from the average Milky Way total-to-selective extinction ratio, but is in good agreement with the colour–brightness corrections empirically derived from the most recent SN Ia Hubble–Lemaitre diagram fits. Thus we suggest that SN ‘siblings’, which will increasingly be discovered in the coming years, can be used to probe the validity of the colour and light-curve shape corrections using in SN Ia cosmology while avoiding important systematic effects in their inference from global multiparameter fits to inhomogeneous data sets, and also help constrain the role of interstellar dust in SN Ia cosmology.

The local vertical density distribution of ultracool dwarfs M7 to L2.5 and their luminosity function

We investigate the form of the local vertical density profile of the stars in the Galactic disk, close to the Galactic plane. We use a homogeneous sample of 34000 ultracool dwarfs M7 to L2.5 that all lie within 350 pc of the plane. We fit a profile of the form sech$^\alpha$, where $\alpha=2$ is the theoretically preferred isothermal profile and $\alpha=0$ is the exponential function. Larger values of $\alpha$ correspond to greater flattening of the profile towards the plane. We employ a likelihood analysis that accounts in a direct way for unresolved binaries in the sample, as well as for the spread in absolute magnitude $M_J$ within each spectral sub-type (Malmquist bias). We measure $\alpha=0.29^{+0.12}_{-0.13}$. The $\alpha=1$ (sech) and flatter profiles are ruled out at high confidence for this sample, while $\alpha=0$ (exponential) is included in the 95% credible interval. Any flattening relative to exponential is modest, and is confined to within 50 pc of the plane. The measured value of $\alpha$ is consistent with the results of the recent analysis by Xiang et al. Our value for $\alpha$ is also similar to that determined for nearby spiral galaxies by de Grijs et al., measured from photometry of galaxies viewed edge on. The measured profile allows an accurate determination of the local space density of ultracool dwarfs M7 to L2.5, and we use this to make a new determination of the luminosity function at the bottom of the main sequence. Our results for the luminosity function are a factor two to three lower than the recent measurement by Bardalez Gagliuffi et al., that uses stars in the local 25 pc radius bubble, but agree well with the older study by Cruz et al.

Chandra Observations of the Planck Early Sunyaev–Zeldovich Sample: A Reexamination of Masses and Mass Proxies

Abstract Using Chandra observations, we derive the Y X proxy and associated total mass measurement, , for 147 clusters with z &lt; 0.35 from the Planck early Sunyaev–Zeldovich catalog, and for 80 clusters with z &lt; 0.22 from an X-ray flux-limited sample. We reextract the Planck Y SZ measurements and obtain the corresponding mass proxy, , from the full Planck mission maps, minimizing Malmquist bias due to observational scatter. The masses reextracted using the more precise X-ray position and characteristic size agree with the published PSZ2 values, but yield a significant reduction in the scatter (by a factor of two) in the – relation. The slope is 0.93 ± 0.03, and the median ratio, , is within the expectations from known X-ray calibration systematics. Y SZ/Y X is 0.88 ± 0.02, in good agreement with predictions from cluster structure, and implying a low level of clumpiness. In agreement with the findings of the Planck Collaboration, the slope of the Y SZ– flux relation is significantly less than unity (0.89 ± 0.01). Using extensive simulations, we show that this result is not due to selection effects, intrinsic scatter, or covariance between quantities. We demonstrate analytically that changing the Y SZ–Y X relation from apparent flux to intrinsic properties results in a best-fit slope that is closer to unity and increases the dispersion about the relation. The redistribution resulting from this transformation implies that the best-fit parameters of the – relation will be sample-dependent.

