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Neural fields or implicit neural representations (INRs) have attracted significant attention in machine learning and signal processing due to their efficient continuous representation of images and 3D volumes. In this work, we build on INRs and introduce a coordinate-based local processing framework for solving imaging inverse problems, termed LoFi (Local Field). Unlike conventional methods for image reconstruction, LoFi processes local information at each coordinate \textit{separately} by multi-layer perceptrons (MLPs), recovering the object at that specific coordinate. Similar to INRs, LoFi can recover images at any continuous coordinate, enabling image reconstruction at multiple resolutions. With comparable or better performance than standard CNNs for image reconstruction, LoFi achieves excellent generalization to out-of-distribution data and memory usage almost independent of image resolution. Remarkably, training on $1024 \times 1024$ images requires just 3GB of memory -- over 20 times less than the memory typically needed by standard CNNs. Additionally, LoFi's local design allows it to train on extremely small datasets with less than 10 samples, without overfitting or the need for regularization or early stopping. Finally, we use LoFi as a denoising prior in a plug-and-play framework for solving general inverse problems to benefit from its continuous image representation and strong generalization. Although trained on low-resolution images, LoFi can be used as a low-dimensional prior to solve inverse problems at any resolution. We validate our framework across a variety of imaging modalities, from low-dose computed tomography to radio interferometric imaging.

Understanding the nature of dark matter in the Universe is an important goal of modern cosmology. A key method for probing this distribution is via weak gravitational lensing mass-mapping - a challenging ill-posed inverse problem where one infers the convergence field from observed shear measurements. Upcoming stage IV surveys, such as those made by the Vera C. Rubin Observatory and Euclid satellite, will provide a greater quantity and precision of data for lensing analyses, necessitating high-fidelity mass-mapping methods that are computationally efficient and that also provide uncertainties for integration into downstream cosmological analyses. In this work we introduce MMGAN, a novel mass-mapping method based on a regularised conditional generative adversarial network (GAN) framework, which generates approximate posterior samples of the convergence field given shear data. We adopt Wasserstein GANs to improve training stability and apply regularisation techniques to overcome mode collapse, issues that otherwise are particularly acute for conditional GANs. We train and validate our model on a mock COSMOS-style dataset before applying it to true COSMOS survey data. Our approach significantly outperforms the Kaiser-Squires technique and achieves similar reconstruction fidelity as alternative state-of-the-art deep learning approaches. Notably, while alternative approaches for generating samples from a learned posterior are slow (e.g. requiring $\sim$10 GPU minutes per posterior sample), MMGAN can produce a high-quality convergence sample in less than a second.

We present an accelerated pipeline, based on high-performance computing techniques and normalizing flows, for joint Bayesian parameter estimation and model selection and demonstrate its efficiency in gravitational wave astrophysics. We integrate the Jim inference toolkit, a normalizing flow-enhanced Markov chain Monte Carlo (MCMC) sampler, with the learned harmonic mean estimator. Our Bayesian evidence estimates run on $1$ GPU are consistent with traditional nested sampling techniques run on $16$ CPU cores, while reducing the computation time by factors of $5\times$ and $15\times$ for $4$-dimensional and $11$-dimensional gravitational wave inference problems, respectively. Our code is available in well-tested and thoroughly documented open-source packages, ensuring accessibility and reproducibility for the wider research community., Comment: accepted to NeurIPS 2024 workshop on Machine Learning and the Physical Sciences

We demonstrate the successful use of scattering representations without further compression for simulation-based inference (SBI) with images (i.e. field-level), illustrated with a cosmological case study. Scattering representations provide a highly effective representational space for subsequent learning tasks, although the higher dimensional compressed space introduces challenges. We overcome these through spatial averaging, coupled with more expressive density estimators. Compared to alternative methods, such an approach does not require additional simulations for either training or computing derivatives, is interpretable, and resilient to covariate shift. As expected, we show that a scattering only approach extracts more information than traditional second order summary statistics., Comment: 9 pages, 2 figures, accepted by NeurIPS workshop on Machine Learning and the Physical Sciences

Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build generative models of complex non-linear fields from a limited amount of data. In the context of upcoming cosmological surveys, the extension of these tools to spherical data is necessary. We develop scattering transforms on the sphere and focus on the construction of maximum-entropy generative models of astrophysical fields. The quality of the generative models, both statistically and visually, is very satisfying, which therefore open up a wide range of new applications for future cosmological studies., Comment: Contribution to the 2024 Cosmology session of the 58th Rencontres de Moriond. For details, please refer to the full article arXiv:2407.07007

Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build generative models of complex non-linear fields from a limited amount of data, and have also been used as the basis of new statistical component separation algorithms. In the context of upcoming cosmological surveys, such as LiteBIRD for the cosmic microwave background polarization or Rubin-LSST and Euclid for study of the large scale structures of the Universe, the extension of these tools to spherical data is necessary. We develop scattering transforms on the sphere and focus on the construction of maximum-entropy generative models of several astrophysical fields. We construct, from a single target field, generative models of homogeneous astrophysical and cosmological fields, whose samples are quantitatively compared to the target fields using common statistics (power spectrum, pixel probability density function and Minkowski functionals). Our sampled fields agree well with the target fields, both statistically and visually. These generative models therefore open up a wide range of new applications for future astrophysical and cosmological studies; particularly those for which very little simulated data is available. We make our code available to the community so that this work can be easily reproduced and developed further., Comment: submitted to A&A, 13 pages, 10 figures, code available at https://github.com/astro-informatics/s2scat

Understanding the large-scale structure of the Universe and unravelling the mysteries of dark matter are fundamental challenges in contemporary cosmology. Reconstruction of the cosmological matter distribution from lensing observables, referred to as 'mass-mapping' is an important aspect of this quest. Mass-mapping is an ill-posed problem, meaning there is inherent uncertainty in any convergence map reconstruction. The demand for fast and efficient reconstruction techniques is rising as we prepare for upcoming surveys. We present a novel approach which utilises deep learning, in particular a conditional Generative Adversarial Network (cGAN), to approximate samples from a Bayesian posterior distribution, meaning they can be interpreted in a statistically robust manner. By combining data-driven priors with recent regularisation techniques, we introduce an approach that facilitates the swift generation of high-fidelity, mass maps. Furthermore, to validate the effectiveness of our approach, we train the model on mock COSMOS-style data, generated using Colombia Lensing's kappaTNG mock weak lensing suite. These preliminary results showcase compelling convergence map reconstructions and ongoing refinement efforts are underway to enhance the robustness of our method further., Comment: 2 pages, 1 figure, submitted for conference proceedings for '58th Recontres de Moriond', 2024

