arXiv subjects

Justin Alsing

Publications and source records attributed to Justin Alsing.

At least 37 records · Page 2Linked to original sources

arXiv2021

Nested sampling with any prior you like

Nested sampling is an important tool for conducting Bayesian analysis in Astronomy and other fields, both for sampling complicated posterior distributions for parameter inference, and for computing marginal likelihoods for model comparison. One technical obstacle to using nested sampling in practice is the requirement (for most common implementations) that prior distributions be provided in the form of transformations from the unit hyper-cube to the target prior density. For many applications - particularly when using the posterior from one experiment as the prior for another - such a transformation is not readily available. In this letter we show that parametric bijectors trained on samples from a desired prior density provide a general-purpose method for constructing transformations from the uniform base density to a target prior, enabling the practical use of nested sampling under arbitrary priors. We demonstrate the use of trained bijectors in conjunction with nested sampling on a number of examples from cosmology.

astro-ph.IM↗

arXiv2021

Non-parametric spatial curvature inference using late-universe cosmological probes

Inferring high-fidelity constraints on the spatial curvature parameter, $Ω_{\rm K}$, under as few assumptions as possible, is of fundamental importance in cosmology. We propose a method to non-parametrically infer $Ω_{\rm K}$ from late-Universe probes alone. Using Gaussian Processes (GP) to reconstruct the expansion history, we combine Cosmic Chronometers (CC) and Type Ia Supernovae (SNe~Ia) data to infer constraints on curvature, marginalized over the expansion history, calibration of the CC and SNe~Ia data, and the GP hyper-parameters. The obtained constraints on $Ω_{\rm K}$ are free from parametric model assumptions for the expansion history, and are insensitive to the overall calibration of both the CC and SNe~Ia data (being sensitive only to relative distances and expansion rates). Applying this method to \textit{Pantheon} SNe~Ia and the latest compilation of CCs, we find $Ω_{\rm K} = -0.03 \pm 0.26$, consistent with spatial flatness at the $\mathcal{O}(10^{-1})$ level, and independent of any early-Universe probes. Applying our methodology to future Baryon Acoustic Oscillations and SNe~Ia data from upcoming Stage IV surveys, we forecast the ability to constrain $Ω_{\rm K}$ at the $\mathcal{O}(10^{-2})$ level.

astro-ph.CO↗

arXiv2021

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.

astro-ph.CO↗

arXiv2020

Likelihood-free inference with neural compression of DES SV weak lensing map statistics

In many cosmological inference problems, the likelihood (the probability of the observed data as a function of the unknown parameters) is unknown or intractable. This necessitates approximations and assumptions, which can lead to incorrect inference of cosmological parameters, including the nature of dark matter and dark energy, or create artificial model tensions. Likelihood-free inference covers a novel family of methods to rigorously estimate posterior distributions of parameters using forward modelling of mock data. We present likelihood-free cosmological parameter inference using weak lensing maps from the Dark Energy Survey (DES) SV data, using neural data compression of weak lensing map summary statistics. We explore combinations of the power spectra, peak counts, and neural compressed summaries of the lensing mass map using deep convolution neural networks. We demonstrate methods to validate the inference process, for both the data modelling and the probability density estimation steps. Likelihood-free inference provides a robust and scalable alternative for rigorous large-scale cosmological inference with galaxy survey data (for DES, Euclid and LSST). We have made our simulated lensing maps publicly available.

astro-ph.CO↗

arXiv2020

SPECULATOR: Emulating stellar population synthesis for fast and accurate galaxy spectra and photometry

We present SPECULATOR - a fast, accurate, and flexible framework for emulating stellar population synthesis (SPS) models for predicting galaxy spectra and photometry. For emulating spectra, we use principal component analysis to construct a set of basis functions, and neural networks to learn the basis coefficients as a function of the SPS model parameters. For photometry, we parameterize the magnitudes (for the filters of interest) as a function of SPS parameters by a neural network. The resulting emulators are able to predict spectra and photometry under both simple and complicated SPS model parameterizations to percent-level accuracy, giving a factor of $10^3$-$10^4$ speed up over direct SPS computation. They have readily-computable derivatives, making them amenable to gradient-based inference and optimization methods. The emulators are also straightforward to call from a GPU, giving an additional order-of-magnitude speed-up. Rapid SPS computations delivered by emulation offers a massive reduction in the computational resources required to infer the physical properties of galaxies from observed spectra or photometry and simulate galaxy populations under SPS models, whilst maintaining the accuracy required for a range of applications.

astro-ph.IM↗

arXiv2019

Cosmic Shear: Inference from Forward Models

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 lognormal 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.

astro-ph.CO↗

arXiv2019

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 $Ω_m$ 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.

astro-ph.CO↗

arXiv2019

Fast likelihood-free cosmology with neural density estimators and active learning

