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We introduce preconditioned Monte Carlo (PMC), a novel Monte Carlo method for Bayesian inference that facilitates efficient sampling of probability distributions with non-trivial geometry. PMC utilizes a Normalizing Flow (NF) in order to decorrelate the parameters of the distribution and then proceeds by sampling from the preconditioned target distribution using an adaptive Sequential Monte Carlo (SMC) scheme. The results produced by PMC include samples from the posterior distribution and an estimate of the model evidence that can be used for parameter inference and model comparison, respectively. The aforementioned framework has been thoroughly tested in a variety of challenging target distributions achieving state-of-the-art sampling performance. In the cases of primordial feature analysis and gravitational wave inference, PMC is approximately 50 and 25 times faster, respectively, than nested sampling (NS). We found that in higher dimensional applications, the acceleration is even greater. Finally, PMC is directly parallelisable, manifesting linear scaling up to thousands of CPUs. [ABSTRACT FROM AUTHOR]

We introduce zeus , a well-tested Python implementation of the Ensemble Slice Sampling (ESS) method for Bayesian parameter inference. ESS is a novel Markov chain Monte Carlo (MCMC) algorithm specifically designed to tackle the computational challenges posed by modern astronomical and cosmological analyses. In particular, the method requires only minimal hand-tuning of 1−2 hyperparameters that are often trivial to set; its performance is insensitive to linear correlations and it can scale up to 1000s of CPUs without any extra effort. Furthermore, its locally adaptive nature allows to sample efficiently even when strong non-linear correlations are present. Lastly, the method achieves a high performance even in strongly multimodal distributions in high dimensions. Compared to emcee , a popular MCMC sampler, zeus performs 9 and 29 times better in a cosmological and an exoplanet application, respectively. [ABSTRACT FROM AUTHOR]

We present matryoshka , a suite of neural-network-based emulators and accompanying python package that have been developed with the goal of producing fast and accurate predictions of the non-linear galaxy power spectrum. The suite of emulators consists of four linear component emulators, from which fast linear predictions of the power spectrum can be made, allowing all non-linearities to be included in predictions from a non-linear boost component emulator. The linear component emulators include an emulator for the matter transfer function that produces predictions in ∼0.0004 s, with an error of |${\lt} 0.08{{\ \rm per\ cent}}$| (at 1σ level) on scales 10−4 < k < 101  h  Mpc−1. In this paper, we demonstrate matryoshka by training the non-linear boost component emulator with analytic training data calculated with Halofit, which has been designed to replicate training data that would be generated using numerical simulations. Combining all the component emulator predictions we achieve an accuracy of |${\lt} 0.75{{\ \rm per\ cent}}$| (at 1σ level) when predicting the real space non-linear galaxy power spectrum on scales 0.0025 < k < 1  h  Mpc−1. We use matryoshka to investigate the impact of the analysis set-up on cosmological constraints by conducting several full shape analyses of the real-space galaxy power spectrum. Specifically we investigate the impact of the minimum scale (or k max), finding an improvement of ∼1.8× in the constraint on σ8 by pushing k max from 0.25 to 0.85  h  Mpc−1, highlighting the potential gains when using clustering emulators such as matryoshka in cosmological analyses. [ABSTRACT FROM AUTHOR]