We advocate for a new paradigm of cosmological likelihood-based inference, leveraging recent developments in machine learning and its underlying technology, to accelerate Bayesian inference in high-dimensional settings. Specifically, we combine (i) emulation, where a machine learning model is trained to mimic cosmological observables, e.g. CosmoPower-JAX; (ii) differentiable and probabilistic programming, e.g. JAX and NumPyro, respectively; (iii) scalable Markov chain Monte Carlo (MCMC) sampling techniques that exploit gradients, e.g. Hamiltonian Monte Carlo; and (iv) decoupled and scalable Bayesian model selection techniques that compute the Bayesian evidence purely from posterior samples, e.g. the learned harmonic mean implemented in harmonic. This paradigm allows us to carry out a complete Bayesian analysis, including both parameter estimation and model selection, in a fraction of the time of traditional approaches. First, we demonstrate the application of this paradigm on a simulated cosmic shear analysis for a Stage IV survey in 37- and 39-dimensional parameter spaces, comparing $\Lambda$CDM and a dynamical dark energy model ($w_0w_a$CDM). We recover posterior contours and evidence estimates that are in excellent agreement with those computed by the traditional nested sampling approach while reducing the computational cost from 8 months on 48 CPU cores to 2 days on 12 GPUs. Second, we consider a joint analysis between three simulated next-generation surveys, each performing a 3x2pt analysis, resulting in 157- and 159-dimensional parameter spaces. Standard nested sampling techniques are simply unlikely to be feasible in this high-dimensional setting, requiring a projected 12 years of compute time on 48 CPU cores; on the other hand, the proposed approach only requires 8 days of compute time on 24 GPUs. All packages used in our analyses are publicly available., Comment: 14 pages, 6 figures. Accepted for publication in the Open Journal of Astrophysics. Codes available at https://github.com/alessiospuriomancini/cosmopower, https://github.com/dpiras/cosmopower-jax, https://github.com/astro-informatics/harmonic/

With the next generation of interferometric telescopes, such as the Square Kilometre Array (SKA), the need for highly computationally efficient reconstruction techniques is particularly acute. The challenge in designing learned, data-driven reconstruction techniques for radio interferometry is that they need to be agnostic to the varying visibility coverages of the telescope, since these are different for each observation. Because of this, learned post-processing or learned unrolled iterative reconstruction methods must typically be retrained for each specific observation, amounting to a large computational overhead. In this work we develop learned post-processing and unrolled iterative methods for varying visibility coverages, proposing training strategies to make these methods agnostic to variations in visibility coverage with minimal to no fine-tuning. Learned post-processing techniques are heavily dependent on the prior information encoded in training data and generalise poorly to other visibility coverages. In contrast, unrolled iterative methods, which include the telescope measurement operator inside the network, achieve state-of-the-art reconstruction quality and computation time, generalising well to other coverages and require little to no fine-tuning. Furthermore, they generalise well to realistic radio observations and are able to reconstruct the high dynamic range of these images.

We present the learned harmonic mean estimator with normalizing flows - a robust, scalable and flexible estimator of the Bayesian evidence for model comparison. Since the estimator is agnostic to sampling strategy and simply requires posterior samples, it can be applied to compute the evidence using any Markov chain Monte Carlo (MCMC) sampling technique, including saved down MCMC chains, or any variational inference approach. The learned harmonic mean estimator was recently introduced, where machine learning techniques were developed to learn a suitable internal importance sampling target distribution to solve the issue of exploding variance of the original harmonic mean estimator. In this article we present the use of normalizing flows as the internal machine learning technique within the learned harmonic mean estimator. Normalizing flows can be elegantly coupled with the learned harmonic mean to provide an approach that is more robust, flexible and scalable than the machine learning models considered previously. We perform a series of numerical experiments, applying our method to benchmark problems and to a cosmological example in up to 21 dimensions. We find the learned harmonic mean estimator is in agreement with ground truth values and nested sampling estimates. The open-source harmonic Python package implementing the learned harmonic mean, now with normalizing flows included, is publicly available., Comment: 14 pages, 8 figures, harmonic code available at https://github.com/astro-informatics/harmonic

The 21-cm hyperfine line of neutral hydrogen is a useful tool to probe the conditions of the Universe during the Dark Ages, Cosmic Dawn, and the Epoch of Reionisation. In most of the current calculations, the 21-cm line signals at given frequencies are computed, using an integrated line-of-sight line opacity, with the correction for cosmological expansion. These calculations have not fully captured the line and continuum interactions in the radiative transfer, in response to evolution of the radiation field and the variations of thermal and dynamic properties of the line-of-sight medium. We construct a covariant formulation for the radiative transfer of the 21-cm line and derive the cosmological 21-cm line radiative transfer (C21LRT) equation. The formulation properly accounts for local emission and absorption processes and the interaction between the line and continuum when the radiation propagates across the expanding Universe to the present observer. Our C21LRT calculations show that methods simply summing the line optical depth could lead to error of $5\%$ in the 21-cm signals for redshift $z \sim 12-35$ and of $>10\%$ for redshift $z \lesssim 8$. Proper covariant radiative transfer is therefore necessary for producing correct theoretical templates for extracting information of the structural evolution of the Universe through the Epoch of Reionisation from the 21-cm tomographic data., Comment: 16 pages, 11 figures, 3 tables

Directional wavelet dictionaries are hierarchical representations which efficiently capture and segment information across scale, location and orientation. Such representations demonstrate a particular affinity to physical signals, which often exhibit highly anisotropic, localised multiscale structure. Many physically important signals are observed over spherical domains, such as the celestial sky in cosmology. Leveraging recent advances in computational harmonic analysis, we design new highly distributable and automatically differentiable directional wavelet transforms on the $2$-dimensional sphere $\mathbb{S}^2$ and $3$-dimensional ball $\mathbb{B}^3 = \mathbb{R}^+ \times \mathbb{S}^2$ (the space formed by augmenting the sphere with the radial half-line). We observe up to a $300$-fold and $21800$-fold acceleration for signals on the sphere and ball, respectively, compared to existing software, whilst maintaining 64-bit machine precision. Not only do these algorithms dramatically accelerate existing spherical wavelet transforms, the gradient information afforded by automatic differentiation unlocks many data-driven analysis techniques previously not possible for these spaces. We publicly release both S2WAV and S2BALL, open-sourced JAX libraries for our transforms that are automatically differentiable and readily deployable both on and over clusters of hardware accelerators (e.g. GPUs & TPUs)., Comment: code available on the sphere at https://github.com/astro-informatics/s2wav and on the ball at https://github.com/astro-informatics/s2ball

