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1.

Alsing, Justin

et al.

Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC). Flatiron Institute, USA; Imperial College London, UK.

Likelihood-free inference provides a framework for performing rigorous Bayesian inference using only forward simulations, properly accounting for all physical and observational effects that can be successfully included in the simulations, The key challenge for likelihood-free applications in cosmology, where simulation is typically expensive, is developing methods that can achieve high-fidelity posterior inference with as few simulations as possible. Density estimation likelihood-free inference (DELFI) methods turn inference into a density-estimation task on a set of simulated data-parameter pairs, and give orders of magnitude improvements over traditional Approximate Bayesian Computation approaches to likelihood-free inference. In this paper, we use neural density estimators (NDEs) to learn the likelihood function from a set of simulated data sets, with active learning to adaptively acquire simulations in the most relevant regions of parameter space on the fly. We demonstrate the approach on a number of cosmological case studies, showing that for typical problems high-fidelity posterior inference can be achieved with just 0(103) simulations or fewer. In addition to enabling efficient simulation-based inference, for simple problems where the form of the likelihood is known, DELFI offers a fast alternative to Markov Chain Monte Carlo (MCMC) sampling, giving orders of magnitude speed-up in some cases. Finally, we introduce PYDELFI a flexible public implementation of DELFI with NDFs and active learning - available at haps://github.com/justinalsing/pydelfi.

Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC). Flatiron Institute, USA; Imperial College London, UK.

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. First, we show how nuisance parameters can be recast as latent variables and hence automatically marginalized over in the likelihood-free framework. Secondly, we derive an asymptotically optimal compression from N data to n summaries - one per interesting parameter - such that the Fisher information is (asymptotically) preserved, but the summaries are insensitive 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 parametrized 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 just simulations, irrespective of whether 10 additional nuisance parameters are included in the problem or not.

Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC). Imperial College London, UK.

The Montreal Protocol, and its subsequent amendments, has successfully prevented catastrophic losses of stratospheric ozone, and signs of recovery are now evident. Nevertheless, recent work has suggested that ozone in the lower stratosphere (< 24 km) continued to decline over the 1998-2016 period, offsetting recovery at higher altitudes and preventing a statistically significant increase in quasi-global (60 degrees S-60 degrees N) total column ozone. In 2017, a large lower stratospheric ozone resurgence over less than 12 months was estimated (using a chemistry transport model; CTM) to have offset the long-term decline in the quasi-global integrated lower stratospheric ozone column. Here, we extend the analysis of space-based ozone observations to December 2018 using the BASIC(SG) ozone composite. We find that the observed 2017 resurgence was only around half that modelled by the CTM, was of comparable magnitude to other strong interannual changes in the past, and was restricted to Southern Hemisphere (SH) midlatitudes (60-30 degrees S). In the SH midlatitude lower stratosphere, the data suggest that by the end of 2018 ozone is still likely lower than in 1998 (probability similar to 80 %). In contrast, tropical and Northern Hemisphere (NH) ozone continue to display ongoing decreases, exceeding 90 % probability. Robust tropical (> 95 %, 30 degrees S-30 degrees N) decreases dominate the quasi-global integrated decrease (99 % probability); the integrated tropical stratospheric column (1-100 hPa, 30 degrees S-30 degrees N) displays a significant overall ozone decrease, with 95 % probability. These decreases do not reveal an inefficacy of the Montreal Protocol; rather, they suggest that other effects are at work, mainly dynamical variability on long or short timescales, counteracting the positive effects of the Montreal Protocol on stratospheric ozone recovery. We demonstrate that large interannual midlatitude (30-60 degrees) variations, such as the 2017 resurgence, are driven by non-linear quasi-biennial oscillation (QBO) phase-dependent seasonal variability. However, this variability is not represented in current regression analyses. To understand if observed lower stratospheric ozone decreases are a transient or long-term phenomenon, progress needs to be made in accounting for this dynamically driven variability.

Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC). Imperial College London, United Kingdom.

Wandelt, Benjamin D.

Feeney, Stephen M.

McEwen, Jason D.

Cosmic shear: Inference from forward models2019In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 100, no 2, article id 023519Article in journal (Refereed)

Abstract [en]

Density-estimation likelihood-free inference (DELFI) has recently been proposed as an efficient method for simulation-based cosmological parameter inference. Compared to the standard likelihood-based Markov chain Monte Carlo (MCMC) approach, DELFI has several advantages: it is highly parallelizable, there is no need to assume a possibly incorrect functional form for the likelihood, and complicated effects (e.g., the mask and detector systematics) are easier to handle with forward models. In light of this, we present two DELFI pipelines to perform weak lensing parameter inference with log-normal realizations of the tomographic shear field-using the C-l summary statistic. The first pipeline accounts for the non-Gaussianities of the shear field, intrinsic alignments, and photometric-redshift error. We validate that it is accurate enough for Stage III experiments and estimate that O(1000) simulations are needed to perform inference on Stage IV data. By comparing the second DELFI pipeline, which makes no assumption about the functional form of the likelihood, with the standard MCMC approach, which assumes a Gaussian likelihood, we test the impact of the Gaussian likelihood approximation in the MCMC analysis. We find it has a negligible impact on Stage IV parameter constraints. Our pipeline is a step towards seamlessly propagating all data-processing, instrumental, theoretical, and astrophysical systematics through to the final parameter constraints.