Abstract
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 (delfi), which learns a parametrized 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 delfi 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 ∼104 simulations, with substantial scope for further improvement, demonstrating the scalability of likelihood-free inference to large and complex cosmological data sets.
Abstract
Estimates of the Hubble constant, H0, from the local distance ladder and from the cosmic microwave background (CMB) are discrepant at the ∼3σ level, indicating a potential issue with the ...standard Λ cold dark matter (ΛCDM) cosmology. A probabilistic (i.e. Bayesian) interpretation of this tension requires a model comparison calculation, which in turn depends strongly on the tails of the H0 likelihoods. Evaluating the tails of the local H0 likelihood requires the use of non-Gaussian distributions to faithfully represent anchor likelihoods and outliers, and simultaneous fitting of the complete distance-ladder data set to ensure correct uncertainty propagation. We have hence developed a Bayesian hierarchical model of the full distance ladder that does not rely on Gaussian distributions and allows outliers to be modelled without arbitrary data cuts. Marginalizing over the full ∼3000-parameter joint posterior distribution, we find H0 = (72.72 ± 1.67) km s−1 Mpc−1 when applied to the outlier-cleaned Riess et al. data, and (73.15 ± 1.78) km s−1 Mpc−1 with supernova outliers reintroduced (the pre-cut Cepheid data set is not available). Using our precise evaluation of the tails of the H0 likelihood, we apply Bayesian model comparison to assess the evidence for deviation from ΛCDM given the distance-ladder and CMB data. The odds against ΛCDM are at worst ∼10:1 when considering the Planck 2015 XIII data, regardless of outlier treatment, considerably less dramatic than naïvely implied by the 2.8σ discrepancy. These odds become ∼60:1 when an approximation to the more-discrepant Planck Intermediate XLVI likelihood is included.
In the study of grain-surface chemistry in the interstellar medium, there exists much uncertainty regarding the reaction mechanisms with few constraints on the abundances of grain-surface molecules. ...Bayesian inference can be performed to determine the likely reaction rates. In this work, we consider methods for reducing the computational expense of performing Bayesian inference on a reaction network by looking at the geometry of the network. Two methods of exploiting the topology of the reaction network are presented. One involves reducing a reaction network to just the reaction chains with constraints on them. After this, new constraints are added to the reaction network and it is shown that one can separate this new reaction network into subnetworks. The fact that networks can be separated into subnetworks is particularly important for the reaction networks of interstellar complex-organic molecules, whose surface reaction networks may have hundreds of reactions. Both methods allow the maximum-posterior reaction rate to be recovered with minimal bias.
ABSTRACT
Upcoming million-star spectroscopic surveys have the potential to revolutionize our view of the formation and chemical evolution of the Milky Way. Realizing this potential requires automated ...approaches to optimize estimates of stellar properties, such as chemical element abundances, from the spectra. The sheer volume and quality of the observations strongly motivate that these approaches should be driven by the data. With this in mind, we introduce SSSpaNG: a data-driven non-Gaussian Process model of stellar spectra. We demonstrate the capabilities of SSSpaNG using a sample of APOGEE red clump stars, whose model parameters we infer using Gibbs sampling. By pooling information between stars to infer their covariance, we permit clear identification of the correlations between spectral pixels. Harnessing this correlation structure, we infer the true spectrum of each red clump star, inpainting missing regions and denoising by a factor of at least two for stars with signal-to-noise ratios of ∼20. As we marginalize over the covariance matrix of the spectra, the effective prior on these true spectra is non-Gaussian and sparsifying, favouring typically small but occasionally large excursions from the mean. The high-fidelity inferred spectra produced with our approach will enable improved chemical elemental abundance estimates for individual stars. Our model also allows us to quantify the information gained by observing portions of a star’s spectrum, and thereby define the most mutually informative spectral regions. Using 25 windows centred on elemental absorption lines, we demonstrate that the iron-peak and alpha-process elements are particularly mutually informative for these spectra and that the majority of information about a target window is contained in the 10-or-so most informative windows. Such mutual information estimates have the potential to inform models of nucleosynthetic yields and the design of future observations. Our code is made publicly available at https://github.com/sfeeney/ddspectra.
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