Next-generation radio interferometers like the Square Kilometer Array have the potential to unlock scientific discoveries thanks to their unprecedented angular resolution and sensitivity. One key to unlocking their potential resides in handling the deluge and complexity of incoming data. This challenge requires building radio interferometric imaging methods that can cope with the massive data sizes and provide high-quality image reconstructions with uncertainty quantification (UQ). This work proposes a method coined QuantifAI to address UQ in radio-interferometric imaging with data-driven (learned) priors for high-dimensional settings. Our model, rooted in the Bayesian framework, uses a physically motivated model for the likelihood. The model exploits a data-driven convex prior, which can encode complex information learned implicitly from simulations and guarantee the log-concavity of the posterior. We leverage probability concentration phenomena of high-dimensional log-concave posteriors that let us obtain information about the posterior, avoiding MCMC sampling techniques. We rely on convex optimisation methods to compute the MAP estimation, which is known to be faster and better scale with dimension than MCMC sampling strategies. Our method allows us to compute local credible intervals, i.e., Bayesian error bars, and perform hypothesis testing of structure on the reconstructed image. In addition, we propose a novel blazing-fast method to compute pixel-wise uncertainties at different scales. We demonstrate our method by reconstructing radio-interferometric images in a simulated setting and carrying out fast and scalable UQ, which we validate with MCMC sampling. Our method shows an improved image quality and more meaningful uncertainties than the benchmark method based on a sparsity-promoting prior. QuantifAI's source code: https://github.com/astro-informatics/QuantifAI., Comment: 30 pages, 14 figures, 10 tables, code available at https://github.com/astro-informatics/QuantifAI

Many areas of science and engineering encounter data defined on spherical manifolds. Modelling and analysis of spherical data often necessitates spherical harmonic transforms, at high degrees, and increasingly requires efficient computation of gradients for machine learning or other differentiable programming tasks. We develop novel algorithmic structures for accelerated and differentiable computation of generalised Fourier transforms on the sphere $\mathbb{S}^2$ and rotation group $\text{SO}(3)$, i.e. spherical harmonic and Wigner transforms, respectively. We present a recursive algorithm for the calculation of Wigner $d$-functions that is both stable to high harmonic degrees and extremely parallelisable. By tightly coupling this with separable spherical transforms, we obtain algorithms that exhibit an extremely parallelisable structure that is well-suited for the high throughput computing of modern hardware accelerators (e.g. GPUs). We also develop a hybrid automatic and manual differentiation approach so that gradients can be computed efficiently. Our algorithms are implemented within the JAX differentiable programming framework in the S2FFT software code. Numerous samplings of the sphere are supported, including equiangular and HEALPix sampling. Computational errors are at the order of machine precision for spherical samplings that admit a sampling theorem. When benchmarked against alternative C codes we observe up to a 400-fold acceleration. Furthermore, when distributing over multiple GPUs we achieve very close to optimal linear scaling with increasing number of GPUs due to the highly parallelised and balanced nature of our algorithms. Provided access to sufficiently many GPUs our transforms thus exhibit an unprecedented effective linear time complexity., Comment: 30 pages, 7 figures, accepted by Journal of Computational Physics, code available at https://github.com/astro-informatics/s2fft

Cosmic strings are linear topological defects that may have been produced during symmetry-breaking phase transitions in the very early Universe. In an expanding Universe the existence of causally separate regions prevents such symmetries from being broken uniformly, with a network of cosmic string inevitably forming as a result. To faithfully generate observables of such processes requires computationally expensive numerical simulations, which prohibits many types of analyses. We propose a technique to instead rapidly emulate observables, thus circumventing simulation. Emulation is a form of generative modelling, often built upon a machine learning backbone. End-to-end emulation often fails due to high dimensionality and insufficient training data. Consequently, it is common to instead emulate a latent representation from which observables may readily be synthesised. Wavelet phase harmonics are an excellent latent representations for cosmological fields, both as a summary statistic and for emulation, since they do not require training and are highly sensitive to non-Gaussian information. Leveraging wavelet phase harmonics as a latent representation, we develop techniques to emulate string induced CMB anisotropies over a 7.2 degree field of view, with sub-arcminute resolution, in under a minute on a single GPU. Beyond generating high fidelity emulations, we provide a technique to ensure these observables are distributed correctly, providing a more representative ensemble of samples. The statistics of our emulations are commensurate with those calculated on comprehensive Nambu-Goto simulations. Our findings indicate these fast emulation approaches may be suitable for wide use in, e.g., simulation based inference pipelines. We make our code available to the community so that researchers may rapidly emulate cosmic string induced CMB anisotropies for their own analysis., Comment: code available at https://github.com/astro-informatics/stringgen

Proximal nested sampling was introduced recently to open up Bayesian model selection for high-dimensional problems such as computational imaging. The framework is suitable for models with a log-convex likelihood, which are ubiquitous in the imaging sciences. The purpose of this article is two-fold. First, we review proximal nested sampling in a pedagogical manner in an attempt to elucidate the framework for physical scientists. Second, we show how proximal nested sampling can be extended in an empirical Bayes setting to support data-driven priors, such as deep neural networks learned from training data., Comment: 9 pages, 4 figures

Computing the marginal likelihood (also called the Bayesian model evidence) is an important task in Bayesian model selection, providing a principled quantitative way to compare models. The learned harmonic mean estimator solves the exploding variance problem of the original harmonic mean estimation of the marginal likelihood. The learned harmonic mean estimator learns an importance sampling target distribution that approximates the optimal distribution. While the approximation need not be highly accurate, it is critical that the probability mass of the learned distribution is contained within the posterior in order to avoid the exploding variance problem. In previous work a bespoke optimization problem is introduced when training models in order to ensure this property is satisfied. In the current article we introduce the use of normalizing flows to represent the importance sampling target distribution. A flow-based model is trained on samples from the posterior by maximum likelihood estimation. Then, the probability density of the flow is concentrated by lowering the variance of the base distribution, i.e. by lowering its "temperature", ensuring its probability mass is contained within the posterior. This approach avoids the need for a bespoke optimisation problem and careful fine tuning of parameters, resulting in a more robust method. Moreover, the use of normalizing flows has the potential to scale to high dimensional settings. We present preliminary experiments demonstrating the effectiveness of the use of flows for the learned harmonic mean estimator. The harmonic code implementing the learned harmonic mean, which is publicly available, has been updated to now support normalizing flows., Comment: 9 pages, 6 figures. arXiv admin note: text overlap with arXiv:2111.12720

