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SPT clusters with DES and HST weak lensing. I. Cluster lensing and Bayesian population modeling of multiwavelength cluster datasets
We present a Bayesian population modeling method to analyze the abundance of galaxy clusters identified by the South Pole Telescope (SPT) with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). We discuss and validate the modeling choices with a particular focus on a robust, weak-lensing-based mass calibration using DES data. For the DES Year 3 data, we report a systematic uncertainty in weak-lensing mass calibration that increases from 1% at z = 0.25 to 10% at z = 0.95 , to which we add 2% in quadrature to account for uncertainties in the impact of baryonic effects. We implement an analysis pipeline that joins the cluster abundance likelihood with a multiobservable likelihood for the Sunyaev-Zel’dovich effect, optical richness, and weak-lensing measurements for each individual cluster. We validate that our analysis pipeline can recover unbiased cosmological constraints by analyzing mocks that closely resemble the cluster sample extracted from the SPT-SZ, SPTpol ECS, and SPTpol 500d surveys and the DES Year 3 and HST-39 weak-lensing datasets. This work represents a crucial prerequisite for the subsequent cosmological analysis of the real dataset.
Exploring the contamination of the DES-Y1 cluster sample with SPT-SZ selected clusters
ABSTRACT We perform a cross validation of the cluster catalogue selected by the red-sequence Matched-filter Probabilistic Percolation algorithm (redMaPPer) in Dark Energy Survey year 1 (DES-Y1) data by matching it with the Sunyaev–Zel’dovich effect (SZE) selected cluster catalogue from the South Pole Telescope SPT-SZ survey. Of the 1005 redMaPPer selected clusters with measured richness $\hat{\lambda }\gt 40$ in the joint footprint, 207 are confirmed by SPT-SZ. Using the mass information from the SZE signal, we calibrate the richness–mass relation using a Bayesian cluster population model. We find a mass trend λ ∝ MB consistent with a linear relation (B ∼ 1), no significant redshift evolution and an intrinsic scatter in richness of σλ = 0.22 ± 0.06. By considering two error models, we explore the impact of projection effects on the richness–mass modelling, confirming that such effects are not detectable at the current level of systematic uncertainties. At low richness SPT-SZ confirms fewer redMaPPer clusters than expected. We interpret this richness dependent deficit in confirmed systems as due to the increased presence at low richness of low-mass objects not correctly accounted for by our richness-mass scatter model, which we call contaminants. At a richness $\hat{\lambda }=40$, this population makes up ${\gt}12{{\ \rm per\ cent}}$ (97.5 percentile) of the total population. Extrapolating this to a measured richness $\hat{\lambda }=20$ yields ${\gt}22{{\ \rm per\ cent}}$ (97.5 percentile). With these contamination fractions, the predicted redMaPPer number counts in different plausible cosmologies are compatible with the measured abundance. The presence of such a population is also a plausible explanation for the different mass trends (B ∼ 0.75) obtained from mass calibration using purely optically selected clusters. The mean mass from stacked weak lensing (WL) measurements suggests that these low-mass contaminants are galaxy groups with masses ∼3–5 × 1013 M⊙ which are beyond the sensitivity of current SZE and X-ray surveys but a natural target for SPT-3G and eROSITA.
Redshift inference from the combination of galaxy colours and clustering in a hierarchical Bayesian model – Application to realistic N -body simulations
ABSTRACT Photometric galaxy surveys constitute a powerful cosmological probe but rely on the accurate characterization of their redshift distributions using only broad-band imaging, and can be very sensitive to incomplete or biased priors used for redshift calibration. A hierarchical Bayesian model has recently been developed to estimate those from the robust combination of prior information, photometry of single galaxies, and the information contained in the galaxy clustering against a well-characterized tracer population. In this work, we extend the method so that it can be applied to real data, developing some necessary new extensions to it, especially in the treatment of galaxy clustering information, and we test it on realistic simulations. After marginalizing over the mapping between the clustering estimator and the actual density distribution of the sample galaxies, and using prior information from a small patch of the survey, we find the incorporation of clustering information with photo-z’s tightens the redshift posteriors and overcomes biases in the prior that mimic those happening in spectroscopic samples. The method presented here uses all the information at hand to reduce prior biases and incompleteness. Even in cases where we artificially bias the spectroscopic sample to induce a shift in mean redshift of $\Delta \bar{z} \approx 0.05,$ the final biases in the posterior are $\Delta \bar{z} \lesssim 0.003.$ This robustness to flaws in the redshift prior or training samples would constitute a milestone for the control of redshift systematic uncertainties in future weak lensing analyses.
