Combining Size and Shape in Weak Lensing

Weak lensing alters the size of images with a similar magnitude to the distortion due to shear. Galaxy size probes the convergence field, and shape the shear field, both of which contain cosmological information. We show the gains expected in the Dark Energy Figure of Merit if galaxy size information is used in combination with galaxy shape. In any normal analysis of cosmic shear, galaxy sizes are also studied, so this is extra statistical information comes for free and is currently unused. There are two main results in this letter: firstly, we show that size measurement can be made uncorrelated with ellipticity measurement, thus allowing the full statistical gain from the combination, provided that $\sqrt{Area}$ is used as a size indicator; secondly, as a proof of concept, we show that when the relevant modes are noise-dominated, as is the norm for lensing surveys, the gains are substantial, with improvements of about 68% in the Figure of Merit expected when systematic errors are ignored. An approximate treatment of such systematics such as intrinsic alignments and size-magnitude correlations respectively suggests that a much better improvement in the Dark Energy Figure of Merit of even a factor of ~4 may be achieved.Comment: Updated to MNRAS published version and added footnot

Nuisance hardened data compression for fast likelihood-free inference

In this paper we show how nuisance parameter marginalized posteriors can be inferred directly from simulations in a likelihood-free setting, without having to jointly infer the higher-dimensional interesting and nuisance parameter posterior first and marginalize a posteriori. The result is that for an inference task with a given number of interesting parameters, the number of simulations required to perform likelihood-free inference can be kept (roughly) the same irrespective of the number of additional nuisances to be marginalized over. To achieve this we introduce two extensions to the standard likelihood-free inference set-up. Firstly we show how nuisance parameters can be re-cast as latent variables and hence automatically marginalized over in the likelihood-free framework. Secondly, we derive an asymptotically optimal compression from $N$ data down to $n$ summaries -- one per interesting parameter -- such that the Fisher information is (asymptotically) preserved, but the summaries are insensitive (to leading order) to the nuisance parameters. This means that the nuisance marginalized inference task involves learning $n$ interesting parameters from $n$ "nuisance hardened" data summaries, regardless of the presence or number of additional nuisance parameters to be marginalized over. We validate our approach on two examples from cosmology: supernovae and weak lensing data analyses with nuisance parameterized systematics. For the supernova problem, high-fidelity posterior inference of $\Omega_m$ and $w_0$ (marginalized over systematics) can be obtained from just a few hundred data simulations. For the weak lensing problem, six cosmological parameters can be inferred from $\mathcal{O}(10^3)$ simulations, irrespective of whether ten additional nuisance parameters are included in the problem or not.Comment: Submitted to MNRAS Mar 201

Neural Stellar Population Synthesis Emulator for the DESI PROVABGS

The Probabilistic Value-Added Bright Galaxy Survey (PROVABGS) catalog will provide the posterior distributions of physical properties of $>10$ million DESI Bright Galaxy Survey (BGS) galaxies. Each posterior distribution will be inferred from joint Bayesian modeling of observed photometry and spectroscopy using Markov Chain Monte Carlo sampling and the [arXiv:2202.01809] stellar population synthesis (SPS) model. To make this computationally feasible, PROVABGS will use a neural emulator for the SPS model to accelerate the posterior inference. In this work, we present how we construct the emulator using the [arXiv:1911.11778] approach and verify that it can be used to accurately infer galaxy properties. We confirm that the emulator is in excellent agreement with the original SPS model with $\ll 1\%$ error and is $100\times$ faster. In addition, we demonstrate that the posteriors of galaxy properties derived using the emulator are also in excellent agreement with those inferred using the original model. The neural emulator presented in this work is essential in bypassing the computational challenge posed in constructing the PROVABGS catalog. Furthermore, it demonstrates the advantages of emulation for scaling sophisticated analyses to millions of galaxies.Comment: 9 pages, 5 figures, submitted to ApJ

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.Comment: 19 pages, 8 figures, comments welcom

