Bayesian Analysis of Two Stellar Populations in Galactic Globular Clusters II: NGC 5024, NGC 5272, and NGC 6352

We use Cycle 21 Hubble Space Telescope (HST) observations and HST archival ACS Treasury observations of Galactic Globular Clusters to find and characterize two stellar populations in NGC 5024 (M53), NGC 5272 (M3), and NGC 6352. For these three clusters, both single and double-population analyses are used to determine a best fit isochrone(s). We employ a sophisticated Bayesian analysis technique to simultaneously fit the cluster parameters (age, distance, absorption, and metallicity) that characterize each cluster. For the two-population analysis, unique population level helium values are also fit to each distinct population of the cluster and the relative proportions of the populations are determined. We find differences in helium ranging from $\sim$0.05 to 0.11 for these three clusters. Model grids with solar $\alpha$-element abundances ([$\alpha$/Fe] =0.0) and enhanced $\alpha$-elements ([$\alpha$/Fe]=0.4) are adopted.Comment: ApJ, 21 pages, 14 figures, 7 table

Stratified Learning: a general-purpose statistical method for improved learning under Covariate Shift

Covariate shift arises when the labelled training (source) data is not representative of the unlabelled (target) data due to systematic differences in the covariate distributions. A supervised model trained on the source data subject to covariate shift may suffer from poor generalization on the target data. We propose a novel, statistically principled and theoretically justified method to improve learning under covariate shift conditions, based on propensity score stratification, a well-established methodology in causal inference. We show that the effects of covariate shift can be reduced or altogether eliminated by conditioning on propensity scores. In practice, this is achieved by fitting learners on subgroups ("strata") constructed by partitioning the data based on the estimated propensity scores, leading to balanced covariates and much-improved target prediction. We demonstrate the effectiveness of our general-purpose method on contemporary research questions in observational cosmology, and on additional benchmark examples, matching or outperforming state-of-the-art importance weighting methods, widely studied in the covariate shift literature. We obtain the best reported AUC (0.958) on the updated "Supernovae photometric classification challenge" and improve upon existing conditional density estimation of galaxy redshift from Sloan Data Sky Survey (SDSS) data

Incorporating Uncertainties in Atomic Data Into the Analysis of Solar and Stellar Observations: A Case Study in Fe XIII

Information about the physical properties of astrophysical objects cannot be measured directly but is inferred by interpreting spectroscopic observations in the context of atomic physics calculations. Ratios of emission lines, for example, can be used to infer the electron density of the emitting plasma. Similarly, the relative intensities of emission lines formed over a wide range of temperatures yield information on the temperature structure. A critical component of this analysis is understanding how uncertainties in the underlying atomic physics propagates to the uncertainties in the inferred plasma parameters. At present, however, atomic physics databases do not include uncertainties on the atomic parameters and there is no established methodology for using them even if they did. In this paper we develop simple models for the uncertainties in the collision strengths and decay rates for Fe XIII and apply them to the interpretation of density sensitive lines observed with the EUV Imagining spectrometer (EIS) on Hinode. We incorporate these uncertainties in a Bayesian framework. We consider both a pragmatic Bayesian method where the atomic physics information is unaffected by the observed data, and a fully Bayesian method where the data can be used to probe the physics. The former generally increases the uncertainty in the inferred density by about a factor of 5 compared with models that incorporate only statistical uncertainties. The latter reduces the uncertainties on the inferred densities, but identifies areas of possible systematic problems with either the atomic physics or the observed intensities.Comment: in press at Ap

The suppression of CMR in Nd(Mn1−xCox)AsO0.95F0.05

This research is supported by the EPSRC (research grant EP/L002493/1). We also acknowledge the UK Science and Technology Facilities Council (STFC) for provision of beam time at ISIS.Peer reviewedPostprin

The ACS Survey of Galactic Globular Clusters XIV: Bayesian Single-Population Analysis of 69 Globular Clusters

We use Hubble Space Telescope (HST) imaging from the ACS Treasury Survey to determine fits for single population isochrones of 69 Galactic globular clusters. Using robust Bayesian analysis techniques, we simultaneously determine ages, distances, absorptions, and helium values for each cluster under the scenario of a \single stellar population on model grids with solar ratio heavy element abundances. The set of cluster parameters is determined in a consistent and reproducible manner for all clusters using the Bayesian analysis suite BASE-9. Our results are used to re-visit the age-metallicity relation. We find correlations with helium and several other parameters such as metallicity, binary fraction, and proxies for cluster mass. The helium abundances of the clusters are also considered in the context of CNO abundances and the multiple population scenario

Bayesian Hierarchical Modelling of Initial-Final Mass Relations Across Star Clusters

The initial-final mass relation (IFMR) of white dwarfs (WDs) plays an important role in stellar evolution. To derive precise estimates of IFMRs and explore how they may vary among star clusters, we propose a Bayesian hierarchical model that pools photometric data from multiple star clusters. After performing a simulation study to show the benefits of the Bayesian hierarchical model, we apply this model to five star clusters: the Hyades, M67, NGC 188, NGC 2168, and NGC 2477, leading to reasonable and consistent estimates of IFMRs for these clusters. We illustrate how a cluster-specific analysis of NGC 188 using its own photometric data can produce an unreasonable IFMR since its WDs have a narrow range of zero-age main sequence (ZAMS) masses. However, the Bayesian hierarchical model corrects the cluster-specific analysis by borrowing strength from other clusters, thus generating more reliable estimates of IFMR parameters. The data analysis presents the benefits of Bayesian hierarchical modelling over conventional cluster-specific methods, which motivates us to elaborate the powerful statistical techniques in this article