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 datasets, 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 $\mathcal{O}(10^3)$ 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 MCMC sampling, giving orders of magnitude speed-up in some cases. Finally, we introduce \textsc{pydelfi} -- a flexible public implementation of DELFI with NDEs and active learning -- available at \url{https://github.com/justinalsing/pydelfi}.

astro-ph.CO↗

arXiv2019

Prospects for resolving the Hubble constant tension with standard sirens

The Hubble constant ($H_0$) estimated from the local Cepheid-supernova (SN) distance ladder is in 3-$σ$ tension with the value extrapolated from cosmic microwave background (CMB) data assuming the standard cosmological model. Whether this tension represents new physics or systematic effects is the subject of intense debate. Here, we investigate how new, independent $H_0$ estimates can arbitrate this tension, assessing whether the measurements are consistent with being derived from the same model using the posterior predictive distribution (PPD). We show that, with existing data, the inverse distance ladder formed from BOSS baryon acoustic oscillation measurements and the Pantheon SN sample yields an $H_0$ posterior near-identical to the Planck CMB measurement. The observed local distance ladder value is a very unlikely draw from the resulting PPD. Turning to the future, we find that a sample of $\sim50$ binary neutron star "standard sirens" (detectable within the next decade) will be able to adjudicate between the local and CMB estimates.

astro-ph.CO↗

arXiv2018

Optimal proposals for Approximate Bayesian Computation

We derive the optimal proposal density for Approximate Bayesian Computation (ABC) using Sequential Monte Carlo (SMC) (or Population Monte Carlo, PMC). The criterion for optimality is that the SMC/PMC-ABC sampler maximise the effective number of samples per parameter proposal. The optimal proposal density represents the optimal trade-off between favoring high acceptance rate and reducing the variance of the importance weights of accepted samples. We discuss two convenient approximations of this proposal and show that the optimal proposal density gives a significant boost in the expected sampling efficiency compared to standard kernels that are in common use in the ABC literature, especially as the number of parameters increases.

math.ST↗

arXiv2018

Evidence for a maximum mass cut-off in the neutron star mass distribution and constraints on the equation of state

We infer the mass distribution of neutron stars in binary systems using a flexible Gaussian mixture model and use Bayesian model selection to explore evidence for multi-modality and a sharp cut-off in the mass distribution. We find overwhelming evidence for a bimodal distribution, in agreement with previous literature, and report for the first time positive evidence for a sharp cut-off at a maximum neutron star mass. We measure the maximum mass to be $2.0M_\odot < m_\mathrm{max} < 2.2M_\odot$ (68\%), $2.0M_\odot < m_\mathrm{max}< 2.6M_\odot$ (90\%), and evidence for a cut-off is robust against the choice of model for the mass distribution and to removing the most extreme (highest mass) neutron stars from the dataset. If this sharp cut-off is interpreted as the maximum stable neutron star mass allowed by the equation of state of dense matter, our measurement puts constraints on the equation of state. For a set of realistic equations of state that support $>2M_\odot$ neutron stars, our inference of $m_\mathrm{max}$ is able to distinguish between models at odds ratios of up to $12:1$, whilst under a flexible piecewise polytropic equation of state model our maximum mass measurement improves constraints on the pressure at $3-7\times$ the nuclear saturation density by $\sim 30-50\%$ compared to simply requiring $m_\mathrm{max}> 2M_\odot$. We obtain a lower bound on the maximum sound speed attained inside the neutron star of $c_s^\mathrm{max} > 0.63c$ (99.8\%), ruling out $c_s^\mathrm{max} < c/\sqrt{3}$ at high significance. Our constraints on the maximum neutron star mass strengthen the case for neutron star-neutron star mergers as the primary source of short gamma-ray bursts.

astro-ph.HE↗

arXiv2018

Generalized massive optimal data compression

Data compression has become one of the cornerstones of modern astronomical data analysis, with the vast majority of analyses compressing large raw datasets down to a manageable number of informative summaries. In this paper we provide a general procedure for optimally compressing $N$ data down to $n$ summary statistics, where $n$ is equal to the number of parameters of interest. We show that compression to the score function -- the gradient of the log-likelihood with respect to the parameters -- yields $n$ compressed statistics that are optimal in the sense that they preserve the Fisher information content of the data. Our method generalizes earlier work on linear Karhunen-Loéve compression for Gaussian data whilst recovering both lossless linear compression and quadratic estimation as special cases when they are optimal. We give a unified treatment that also includes the general non-Gaussian case as long as mild regularity conditions are satisfied, producing optimal non-linear summary statistics when appropriate. As a worked example, we derive explicitly the $n$ optimal compressed statistics for Gaussian data in the general case where both the mean and covariance depend on the parameters.