Redshift evolution of the underlying type Ia supernova stretch distribution

The detailed nature of type Ia supernovae (SNe Ia) remains uncertain, and as survey statistics increase, the question of astrophysical systematic uncertainties arises, notably that of the evolution of SN Ia populations. We study the dependence on redshift of the SN Ia SALT2.4 light-curve stretch, which is a purely intrinsic SN property, to probe its potential redshift drift. The SN stretch has been shown to be strongly correlated with the SN environment, notably with stellar age tracers. We modeled the underlying stretch distribution as a function of redshift, using the evolution of the fraction of young and old SNe Ia as predicted using the SNfactory dataset, and assuming a constant underlying stretch distribution for each age population consisting of Gaussian mixtures. We tested our prediction against published samples that were cut to have marginal magnitude selection effects, so that any observed change is indeed astrophysical and not observational in origin. In this first study, there are indications that the underlying SN Ia stretch distribution evolves as a function of redshift, and that the age drifting model is a better description of the data than any time-constant model, including the sample-based asymmetric distributions that are often used to correct Malmquist bias at a significance higher than 5σ. The favored underlying stretch model is a bimodal one, composed of a high-stretch mode shared by both young and old environments, and a low-stretch mode that is exclusive to old environments. The precise effect of the redshift evolution of the intrinsic properties of a SN Ia population on cosmology remains to be studied. The astrophysical drift of the SN stretch distribution does affect current Malmquist bias corrections, however, and thereby the distances that are derived based on SN that are affected by observational selection effects. We highlight that this bias will increase with surveys covering increasingly larger redshift ranges, which is particularly important for the Large Synoptic Survey Telescope.

The Red Supergiant Content of M31 and M33

Abstract We identify red supergiants (RSGs) in our spiral neighbors M31 and M33 using near-IR (NIR) photometry complete to a luminosity limit of . Our archival survey data cover 5 deg2 of M31, and 3 deg2 for M33, and are likely spatially complete for these massive stars. Gaia is used to remove foreground stars, after which the RSGs can be separated from asymptotic giant branch (AGB) stars in the color–magnitude diagram. The photometry is used to derive effective temperatures and bolometric luminosities via MARCS stellar atmosphere models. The resulting H-R diagrams show superb agreement with the evolutionary tracks of the Geneva evolutionary group. Our census includes 6400 RSGs in M31 and 2850 RSGs in M33 within their Holmberg radii; by contrast, only a few hundred RSGs are known so far in the Milky Way. Our catalog serves as the basis for a study of the RSG binary frequency being published separately, as well as future studies relating to the evolution of massive stars. Here we use the matches between the NIR-selected RSGs and their optical counterparts to show that the apparent similarity in the reddening of OB stars in M31 and M33 is the result of Malmquist bias; the average extinction in M31 is likely higher than that of M33. As expected, the distribution of RSGs follows that of the spiral arms, while the much older AGB population is more uniformly spread across each galaxy’s disk.

Statistical distances of the northern sky bright K and M dwarfs with apparent magnitude J < 9

ABSTRACT In this paper, we estimate distances and generate the mean absolute magnitudes and dispersions for K and M bright dwarfs using two different approaches. The methods are based on the assumption that the absolute and apparent magnitude follows the exponential and Gaussian distributions functions. The effect of Malmquist bias has been studied to show how effective bias is in comparison. We found that the range between the calculated distances for the spectral subtypes K is small (2.6 pcs), while the range in the distance of the spectral subtypes M is a little big (21.6 pcs), and this may be due to the different chemical compositions and evolution scenarios for each spectral subtype. This means that these dwarfs are situated in the same cloud as near and far sides. We spread the dwarfs above and below the galactic plane to gain certain physical properties based on the statistical study and also on the spectral subtypes. The estimated distances from the two approaches are approximately the same but there are noticeable differences between the generated mean absolute magnitudes and dispersions.

High-redshift long gamma-ray bursts Hubble diagram as a test of basic cosmological relations

ABSTRACT We examine the prospects of the high-redshift long gamma-ray bursts (LGRBs) Hubble diagram as a test of the basic cosmological principles. Analysis of the Hubble diagram allows us to test several fundamental cosmological principles using the directly observed flux–distance–redshift relation. Modern LGRBs data together with the correlation between the spectral peak energy and the isotropic equivalent radiated energy (the so-called Amati relation) can be used for construction of the Hubble diagram at the model-independent level. We emphasize observational selection effects, which inevitably exist and distort the theoretically predicted relations. An example is the weak and strong gravitational lensing bias effect for high-redshift LGRB in the presence of limited observational sensitivity (Malmquist bias). After bias correction, there is a tendency to vacuum-dominated models with $\Omega _\Lambda \rightarrow 0.9$, Ωm → 0.1. Forthcoming gamma-ray observations by the Transient High-Energy Sky and Early Universe Surveyor (THESEUS) space mission together with ground- and space-based multimessenger facilities will allow us to improve essentially the restrictions on alternative basic principles of cosmological models.