A new golden age in astronomy is upon us, dominated by data. Large astronomical surveys are broadcasting unprecedented rates of information, demanding machine learning as a critical component in modern scientific pipelines to handle the deluge of data. The upcoming Legacy Survey of Space and Time (LSST) of the Vera C. Rubin Observatory will raise the big-data bar for time-domain astronomy, with an expected 10 million alerts per-night, and generating many petabytes of data over the lifetime of the survey. Fast and efficient classification algorithms that can operate in real-time, yet robustly and accurately, are needed for time-critical events where additional resources can be sought for follow-up analyses. In order to handle such data, state-of-the-art deep learning architectures coupled with tools that leverage modern hardware accelerators are essential. We showcase how the use of modern deep compression methods can achieve a $18\times$ reduction in model size, whilst preserving classification performance. We also show that in addition to the deep compression techniques, careful choice of file formats can improve inference latency, and thereby throughput of alerts, on the order of $8\times$ for local processing, and $5\times$ in a live production setting. To test this in a live setting, we deploy this optimised version of the original time-series transformer, t2, into the community alert broking system of FINK on real Zwicky Transient Facility (ZTF) alert data, and compare throughput performance with other science modules that exist in FINK. The results shown herein emphasise the time-series transformer's suitability for real-time classification at LSST scale, and beyond, and introduce deep model compression as a fundamental tool for improving deploy-ability and scalable inference of deep learning models for transient classification., Comment: 16 pages, 11 figures

Inspired by recent interest in geometric deep learning, this work generalises the recently developed Slepian scale-discretised wavelets on the sphere to Riemannian manifolds. Through the sifting convolution, one may define translations and, thus, convolutions on manifolds - which are otherwise not well-defined in general. Slepian wavelets are constructed on a region of a manifold and are therefore suited to problems where data only exists in a particular region. The Slepian functions, on which Slepian wavelets are built, are the basis functions of the Slepian spatial-spectral concentration problem on the manifold. A tiling of the Slepian harmonic line with smoothly decreasing generating functions defines the scale-discretised wavelets; allowing one to probe spatially localised, scale-dependent features of a signal. By discretising manifolds as graphs, the Slepian functions and wavelets of a triangular mesh are presented. Through a wavelet transform, the wavelet coefficients of a field defined on the mesh are found and used in a straightforward thresholding denoising scheme., Comment: 12 pages, 12 figures

The Segmented Planar Imaging Detector for Electro-Optical Reconnaissance (SPIDER) is an optical interferometric imaging device that aims to offer an alternative to the large space telescope designs of today with reduced size, weight and power consumption. This is achieved through interferometric imaging. State-of-the-art methods for reconstructing images from interferometric measurements adopt proximal optimization techniques, which are computationally expensive and require handcrafted priors. In this work we present two data-driven approaches for reconstructing images from measurements made by the SPIDER instrument. These approaches use deep learning to learn prior information from training data, increasing the reconstruction quality, and significantly reducing the computation time required to recover images by orders of magnitude. Reconstruction time is reduced to ${\sim} 10$ milliseconds, opening up the possibility of real-time imaging with SPIDER for the first time. Furthermore, we show that these methods can also be applied in domains where training data is scarce, such as astronomical imaging, by leveraging transfer learning from domains where plenty of training data are available., Comment: 21 pages, 14 figures

Uncertainty quantification is a crucial step of cosmological mass-mapping that is often ignored. Suggested methods are typically only approximate or make strong assumptions of Gaussianity of the shear field. Probabilistic sampling methods, such as Markov chain Monte Carlo (MCMC), draw samples form a probability distribution, allowing for full and flexible uncertainty quantification, however these methods are notoriously slow and struggle in the high-dimensional parameter spaces of imaging problems. In this work we use, for the first time, a trans-dimensional MCMC sampler for mass-mapping, promoting sparsity in a wavelet basis. This sampler gradually grows the parameter space as required by the data, exploiting the extremely sparse nature of mass maps in wavelet space. The wavelet coefficients are arranged in a tree-like structure, which adds finer scale detail as the parameter space grows. We demonstrate the trans-dimensional sampler on galaxy cluster-scale images where the planar modelling approximation is valid. In high-resolution experiments, this method produces naturally parsimonious solutions, requiring less than 1% of the potential maximum number of wavelet coefficients and still producing a good fit to the observed data. In the presence of noisy data, trans-dimensional MCMC produces a better reconstruction of mass-maps than the standard smoothed Kaiser-Squires method, with the addition that uncertainties are fully quantified. This opens up the possibility for new mass maps and inferences about the nature of dark matter using the new high-resolution data from upcoming weak lensing surveys such as Euclid.

The Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) will discover an unprecedented number of supernovae (SNe), making spectroscopic classification for all the events infeasible. LSST will thus rely on photometric classification, whose accuracy depends on the not-yet-finalized LSST observing strategy. In this work, we analyze the impact of cadence choices on classification performance using simulated multi-band light curves. First, we simulate SNe with an LSST baseline cadence, a non-rolling cadence, and a presto-color cadence which observes each sky location three times per night instead of twice. Each simulated dataset includes a spectroscopically-confirmed training set, which we augment to be representative of the test set as part of the classification pipeline. Then, we use the photometric transient classification library snmachine to build classifiers. We find that the active region of the rolling cadence used in the baseline observing strategy yields a 25% improvement in classification performance relative to the background region. This improvement in performance in the actively-rolling region is also associated with an increase of up to a factor of 2.7 in the number of cosmologically-useful Type Ia supernovae relative to the background region. However, adding a third visit per night as implemented in presto-color degrades classification performance due to more irregularly sampled light curves. Overall, our results establish desiderata on the observing cadence related to classification of full SNe light curves, which in turn impacts photometric SNe cosmology with LSST., Comment: 22 pages, 14 figures. Changed to match version accepted by the Astrophysical Journal Supplement Series (accepted 06/02/2023)