astro-ph.CO↗

arXiv2018

Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology

Many statistical models in cosmology can be simulated forwards but have intractable likelihood functions. Likelihood-free inference methods allow us to perform Bayesian inference from these models using only forward simulations, free from any likelihood assumptions or approximations. Likelihood-free inference generically involves simulating mock data and comparing to the observed data; this comparison in data-space suffers from the curse of dimensionality and requires compression of the data to a small number of summary statistics to be tractable. In this paper we use massive asymptotically-optimal data compression to reduce the dimensionality of the data-space to just one number per parameter, providing a natural and optimal framework for summary statistic choice for likelihood-free inference. Secondly, we present the first cosmological application of Density Estimation Likelihood-Free Inference (\textsc{delfi}), which learns a parameterized model for joint distribution of data and parameters, yielding both the parameter posterior and the model evidence. This approach is conceptually simple, requires less tuning than traditional Approximate Bayesian Computation approaches to likelihood-free inference and can give high-fidelity posteriors from orders of magnitude fewer forward simulations. As an additional bonus, it enables parameter inference and Bayesian model comparison simultaneously. We demonstrate Density Estimation Likelihood-Free Inference with massive data compression on an analysis of the joint light-curve analysis supernova data, as a simple validation case study. We show that high-fidelity posterior inference is possible for full-scale cosmological data analyses with as few as $\sim 10^4$ simulations, with substantial scope for further improvement, demonstrating the scalability of likelihood-free inference to large and complex cosmological datasets.

astro-ph.CO↗

arXiv2017

Cosmological parameters, shear maps and power spectra from CFHTLenS using Bayesian hierarchical inference

We apply two Bayesian hierarchical inference schemes to infer shear power spectra, shear maps and cosmological parameters from the CFHTLenS weak lensing survey - the first application of this method to data. In the first approach, we sample the joint posterior distribution of the shear maps and power spectra by Gibbs sampling, with minimal model assumptions. In the second approach, we sample the joint posterior of the shear maps and cosmological parameters, providing a new, accurate and principled approach to cosmological parameter inference from cosmic shear data. As a first demonstration on data we perform a 2-bin tomographic analysis to constrain cosmological parameters and investigate the possibility of photometric redshift bias in the CFHTLenS data. Under the baseline $Λ$CDM model we constrain $S_8 = σ_8(Ω_\mathrm{m}/0.3)^{0.5} = 0.67 ^{\scriptscriptstyle+ 0.03 }_{\scriptscriptstyle- 0.03 }$ $(68\%)$, consistent with previous CFHTLenS analysis but in tension with Planck. Adding neutrino mass as a free parameter we are able to constrain $\sum m_ν< 4.6\mathrm{eV}$ (95%) using CFHTLenS data alone. Including a linear redshift dependent photo-$z$ bias $Δz = p_2(z - p_1)$, we find $p_1=-0.25 ^{\scriptscriptstyle+ 0.53 }_{\scriptscriptstyle- 0.60 }$ and $p_2 = -0.15 ^{\scriptscriptstyle+ 0.17 }_{\scriptscriptstyle- 0.15 }$, and tension with Planck is only alleviated under very conservative prior assumptions. Neither the non-minimal neutrino mass or photo-$z$ bias models are significantly preferred by the CFHTLenS (2-bin tomography) data.

astro-ph.CO↗

arXiv2017

The Limits of Cosmic Shear

In this paper we discuss the commonly-used limiting cases, or approximations, for two-point cosmic shear statistics. We discuss the most prominent assumptions in this statistic: the flat-sky (small angle limit), the Limber (Bessel-to-delta function limit) and the Hankel transform (large l-mode limit) approximations; that the vast majority of cosmic shear results to date have used simultaneously. We find that the combined effect of these approximations can suppress power by >1% on scales of l<40. A fully non-approximated cosmic shear study should use a spherical-sky, non-Limber-approximated power spectrum analysis; and a transform involving Wigner small-d matrices in place of the Hankel transform. These effects, unaccounted for, would constitute at least 11% of the total budget for systematic effects for a power spectrum analysis of a Euclid-like experiment; but they are unnecessary.

astro-ph.CO↗

arXiv2016

Bayesian hierarchical modelling of weak lensing - the golden goal

To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into component steps. Starting with a catalogue of shear estimates in tomographic bins, we build a model that allows us to sample simultaneously from the the underlying tomographic shear fields and the relevant power spectra (E-mode, B-mode, and E-B, for auto- and cross-power spectra). The procedure deals easily with masked data and intrinsic alignments. Using Gibbs sampling and messenger fields, we show with simulated data that the large (over 67000-)dimensional parameter space can be efficiently sampled and the full joint posterior probability density function for the parameters can feasibly be obtained. The method correctly recovers the underlying shear fields and all of the power spectra, including at levels well below the shot noise.

astro-ph.CO↗

arXiv2016

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.

astro-ph.CO↗

arXiv2015

Testing General Relativity with Present and Future Astrophysical Observations

One century after its formulation, Einstein's general relativity has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that general relativity should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of general relativity. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

gr-qc↗