H i gas content of SDSS galaxies revealed by ALFALFA: implications for the mass–metallicity relation and the environmental dependence of H i in the local Universe

ABSTRACT The neutral hydrogen (H i) gas is an important barometer of recent star formation and metal enrichment activities in galaxies. I develop a novel statistical method for predicting the H i-to-stellar mass ratio, $f_{\mathrm{H\,{\small I}}}$, of galaxies from their stellar mass and optical colour, and apply it to a volume-limited galaxy sample jointly observed by the Sloan Digital Sky Survey and the Arecibo Legacy Fast ALFA survey. I eliminate the impact of the Malmquist bias against H i-deficient systems on the $f_{\mathrm{H\,{\small I}}}$ predictor by properly accounting for the H i detection probability of each galaxy in the analysis. The best-fitting $f_{\mathrm{H\,{\small I}}}$ predictor, with an estimated scatter of 0.272 dex, provides excellent description to the observed H i mass function. After defining an H i excess parameter as the deviation of the observed $f_{\mathrm{H\,{\small I}}}$ from the expected value, I confirm that there exists a strong secondary dependence of the mass–metallicity relation on H i excess. By further examining the 2D metallicity distribution on the specific star formation rate (sSFR) versus H i excess plane, I show that the metallicity dependence on H i is likely more fundamental than that on sSFR. In addition, I find that the environmental dependence of H i in the local Universe can be effectively described by the cross-correlation coefficient between H i excess and the red galaxy overdensity ρcc = − 0.18. This weak anticorrelation also successfully explains the observed dependence of H i clustering on $f_{\mathrm{H\,{\small I}}}$. My method provides a useful framework for learning H i gas evolution from the synergy between future H i and optical galaxy surveys.

ВПЛИВ СТАТИСТИЧНИХ ЕФЕКТІВ НА ВЕЛИЧИНУ СТАЛОЇ ГАББЛА, ОТРИМАНУ ЗА ШВИДКОСТЯМИ ГАЛАКТИК

We can obtain the Hubble constant value for the late Universe from the sample of radial velocities of galaxies and independent estimations of distances to them based on any statistical relation such as Cepheid variables, Tully-Fisher relation etc. Usually, the method of least squares is used when processing such data. However, the value of the Hubble constant is somewhat underestimated due to a statistical effect similar to the wellknown Malmquist bias. The main source of underestimation is associated with the deviation of the distances determined from the statistical dependence from their true values. The decrease of obtained Hubble constant value is about 5% for an error in the distance estimation of 20% and about 9% with an error of 30%. This impact cannot explain the recently discovered tensions between the values of Hubble constant obtained from the early and the late Universe. The estimation H0 = 67.4 km/s/Mpc obtained from observations in the recombination era account for about 92% of the average of the estimations based on observations of not very distant objects H0 = 73.3 km/s/ Mpc. Indeed, the described effect leads to underestimation of the largest of these values.

Steve: A Hierarchical Bayesian Model for Supernova Cosmology

Abstract We present a new Bayesian hierarchical model (BHM) named Steve for performing Type Ia supernova (SN Ia) cosmology fits. This advances previous works by including an improved treatment of Malmquist bias, accounting for additional sources of systematic uncertainty, and increasing numerical efficiency. Given light-curve fit parameters, redshifts, and host-galaxy masses, we fit Steve simultaneously for parameters describing cosmology, SN Ia populations, and systematic uncertainties. Selection effects are characterized using Monte Carlo simulations. We demonstrate its implementation by fitting realizations of SN Ia data sets where the SN Ia model closely follows that used in Steve. Next, we validate on more realistic SNANA simulations of SN Ia samples from the Dark Energy Survey and low-redshift surveys (DES Collaboration et al. 2018). These simulated data sets contain more than 60,000 SNe Ia, which we use to evaluate biases in the recovery of cosmological parameters, specifically the equation of state of dark energy, w. This is the most rigorous test of a BHM method applied to SN Ia cosmology fitting and reveals small w biases that depend on the simulated SN Ia properties, in particular the intrinsic SN Ia scatter model. This w bias is less than 0.03 on average, less than half the statistical uncertainty on w. These simulation test results are a concern for BHM cosmology fitting applications on large upcoming surveys; therefore, future development will focus on minimizing the sensitivity of Steve to the SN Ia intrinsic scatter model.