Proactive Frequency Stability Scheme Based on Bayesian Filters and Spectral Clustering
Not Available
Copacabana: a probabilistic membership assignment method for galaxy clusters
Cosmological analyses using galaxy clusters in optical/near-infrared photometric surveys require robust characterization of their galaxy content. Precisely determining which galaxies belong to a cluster is crucial. In this paper, we present the COlor Probabilistic Assignment of Clusters And BAyesiaN Analysis (Copacabana) algorithm. Copacabana computes membership probabilities for all galaxies within an aperture centred on the cluster using photometric redshifts, colours, and projected radial probability density functions. We use simulations to validate Copacabana and we show that it achieves up to 89 per cent membership accuracy with a mild dependence on photometric redshift uncertainties and choice of aperture size. We find that the precision of the photometric redshifts has the largest impact on the determination of the membership probabilities followed by the choice of the cluster aperture size. We also quantify how much these uncertainties in the membership probabilities affect the stellar mass–cluster mass scaling relation, a relation that directly impacts cosmology. Using the sum of the stellar masses weighted by membership probabilities (μ * ) as the observable, we find that Copacabana can reach an accuracy of 0.06 dex in the measurement of the scaling relation at low redshift for a Legacy Survey of Space and Time type survey. These results indicate the potential of Copacabana and μ * to be used in cosmological analyses of optically selected clusters in the future.
A Multi-Armed Bayesian Ordinal Outcome Utility-Based Sequential Trial with a Pairwise Null Clustering Prior
A multi-armed trial based on ordinal outcomes is proposed that leverages a flexible non-proportional odds cumulative logit model and numerical utility scores for each outcome to determine treatment optimality. This trial design uses a Bayesian clustering prior on the treatment effects that encourages the pairwise null hypothesis of no differences between treatments. A group sequential design is proposed to determine which treatments are clinically different with an adaptive decision boundary that becomes more aggressive as the sample size or clinical significance grows, or the number of active treatments decreases. A simulation study is conducted for 3 and 5 treatment arms, which shows that the design has superior operating characteristics (family wise error rate, generalized power, average sample size) compared to utility designs that do not allow clustering, a frequentist proportional odds model, or a permutation test based on empirical mean utilities.
Precision calibration of calorimeter signals in the ATLAS experiment using an uncertainty-aware neural network
The ATLAS experiment at the Large Hadron Collider explores the use of modern neural networks for a multi-dimensional calibration of its calorimeter signal defined by clusters of topologically connected cells (topo-clusters). The Bayesian neural network (BNN) approach not only yields a continuous and smooth calibration function that improves performance relative to the standard calibration but also provides uncertainties on the calibrated energies for each topo-cluster. The results obtained by using a trained BNN are compared to the standard local hadronic calibration and to a calibration provided by training a deep neural network. The uncertainties predicted by the BNN are interpreted in the context of a fractional contribution to the systematic uncertainties of the trained calibration. They are also compared to uncertainty predictions obtained from an alternative estimator employing repulsive ensembles.
Protein Conformational States—A First Principles Bayesian Method
Automated identification of protein conformational states from simulation of an ensemble of structures is a hard problem because it requires teaching a computer to recognize shapes. We adapt the naïve Bayes classifier from the machine learning community for use on atom-to-atom pairwise contacts. The result is an unsupervised learning algorithm that samples a ‘distribution’ over potential classification schemes. We apply the classifier to a series of test structures and one real protein, showing that it identifies the conformational transition with >95% accuracy in most cases. A nontrivial feature of our adaptation is a new connection to information entropy that allows us to vary the level of structural detail without spoiling the categorization. This is confirmed by comparing results as the number of atoms and time-samples are varied over 1.5 orders of magnitude. Further, the method’s derivation from Bayesian analysis on the set of inter-atomic contacts makes it easy to understand and extend to more complex cases.