No existing spherical convolutional neural network (CNN) framework is both computationally scalable and rotationally equivariant. Continuous approaches capture rotational equivariance but are often prohibitively computationally demanding. Discrete approaches offer more favorable computational performance but at the cost of equivariance. We develop a hybrid discrete-continuous (DISCO) group convolution that is simultaneously equivariant and computationally scalable to high-resolution. While our framework can be applied to any compact group, we specialize to the sphere. Our DISCO spherical convolutions exhibit $\text{SO}(3)$ rotational equivariance, where $\text{SO}(n)$ is the special orthogonal group representing rotations in $n$-dimensions. When restricting rotations of the convolution to the quotient space $\text{SO}(3)/\text{SO}(2)$ for further computational enhancements, we recover a form of asymptotic $\text{SO}(3)$ rotational equivariance. Through a sparse tensor implementation we achieve linear scaling in number of pixels on the sphere for both computational cost and memory usage. For 4k spherical images we realize a saving of $10^9$ in computational cost and $10^4$ in memory usage when compared to the most efficient alternative equivariant spherical convolution. We apply the DISCO spherical CNN framework to a number of benchmark dense-prediction problems on the sphere, such as semantic segmentation and depth estimation, on all of which we achieve the state-of-the-art performance., Comment: 19 pages, 7 figures, accepted by ICLR 2023

We introduce two kurt-spectra to probe fourth-order statistics of weak lensing convergence maps. Using state-of-the-art numerical simulations, we study the shapes of these kurt-spectra as a function of source redshifts and smoothing angular scales. We employ a pseudo-$C_{\ell}$ approach to estimate the spectra from realistic convergence maps in the presence of an observational mask and noise for stage-IV large-scale structure surveys. We compare these results against theoretical predictions calculated using the FFTLog formalism, and find that a simple nonlinear clustering model-the hierarchical ansatz-can reproduce the numerical trends for the kurt-spectra in the nonlinear regime. In addition, we provide estimators for beyond fourth-order spectra where no definitive analytical results are available, and present corresponding results from numerical simulations., Comment: 32 pages, 6 figures, accepted for publication in JCAP

We resurrect the infamous harmonic mean estimator for computing the marginal likelihood (Bayesian evidence) and solve its problematic large variance. The marginal likelihood is a key component of Bayesian model selection to evaluate model posterior probabilities; however, its computation is challenging. The original harmonic mean estimator, first proposed by Newton and Raftery in 1994, involves computing the harmonic mean of the likelihood given samples from the posterior. It was immediately realised that the original estimator can fail catastrophically since its variance can become very large (possibly not finite). A number of variants of the harmonic mean estimator have been proposed to address this issue although none have proven fully satisfactory. We present the \emph{learnt harmonic mean estimator}, a variant of the original estimator that solves its large variance problem. This is achieved by interpreting the harmonic mean estimator as importance sampling and introducing a new target distribution. The new target distribution is learned to approximate the optimal but inaccessible target, while minimising the variance of the resulting estimator. Since the estimator requires samples of the posterior only, it is agnostic to the sampling strategy used. We validate the estimator on a variety of numerical experiments, including a number of pathological examples where the original harmonic mean estimator fails catastrophically. We also consider a cosmological application, where our approach leads to $\sim$ 3 to 6 times more samples than current state-of-the-art techniques in 1/3 of the time. In all cases our learnt harmonic mean estimator is shown to be highly accurate. The estimator is computationally scalable and can be applied to problems of dimension $O(10^3)$ and beyond. Code implementing the learnt harmonic mean estimator is made publicly available, Comment: 42 pages, 10 figures, code available at https://github.com/astro-informatics/harmonic

The Vera C. Rubin Observatory will increase the number of observed supernovae (SNe) by an order of magnitude; however, it is impossible to spectroscopically confirm the class for all the SNe discovered. Thus, photometric classification is crucial but its accuracy depends on the not-yet-finalized observing strategy of Rubin Observatory's Legacy Survey of Space and Time (LSST). We quantitatively analyze the impact of the LSST observing strategy on SNe classification using simulated multi-band light curves from the Photometric LSST Astronomical Time-Series Classification Challenge (PLAsTiCC). First, we augment the simulated training set to be representative of the photometric redshift distribution per supernovae class, the cadence of observations, and the flux uncertainty distribution of the test set. Then we build a classifier using the photometric transient classification library snmachine, based on wavelet features obtained from Gaussian process fits, yielding similar performance to the winning PLAsTiCC entry. We study the classification performance for SNe with different properties within a single simulated observing strategy. We find that season length is important, with light curves of 150 days yielding the highest performance. Cadence also has an important impact on SNe classification; events with median inter-night gap <3.5 days yield higher classification performance. Interestingly, we find that large gaps (>10 days) in light curve observations do not impact performance if sufficient observations are available on either side, due to the effectiveness of the Gaussian process interpolation. This analysis is the first exploration of the impact of observing strategy on photometric supernova classification with LSST., Comment: 18 pages, 13 figures. Changed to match version accepted by the Astrophysical Journal Supplement Series (accepted 28/10/2021). Software publicly available at https://github.com/LSSTDESC/snmachine

Inverse problems defined on the sphere arise in many fields, including seismology and cosmology where problems are defined on the globe and the cosmic sphere. These are generally high-dimensional and computationally very complex and, as a result, sampling the posterior of spherical inverse problems is a challenging task. In this work, we describe a framework that leverages a proximal Markov chain Monte Carlo (MCMC) algorithm to efficiently sample the high-dimensional space of spherical inverse problems with a sparsity-promoting wavelet prior. We detail the modifications needed for the algorithm to be applied to spherical problems, and give special consideration to the crucial forward modelling step which contains spherical harmonic transforms that are computationally expensive. By sampling the posterior, our framework allows for full and flexible uncertainty quantification, something which is not possible with other methods based on, for example, convex optimisation. We demonstrate our framework in practice on full-sky cosmological mass-mapping and on a common problem in global seismic tomography. We find that our approach is potentially useful at moderate resolutions, such as those of interest in seismology. Our framework is generally limited by resolution requirements, such as those required for astrophysical applications, due to the poor scaling of the complexity of spherical harmonic transforms with resolution. A new Python package, pxmcmc, containing the proximal MCMC sampler, measurement operators, wavelet transforms and sparse priors is made publicly available.

