The Hubble Constant from Strongly Lensed Supernovae with Standardizable Magnifications

The dominant uncertainty in the current measurement of the Hubble constant (H 0) with strong gravitational lensing time delays is attributed to uncertainties in the mass profiles of the main deflector galaxies. Strongly lensed supernovae (glSNe) can provide, in addition to measurable time delays, lensing magnification constraints when knowledge about the unlensed apparent brightness of the explosion is imposed. We present a hierarchical Bayesian framework to combine a data set of SNe that are not strongly lensed and a data set of strongly lensed SNe with measured time delays. We jointly constrain (i) H 0 using the time delays as an absolute distance indicator, (ii) the lens model profiles using the magnification ratio of lensed and unlensed fluxes on the population level, and (iii) the unlensed apparent magnitude distribution of the SN population and the redshift–luminosity relation of the relative expansion history of the universe. We apply our joint inference framework on a future expected data set of glSNe and forecast that a sample of 144 glSNe of Type Ia with well-measured time series and imaging data will measure H 0 to 1.5%. We discuss strategies to mitigate systematics associated with using absolute flux measurements of glSNe to constrain the mass density profiles. Using the magnification of SN images is a promising and complementary alternative to using stellar kinematics. Future surveys, such as the Rubin and Roman observatories, will be able to discover the necessary number of glSNe, and with additional follow-up observations, this methodology will provide precise constraints on mass profiles and H 0.

Bayesian analysis of static light scattering data for globular proteins

Static light scattering is a popular physical chemistry technique that enables calculation of physical attributes such as the radius of gyration and the second virial coefficient for a macromolecule (e.g., a polymer or a protein) in solution. The second virial coefficient is a physical quantity that characterizes the magnitude and sign of pairwise interactions between particles, and hence is related to aggregation propensity, a property of considerable scientific and practical interest. Estimating the second virial coefficient from experimental data is challenging due both to the degree of precision required and the complexity of the error structure involved. In contrast to conventional approaches based on heuristic ordinary least squares estimates, Bayesian inference for the second virial coefficient allows explicit modeling of error processes, incorporation of prior information, and the ability to directly test competing physical models. Here, we introduce a fully Bayesian model for static light scattering experiments on small-particle systems, with joint inference for concentration, index of refraction, oligomer size, and the second virial coefficient. We apply our proposed model to study the aggregation behavior of hen egg-white lysozyme and human γS-crystallin using in-house experimental data. Based on these observations, we also perform a simulation study on the primary drivers of uncertainty in this family of experiments, showing in particular the potential for improved monitoring and control of concentration to aid inference.

Origins of a relatively tight lower bound on anthropogenic aerosol radiative forcing from Bayesian analysis of historical observations

A variety of empirical estimates have been published for the lower bounds on aerosol radiative forcing, clustered around -1.0 Wm−2 or -2.0 Wm−2. The reasons for obtaining such different constraints are not well understood. In this study, we explore bounds on aerosol radiative forcing using a Bayesian model of aerosol forcing and Earth’s multi-timescale temperature response to radiative forcing. We first demonstrate the ability of a simple aerosol model to emulate aerosol radiative forcing simulated by ten general circulation models. A joint inference of climate sensitivity and effective aerosol forcing from historical surface temperatures is then made over 1850–2019. We obtain a maximum likelihood estimate of aerosol radiative forcing of -0.85 Wm−2 [5-95% credible interval -1.3 to -0.50 Wm−2] for 2010–2019 relative to 1750 and an equilibrium climate sensitivity of 3.4°C [5-95% credible interval 1.8 to 6.1°C]. The wide range of climate sensitivity reflects difficulty in empirically constraining long-term responses using historical temperatures, as noted elsewhere. A relatively tight bound on aerosol forcing is nonetheless obtained from the structure of temperature and aerosol precursor emissions and, particularly, from the rapid growth in emissions between 1950–1980. Obtaining a fifth-percentile lower bound on aerosol forcing around -2.0 Wm−2 requires prescribing internal climate variance that is a factor of five larger than the CMIP6 mean and assuming large, correlated errors in global temperature observations. Ocean heat uptake observations may further constrain aerosol radiative forcing but require a better understanding of the relationship between time-variable radiative feedbacks and radiative forcing.