Alleviating prior dependencies for DESI DR1 clustering fits through reparameterization
Bayesian analyses of the full-shape clustering of Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) exhibit prior-volume projection effects, whereby weakly constrained nuisance parameters of the Effective Field Theory of Large Scale Structure (EFTofLSS) shift marginalized cosmological posteriors away from the posterior maximum. We reanalyze DESI DR1 power spectrum multipoles using two complementary mitigation strategies: (i) nonlinear orthogonalization to decorrelate nuisance and cosmological parameter priors, and (ii) a fully reparameterization-invariant Jeffreys prior over all EFTofLSS coefficients, evaluated on-the-fly via closed-form Jacobians. Including data from DESI, Big-Bang Nuclesynthesis and a constraint on $n_{\mathrm{s}}$, baseline priors lead to multi-$σ$ projection in the Hubble parameter $H_{0}$ and dark energy equation of state parameters $w_{0}$ and $w_{a}$; the Jeffreys prior successfully recenters these posteriors to enclose the maximum a posteriori estimate within the 68% credible regions, demonstrating clear mitigation of projection effects for these late-time expansion parameters. A hybrid Jeffreys+baseline-Gaussian configuration controls residual over-broad tails in the physical cold dark matter density $ω_{\mathrm{c}}$ while preserving the volume correction, and is our favoured approach. We compare the credible intervals derived using our methodology to those obtained using Halo Occupation Distribution (HOD)-informed priors and to confidence intervals derived using frequentist profile likelihood analyses, finding agreement in both central values and degeneracy directions in the $w_{0}$--$w_{a}$ plane. This demonstrates that, once projection effects are properly controlled, we can make robust inferences about the late-time cosmological expansion independent of the statistical framework adopted.
Bayesian prior construction for uncertainty quantification in first-principles statistical mechanics
First-principles statistical mechanics enables the prediction of thermodynamic and kinetic properties of materials, but is computationally expensive. Many approaches require surrogate models to calculate energies within Monte Carlo or molecular dynamics simulations. Inexpensive surrogates such as cluster expansions enable otherwise intractable calculations by interpolating data from higher accuracy methods, such as Density Functional Theory (DFT). Surrogate models introduce uncertainty into downstream calculations, in addition to any uncertainty inherent to DFT calculations. Bayesian frameworks address this by quantifying uncertainty and incorporating expert knowledge through priors. However, constructing effective priors remains challenging. This work introduces and describes practical strategies for building Bayesian cluster expansions, focusing on basis truncation, hyperparameter selection, and ground state replication. We analyze multiple basis truncation schemes, compare cross-validation to the evidence-approximation for hyperparameter optimization, and provide methods to find and enforce ground-state-preserving models through priors. Additionally, we compare the uncertainties between different approximations to DFT (LDA, PBE, SCAN) against the uncertainty introduced with the use of cluster expansion surrogate models. These approaches are demonstrated on the BCC Li x Mg 1-x and Li x Al 1-x alloys, which are both of interest for solid-state Li batteries. Our results provide guidelines for constructing and utilizing Bayesian cluster expansions, thereby improving the transparency of materials modeling. Furthermore, the approaches and insights developed in this work can be transferred to a wide range of cluster expansion surrogate models, including the atomic cluster expansion and related machine-learned interatomic potential architectures.
Population Subdivision in the Gopher Frog (Rana capito) across the Fragmented Longleaf Pine-Wiregrass Savanna of the Southeastern USA
Delineating genetically distinct population segments of threatened species and quantifying population connectivity are important steps in developing effective conservation and management strategies aimed at preventing extinction. The gopher frog (Rana capito) is a xeric-adapted, pond-breeding species endemic to the Gulf and Atlantic coastal plains of the southeastern United States. This species has experienced extensive habitat loss and fragmentation in the formerly widespread longleaf pine-wiregrass savanna where it lives, resulting in individual abundance declines and population extinctions throughout its range. We used individual-based clustering methods along with Bayesian inference of historical migration based on almost 1500 multilocus microsatellite genotypes to examine genetic structure in this taxon. Clustering analyses identified panhandle and peninsular populations in Florida as distinct genetic clusters separated by the Aucilla River, consistent with the division between the Coastal Plain and peninsular mitochondrial lineages, respectively. Analysis of historical migration indicated an east–west population divergence event followed by immigration to the east. Together, our results indicate that the genetically distinct Coastal Plain and peninsular Florida lineages should be considered separately for conservation and management purposes.