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal likelihood (model evidence), which is computationally challenging, prohibiting its use in many high-dimensional Bayesian inverse problems. With Bayesian imaging applications in mind, in this work we present the proximal nested sampling methodology to objectively compare alternative Bayesian imaging models for applications that use images to inform decisions under uncertainty. The methodology is based on nested sampling, a Monte Carlo approach specialised for model comparison, and exploits proximal Markov chain Monte Carlo techniques to scale efficiently to large problems and to tackle models that are log-concave and not necessarily smooth (e.g., involving l_1 or total-variation priors). The proposed approach can be applied computationally to problems of dimension O(10^6) and beyond, making it suitable for high-dimensional inverse imaging problems. It is validated on large Gaussian models, for which the likelihood is available analytically, and subsequently illustrated on a range of imaging problems where it is used to analyse different choices of dictionary and measurement model.

This work presents the construction of a novel spherical wavelet basis designed for incomplete spherical datasets, i.e. datasets which are missing in a particular region of the sphere. The eigenfunctions of the Slepian spatial-spectral concentration problem (the Slepian functions) are a set of orthogonal basis functions which are more concentrated within a defined region. Slepian functions allow one to compute a convolution on the incomplete sphere by leveraging the recently proposed sifting convolution and extending it to any set of basis functions. Through a tiling of the Slepian harmonic line, one may construct scale-discretised wavelets. An illustration is presented based on an example region on the sphere defined by the topographic map of the Earth. The Slepian wavelets and corresponding wavelet coefficients are constructed from this region and are used in a straightforward denoising example., Comment: 12 pages, 14 figures

Future surveys such as the Legacy Survey of Space and Time (LSST) of the Vera C. Rubin Observatory will observe an order of magnitude more astrophysical transient events than any previous survey before. With this deluge of photometric data, it will be impossible for all such events to be classified by humans alone. Recent efforts have sought to leverage machine learning methods to tackle the challenge of astronomical transient classification, with ever improving success. Transformers are a recently developed deep learning architecture, first proposed for natural language processing, that have shown a great deal of recent success. In this work we develop a new transformer architecture, which uses multi-head self attention at its core, for general multi-variate time-series data. Furthermore, the proposed time-series transformer architecture supports the inclusion of an arbitrary number of additional features, while also offering interpretability. We apply the time-series transformer to the task of photometric classification, minimising the reliance of expert domain knowledge for feature selection, while achieving results comparable to state-of-the-art photometric classification methods. We achieve a logarithmic-loss of 0.507 on imbalanced data in a representative setting using data from the Photometric LSST Astronomical Time-Series Classification Challenge (PLAsTiCC). Moreover, we achieve a micro-averaged receiver operating characteristic area under curve of 0.98 and micro-averaged precision-recall area under curve of 0.87., Comment: Manuscript Accepted to RAS Techniques and Instruments. 15 pages, 12 figures

We develop variational regularization methods which leverage sparsity-promoting priors to solve severely ill posed inverse problems defined on the 3D ball (i.e. the solid sphere). Our method solves the problem natively on the ball and thus does not suffer from discontinuities that plague alternate approaches where each spherical shell is considered independently. Additionally, we leverage advances in probability density theory to produce Bayesian variational methods which benefit from the computational efficiency of advanced convex optimization algorithms, whilst supporting principled uncertainty quantification. We showcase these variational regularization and uncertainty quantification techniques on an illustrative example. The C++ code discussed throughout is provided under a GNU general public license.

Inverse problems defined naturally on the sphere are becoming increasingly of interest. In this article we provide a general framework for evaluation of inverse problems on the sphere, with a strong emphasis on flexibility and scalability. We consider flexibility with respect to the prior selection (regularization), the problem definition - specifically the problem formulation (constrained/unconstrained) and problem setting (analysis/synthesis) - and optimization adopted to solve the problem. We discuss and quantify the trade-offs between problem formulation and setting. Crucially, we consider the Bayesian interpretation of the unconstrained problem which, combined with recent developments in probability density theory, permits rapid, statistically principled uncertainty quantification (UQ) in the spherical setting. Linearity is exploited to significantly increase the computational efficiency of such UQ techniques, which in some cases are shown to permit analytic solutions. We showcase this reconstruction framework and UQ techniques on a variety of spherical inverse problems. The code discussed throughout is provided under a GNU general public license, in both C++ and Python.

Despite the technological advancements in Virtual Reality (VR), users are constantly combating feelings of nausea and disorientation, the so called cybersickness. Cybersickness symptoms cause severe discomfort and hinder the immersive VR experience. Here we investigated cybersickness in 360-degree head-mounted display VR. In traditional 360-degree VR experiences, translational movement in the real world is not reflected in the virtual world, and therefore self-motion information is not corroborated by matching visual and vestibular cues, which may trigger symptoms of cybersickness. We have evaluated whether a new Artificial Intelligence (AI) software designed to supplement the 360-degree VR experience with artificial 6-degrees-of-freedom motion may reduce cybersickness. Explicit (simulator sickness questionnaire and fast motion sickness rating) and implicit (heart rate) measurements were used to evaluate cybersickness symptoms during and after 360-degree VR exposure. Simulator sickness scores showed a significant reduction in feelings of nausea during the AI supplemented 6-degrees-of-freedom motion VR compared to traditional 360-degree VR. However, 6-degrees-of-freedom motion VR did not reduce oculomotor or disorientation measures of sickness. No changes have been observed in fast motion sickness and heart rate measures. Improving the congruency between visual and vestibular cues in 360-degree VR, as provided by the AI supplemented 6-degrees-of-freedom motion system considered, is essential to provide a more engaging, immersive and safe VR, which is critical for educational, cultural and entertainment applications., Comment: 27 pages, 1 figure; Software available at https://www.kagenova.com/products/copernic360/

Convolutional neural networks (CNNs) constructed natively on the sphere have been developed recently and shown to be highly effective for the analysis of spherical data. While an efficient framework has been formulated, spherical CNNs are nevertheless highly computationally demanding; typically they cannot scale beyond spherical signals of thousands of pixels. We develop scattering networks constructed natively on the sphere that provide a powerful representational space for spherical data. Spherical scattering networks are computationally scalable and exhibit rotational equivariance, while their representational space is invariant to isometries and provides efficient and stable signal representations. By integrating scattering networks as an additional type of layer in the generalized spherical CNN framework, we show how they can be leveraged to scale spherical CNNs to the high-resolution data typical of many practical applications, with spherical signals of many tens of megapixels and beyond., Comment: 18 pages, 6 figures, accepted by ICLR, code at https://www.kagenova.com/products/fourpiAI/