Hierarchical Cosmic Shear Power Spectrum Inference

We develop a Bayesian hierarchical modelling approach for cosmic shear power spectrum inference, jointly sampling from the posterior distribution of the cosmic shear field and its (tomographic) power spectra. Inference of the shear power spectrum is a powerful intermediate product for a cosmic shear analysis, since it requires very few model assumptions and can be used to perform inference on a wide range of cosmological models \emph{a posteriori} without loss of information. We show that joint posterior for the shear map and power spectrum can be sampled effectively by Gibbs sampling, iteratively drawing samples from the map and power spectrum, each conditional on the other. This approach neatly circumvents difficulties associated with complicated survey geometry and masks that plague frequentist power spectrum estimators, since the power spectrum inference provides prior information about the field in masked regions at every sampling step. We demonstrate this approach for inference of tomographic shear $E$-mode, $B$-mode and $EB$-cross power spectra from a simulated galaxy shear catalogue with a number of important features; galaxies distributed on the sky and in redshift with photometric redshift uncertainties, realistic random ellipticity noise for every galaxy and a complicated survey mask. The obtained posterior distributions for the tomographic power spectrum coefficients recover the underlying simulated power spectra for both $E$- and $B$-modes.Comment: 16 pages, 8 figures, accepted by MNRA

Fishnets: Information-Optimal, Scalable Aggregation for Sets and Graphs

Set-based learning is an essential component of modern deep learning and network science. Graph Neural Networks (GNNs) and their edge-free counterparts Deepsets have proven remarkably useful on ragged and topologically challenging datasets. The key to learning informative embeddings for set members is a specified aggregation function, usually a sum, max, or mean. We propose Fishnets, an aggregation strategy for learning information-optimal embeddings for sets of data for both Bayesian inference and graph aggregation. We demonstrate that i) Fishnets neural summaries can be scaled optimally to an arbitrary number of data objects, ii) Fishnets aggregations are robust to changes in data distribution, unlike standard deepsets, iii) Fishnets saturate Bayesian information content and extend to regimes where MCMC techniques fail and iv) Fishnets can be used as a drop-in aggregation scheme within GNNs. We show that by adopting a Fishnets aggregation scheme for message passing, GNNs can achieve state-of-the-art performance versus architecture size on ogbn-protein data over existing benchmarks with a fraction of learnable parameters and faster training time.Comment: 13 pages, 9 figures, 2 tables. Submitted to ICLR 202

Optimal simulation-based Bayesian decisions

We present a framework for the efficient computation of optimal Bayesian decisions under intractable likelihoods, by learning a surrogate model for the expected utility (or its distribution) as a function of the action and data spaces. We leverage recent advances in simulation-based inference and Bayesian optimization to develop active learning schemes to choose where in parameter and action spaces to simulate. This allows us to learn the optimal action in as few simulations as possible. The resulting framework is extremely simulation efficient, typically requiring fewer model calls than the associated posterior inference task alone, and a factor of $100-1000$ more efficient than Monte-Carlo based methods. Our framework opens up new capabilities for performing Bayesian decision making, particularly in the previously challenging regime where likelihoods are intractable, and simulations expensive.Comment: 12 pages, 4 figure

Weak Lensing with Sizes, Magnitudes and Shapes

Weak lensing can be observed through a number of effects on the images of distant galaxies; their shapes are sheared, their sizes and fluxes (magnitudes) are magnified and their positions on the sky are modified by the lensing field. Galaxy shapes probe the shear field whilst size, magnitude and number density probe the convergence field. Both contain cosmological information. In this paper we are concerned with the magnification of the size and magnitude of individual galaxies as a probe of cosmic convergence. We develop a Bayesian approach for inferring the convergence field from a measured size, magnitude and redshift and demonstrate that the inference on convergence requires detailed knowledge of the joint distribution of intrinsic sizes and magnitudes. We build a simple parameterised model for the size-magnitude distribution and estimate this distribution for CFHTLenS galaxies. In light of the measured distribution, we show that the typical dispersion on convergence estimation is ~0.8, compared to ~0.38 for shear. We discuss the possibility of physical systematics for magnification (similar to intrinsic alignments for shear) and compute the expected gains in the Dark Energy Figure-of-Merit (FoM) from combining magnification with shear for different scenarios regarding systematics: when accounting for intrinsic alignments but no systematics on the magnification signal, including magnification could improve the FoM by upto a factor of ~2.5, whilst when accounting for physical systematics in both shear and magnification we anticipate a gain between ~25% and ~65%. In addition to the statistical gains, the fact that cosmic shear and magnification are subject to different systematics makes magnification an attractive complement to any cosmic shear analysis.Comment: 15 pages, 5 figures, accepted by MNRA