Bayesian calibration for summary statistics with applications to a cluster dynamics model.
Abstract not provided.
Q-Cluster: Quantum Error Mitigation Through Noise-Aware Unsupervised Learning
Quantum error mitigation (QEM) is critical in reducing the impact of noise in the pre-fault-tolerant era, and is expected to complement error correction in fault-tolerant quantum computing (FTQC). In this work, we propose a novel QEM approach, Q-Cluster, that uses unsupervised learning (clustering) to reshape the measured bit-string distribution. Our approach starts with a simplified bit-flip noise model. It first performs clustering on noisy measurement results, i.e., bit-strings, based on the Hamming distance. The centroid of each cluster is calculated using a qubit-wise majority vote. Next, the noisy distribution is adjusted with the clustering outcomes and the bitflip error rates using Bayesian inference. Our simulation results show that Q-Cluster can mitigate high noise rates (up to 40% per qubit) with the simple bit-flip noise model. However, real quantum computers do not fit such a simple noise model. To address the problem, we (a) apply Pauli twirling to tailor the complex noise channels to Pauli errors, and (b) employ a machine learning model, ExtraTrees regressor, to estimate an effective bit-flip error rate using a feature vector consisting of machine calibration data (gate & measurement error rates), circuit features (number of qubits, numbers of different types of gates, etc.) and the shape of the noisy distribution (entropy). Our experimental results show that our proposed Q-Cluster scheme improves the fidelity by a factor of 1.46x, on average, compared to the unmitigated output distribution, for a set of low-entropy benchmarks on five different IBM quantum machines. Our approach outperforms the state-of-art QEM approaches RZNE [28], M3 [24], Hammer [35], and QBEEP [33] by 1.26x,1.29x,1.47x, and 2.65 x, respectively.
CODEX weak lensing mass catalogue and implications on the mass–richness relation
The COnstrain Dark Energy with X-ray clusters (CODEX) sample contains the largest flux limited sample of X-ray clusters at 0.35 < z < 0.65. It was selected from ROSAT data in the 10 000 square degrees of overlap with BOSS, mapping a total number of 2770 high-z galaxy clusters. We present here the full results of the CFHT CODEX programme on cluster mass measurement, including a reanalysis of CFHTLS Wide data, with 25 individual lensing-constrained cluster masses. We employ lensfit shape measurement and perform a conservative colour–space selection and weighting of background galaxies. Using the combination of shape noise and an analytic covariance for intrinsic variations of cluster profiles at fixed mass due to large-scale structure, miscentring, and variations in concentration and ellipticity, we determine the likelihood of the observed shear signal as a function of true mass for each cluster. We combine 25 individual cluster mass likelihoods in a Bayesian hierarchical scheme with the inclusion of optical and X-ray selection functions to derive constraints on the slope α, normalization β, and scatter σln λ|μ of our richness–mass scaling relation model in log-space: ${\langle {\rm In}\,\, \lambda\!\!\mid\!\!\mu\rangle = \alpha\mu + \beta,} $ with μ = ln (M 200c /M piv ), and M piv = 10 14.81 M ⊙ . We find a slope $\alpha = 0.49^{+0.20}_{-0.15}$, normalization $\exp (\beta) = 84.0^{+9.2}_{-14.8}$, and $\sigma _{\ln \lambda | \mu } = 0.17^{+0.13}_{-0.09}$ using CFHT richness estimates. In comparison to other weak lensing richness–mass relations, we find the normalization of the richness statistically agreeing with the normalization of other scaling relations from a broad redshift range (0.0 < z < 0.65) and with different cluster selection (X-ray, Sunyaev–Zeldovich, and optical).