We present a framework for the optimal filtering of spherical signals contaminated by realizations of an additive, zero-mean, uncorrelated and anisotropic noise process on the sphere. Filtering is performed in the wavelet domain given by the scale-discretized wavelet transform on the sphere. The proposed filter is optimal in the sense that it minimizes the mean square error between the filtered wavelet representation and wavelet representation of the noise-free signal. We also present a simplified formulation of the filter for the case when azimuthally symmetric wavelet functions are used. We demonstrate the use of the proposed optimal filter for denoising of an Earth topography map in the presence of additive, zero-mean, uncorrelated and white Gaussian noise, and show that the proposed filter performs better than the hard thresholding method and weighted spherical harmonic~(weighted-SPHARM) signal estimation framework., Comment: 5 pages

Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical CNN framework that encompasses various existing approaches and allows them to be leveraged alongside each other. The only existing non-linear spherical CNN layer that is strictly equivariant has complexity $\mathcal{O}(C^2L^5)$, where $C$ is a measure of representational capacity and $L$ the spherical harmonic bandlimit. Such a high computational cost often prohibits the use of strictly equivariant spherical CNNs. We develop two new strictly equivariant layers with reduced complexity $\mathcal{O}(CL^4)$ and $\mathcal{O}(CL^3 \log L)$, making larger, more expressive models computationally feasible. Moreover, we adopt efficient sampling theory to achieve further computational savings. We show that these developments allow the construction of more expressive hybrid models that achieve state-of-the-art accuracy and parameter efficiency on spherical benchmark problems., Comment: 20 pages, 4 figures, accepted by ICLR, code at https://www.kagenova.com/products/fourpiAI/

Since the 1970s, much of traditional interferometric imaging has been built around variations of the CLEAN algorithm, in both terminology, methodology, and algorithm development. Recent developments in applying new algorithms from convex optimization to interferometry has allowed old concepts to be viewed from a new perspective, ranging from image restoration to the development of computationally distributed algorithms. We present how this has ultimately led the authors to new perspectives in wide-field imaging, allowing for the first full individual non-coplanar corrections applied during imaging over extremely wide-fields of view for the Murchison Widefield Array (MWA) telescope. Furthermore, this same mathematical framework has provided a novel understanding of wide-band polarimetry at low frequencies, where instrumental channel depolarization can be corrected through the new $\delta\lambda^2$-projection algorithm. This is a demonstration that new algorithm development outside of traditional radio astronomy is valuable for the new theoretical and practical perspectives gained. These perspectives are timely with the next generation of radio telescopes coming online., Comment: 4 pages, 1 figure. URSI GASS 2020, Rome, Italy, 29 August - 5 September 2020

A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the adoption of an alternative translation operator on the sphere. This translation operator follows by analogy with the Euclidean translation when viewed in harmonic space. The sifting convolution satisfies a variety of desirable properties that are lacking in alternate definitions, namely: it supports directional kernels; it has an output which remains on the sphere; and is efficient to compute. An illustration of the sifting convolution on a topographic map of the Earth demonstrates that it supports directional kernels to perform anisotropic filtering, while its output remains on the sphere., Comment: 5 pages, 3 figures

To date weak gravitational lensing surveys have typically been restricted to small fields of view, such that the $\textit{flat-sky approximation}$ has been sufficiently satisfied. However, with Stage IV surveys ($\textit{e.g. LSST}$ and $\textit{Euclid}$) imminent, extending mass-mapping techniques to the sphere is a fundamental necessity. As such, we extend the sparse hierarchical Bayesian mass-mapping formalism presented in previous work to the spherical sky. For the first time, this allows us to construct $\textit{maximum a posteriori}$ spherical weak lensing dark-matter mass-maps, with principled Bayesian uncertainties, without imposing or assuming Gaussianty. We solve the spherical mass-mapping inverse problem in the analysis setting adopting a sparsity promoting Laplace-type wavelet prior, though this theoretical framework supports all log-concave posteriors. Our spherical mass-mapping formalism facilitates principled statistical interpretation of reconstructions. We apply our framework to convergence reconstruction on high resolution N-body simulations with pseudo-Euclid masking, polluted with a variety of realistic noise levels, and show a significant increase in reconstruction fidelity compared to standard approaches. Furthermore we perform the largest joint reconstruction to date of the majority of publicly available shear observational datasets (combining DESY1, KiDS450 and CFHTLens) and find that our formalism recovers a convergence map with significantly enhanced small-scale detail. Within our Bayesian framework we validate, in a statistically rigorous manner, the community's intuition regarding the need to smooth spherical Kaiser-Squires estimates to provide physically meaningful convergence maps. Such approaches cannot reveal the small-scale physical structures that we recover within our framework.

Radio astronomy is transitioning to a big-data era due to the emerging generation of radio interferometric (RI) telescopes, such as the Square Kilometre Array (SKA), which will acquire massive volumes of data. In this article we review methods proposed recently to resolve the ill-posed inverse problem of imaging the raw visibilities acquired by RI telescopes in the big-data scenario. We focus on the recently proposed online reconstruction method [4] and the considerable savings in data storage requirements and computational cost that it yields., Comment: 4 pages; 2 figures; URSI GASS 2020. arXiv admin note: substantial text overlap with arXiv:1712.04462

The deconvolution, or cleaning, of radio interferometric images often involves computing model visibilities from a list of clean components, in order that the contribution from the model can be subtracted from the observed visibilities. This step is normally performed using a forward fast Fourier transform (FFT), followed by a 'degridding' step that interpolates over the uv plane to construct the model visibilities. An alternative approach is to calculate the model visibilities directly by summing over all the members of the clean component list, which is a more accurate method that can also be much slower. However, if the clean components are used to construct a model image on the surface of the celestial sphere then the model visibilities can be generated directly from the wavelet coefficients, and the sparsity of the model means that most of these coefficients are zero, and can be ignored. We have constructed a prototype imager that uses a spherical-wavelet representation of the model image to generate model visibilities during each major cycle, and find empirically that the execution time scales with the wavelet resolution level, J, as O(1.07 J), and with the number of distinct clean components, N_C, as O(N_C). The prototype organises the wavelet coefficients into a tree structure, and does not store or process the zero wavelet coefficients., Comment: 12 pages, 12 figures

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., Comment: Physical Review D. accepted