Variational Deep Logic Network for Joint Inference of Entities and Relations

Nowadays, deep learning models have been widely adopted and achieved promising results on various application domains. Despite of their intriguing performance, most deep learning models function as black-boxes, lacking explicit reasoning capabilities and explanations, which are usually essential for complex problems. Take joint inference in information extraction as an example. This task requires the identification of multiple structured knowledge from texts, which is inter-correlated, including entities, events and the relationships between them. Various deep neural networks have been proposed to jointly perform entity extraction and relation prediction, which only propagate information implicitly via representation learning. However, they fail to encode the intensive correlations between entity types and relations to enforce their co-existence. On the other hand, some approaches adopt rules to explicitly constrain certain relational facts. However, the separation of rules with representation learning usually restrains the approaches with error propagation. Moreover, the pre-defined rules are inflexible and might bring negative effects when data is noisy. To address these limitations, we propose a variational deep logic network that incorporates both representation learning and relational reasoning via the variational EM algorithm. The model consists of a deep neural network to learn high-level features with implicit interactions via the self-attention mechanism and a relational logic network to explicitly exploit target interactions. These two components are trained interactively to bring the best of both worlds. We conduct extensive experiments ranging from fine-grained sentiment terms extraction, end-to-end relation prediction to end-to-end event extraction to demonstrate the effectiveness of our proposed method.

On the Admissibility of Simultaneous Bootstrap Confidence Intervals

Simultaneous confidence intervals are commonly used in joint inference of multiple parameters. When the underlying joint distribution of the estimates is unknown, nonparametric methods can be applied to provide distribution-free simultaneous confidence intervals. In this note, we propose new one-sided and two-sided nonparametric simultaneous confidence intervals based on the percentile bootstrap approach. The admissibility of the proposed intervals is established. The numerical results demonstrate that the proposed confidence intervals maintain the correct coverage probability for both normal and non-normal distributions. For smoothed bootstrap estimates, we extend Efron’s (2014) nonparametric delta method to construct nonparametric simultaneous confidence intervals. The methods are applied to construct simultaneous confidence intervals for LASSO regression estimates.

Joint inference of CFC lifetimes and banks suggests previously unidentified emissions

Chlorofluorocarbons (CFCs) are harmful ozone depleting substances and greenhouse gases. CFC production was phased-out under the Montreal Protocol, however recent studies suggest new and unexpected emissions of CFC-11. Quantifying CFC emissions requires accurate estimates of both atmospheric lifetimes and ongoing emissions from old equipment (i.e. ‘banks’). In a Bayesian framework we simultaneously infer lifetimes, banks and emissions of CFC-11, 12 and 113 using available constraints. We find lifetimes of all three gases are likely shorter than currently recommended values, suggesting that best estimates of inferred emissions are larger than recent evaluations. Our analysis indicates that bank emissions are decreasing faster than total emissions, and we estimate new, unexpected emissions during 2014-2016 were 23.2, 18.3, and 7.8 Gg/yr for CFC-11, 12 and 113, respectively. While recent studies have focused on unexpected CFC-11 emissions, our results call for further investigation of potential sources of emissions of CFC-12 and CFC-113, along with CFC-11.

Joint inference of migration and reassortment patterns for viruses with segment genomes

The structured coalescent allows inferring migration patterns between viral sub-populations from genetic sequence data. However, these analyses typically assume that no genetic recombination process impacted the sequence evolution of pathogens. For segmented viruses, such as influenza, that can undergo reassortment this assumption is broken. Reassortment reshuffles the segments of different parent lineages upon a coinfection event, which means that the shared history of viruses has to be represented by a network instead of a tree. Therefore, full genome analyses of such viruses is complex or even impossible. While this problem has been addressed for unstructured populations, it is still impossible to account for population structure, such as induced by different host populations, while also accounting for reassortment% at the same time. We address this by extending the structured coalescent to account for reassortment and present a framework for investigating possible ties between reassortment and migration (host jump) events. This method can accurately estimate sub-population dependent effective populations sizes, reassortment and migration rates from simulated data. Additionally, we apply the new model to avian influenza A/H5N1 sequences, sampled from two avian host types, Anseriformes and Galliformes. We contrast our results with a structured coalescent without reassortment inference, which assumes independently evolving segments. This reveals that taking into account segment reassortment and using sequencing data from several viral segments for joint phylodynamic inference leads to different estimates for effective population sizes, migration and clock rates. This new model is implemented as the Structured Coalescent with Reassortment (SCoRe) package for BEAST 2.5 and is available at https://github.com/jugne/SCORE.