We present a new algorithm to perform wide-field radio interferometric image reconstruction, with exact non-coplanar correction, that scales to big-data. This algorithm allows us to image 2 billion visibilities on 50 nodes of a computing cluster for a 25 by 25 degree field of view, in a little over an hour. We build on the recently developed distributed $w$-stacking $w$-projection hybrid algorithm, extending it to include a new distributed degridding algorithm that balances the computational load of the $w$-projection gridding kernels. The implementation of our algorithm is made publicly available in the PURIFY software package. Wide-field image reconstruction for data sets of this size cannot be performed effectively using the allocated computational resources without computational load balancing, demonstrating that our algorithms are critical for next-generation wide-field radio interferometers., Comment: 4 pages, 1 figure

The concept of a recently proposed small-scale interferometric optical imaging device, an instrument known as the Segmented Planar Imaging Detector for Electro-optical Reconnaissance (SPIDER), is of great interest for its possible applications in astronomy and space science. Due to low weight, low power consumption, and high resolution, the SPIDER telescope could replace the large space telescopes that exist today. Unlike traditional optical interferometry the SPIDER accurately retrieves both phase and amplitude information, making the measurement process analogous to a radio interferometer. State of the art sparse radio interferometric image reconstruction techniques have been gaining traction in radio astronomy and reconstruct accurate images of the radio sky. In this work we describe algorithms from radio interferometric imaging and sparse image reconstruction and demonstrate their application to the SPIDER concept telescope through simulated observation and reconstruction of the optical sky. Such algorithms are important for providing high fidelity images from SPIDER observations, helping to power the SPIDER concept for scientific and astronomical analysis., Comment: 4 Pages, 2 Figures, 1 Table

Next generation radio interferometric telescopes are entering an era of big data with extremely large data sets. While these telescopes can observe the sky in higher sensitivity and resolution than before, computational challenges in image reconstruction need to be overcome to realize the potential of forthcoming telescopes. New methods in sparse image reconstruction and convex optimization techniques (cf. compressive sensing) have shown to produce higher fidelity reconstructions of simulations and real observations than traditional methods. This article presents distributed and parallel algorithms and implementations to perform sparse image reconstruction, with significant practical considerations that are important for implementing these algorithms for Big Data. We benchmark the algorithms presented, showing that they are considerably faster than their serial equivalents. We then pre-sample gridding kernels to scale the distributed algorithms to larger data sizes, showing application times for 1 Gb to 2.4 Tb data sets over 25 to 100 nodes for up to 50 billion visibilities, and find that the run-times for the distributed algorithms range from 100 milliseconds to 3 minutes per iteration. This work presents an important step in working towards computationally scalable and efficient algorithms and implementations that are needed to image observations of both extended and compact sources from next generation radio interferometers such as the SKA. The algorithms are implemented in the latest versions of the SOPT (https://github.com/astro-informatics/sopt) and PURIFY (https://github.com/astro-informatics/purify) software packages {(Versions 3.1.0)}, which have been released alongside of this article., Comment: 25 pages, 5 figures

Polarization of radiation is a powerful tool to study cosmic magnetism and analysis of polarization can be used as a diagnostic tool for large-scale structures. In this paper, we present a solid theoretical foundation for using polarized light to investigate large-scale magnetic field structures: the cosmological polarized radiative transfer (CPRT) formulation. The CPRT formulation is fully covariant. It accounts for cosmological and relativistic effects in a self-consistent manner and explicitly treats Faraday rotation, as well as Faraday conversion, emission, and absorption processes. The formulation is derived from the first principles of conservation of phase-space volume and photon number. Without loss of generality, we consider a flat Friedmann-Robertson-Walker (FRW) space-time metric and construct the corresponding polarized radiative transfer equations. We propose an all-sky CPRT calculation algorithm, based on a ray-tracing method, which allows cosmological simulation results to be incorporated and, thereby, model templates of polarization maps to be constructed. Such maps will be crucial in our interpretation of polarized data, such as those to be collected by the Square Kilometer Array (SKA). We describe several tests which are used for verifying the code and demonstrate applications in the study of the polarization signatures in different distributions of electron number density and magnetic fields. We present a pencil-beam CPRT calculation and an all-sky calculation, using a simulated galaxy cluster or a model magnetized universe obtained from GCMHD+ simulations as the respective input structures. The implications on large-scale magnetic field studies are discussed; remarks on the standard methods using rotation measure are highlighted., Comment: 32 pages, 14 figures

Weak lensing convergence maps - upon which higher order statistics can be calculated - can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic - the peak count as a function of signal to noise ratio (SNR). We adopt the sparse hierarchical Bayesian mass-mapping framework developed in previous work, which provides robust reconstructions and principled statistical interpretation of reconstructed convergence maps without the need to assume or impose Gaussianity. We demonstrate our uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.6 (large scale structure) N-body simulations. For the first time, this methodology allows one to recover approximate Bayesian upper and lower limits on the cumulative peak statistic at well defined confidence levels.

A crucial aspect of mass-mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l1-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass-mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artifacts of the reconstruction. Here we present this new formalism, demonstrate the method on simulations, before applying the developed formalism to two observational datasets of the Abel-520 cluster. Initial reconstructions of the Abel-520 catalogs reported the detection of an anomalous 'dark core' -- an over dense region with no optical counterpart -- which was taken to be evidence for self-interacting dark-matter. In our Bayesian framework it is found that neither Abel-520 dataset can conclusively determine the physicality of such dark cores at 99% confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.

Until recently mass-mapping techniques for weak gravitational lensing convergence reconstruction have lacked a principled statistical framework upon which to quantify reconstruction uncertainties, without making strong assumptions of Gaussianity. In previous work we presented a sparse hierarchical Bayesian formalism for convergence reconstruction that addresses this shortcoming. Here, we draw on the concept of local credible intervals (cf. Bayesian error bars) as an extension of the uncertainty quantification techniques previously detailed. These uncertainty quantification techniques are benchmarked against those recovered via Px-MALA - a state of the art proximal Markov Chain Monte Carlo (MCMC) algorithm. We find that typically our recovered uncertainties are everywhere conservative, of similar magnitude and highly correlated (Pearson correlation coefficient $\geq 0.85$) with those recovered via Px-MALA. Moreover, we demonstrate an increase in computational efficiency of $\mathcal{O}(10^6)$ when using our sparse Bayesian approach over MCMC techniques. This computational saving is critical for the application of Bayesian uncertainty quantification to large-scale stage IV surveys such as LSST and Euclid.