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We present the public release of the Bayesian sampling algorithm for cosmology, CosmoPMC (Cosmology Population Monte Carlo). CosmoPMC explores the parameter space of various cosmological probes, and also provides a robust estimate of the Bayesian evidence. CosmoPMC is based on an adaptive importance sampling method called Population Monte Carlo (PMC). Various cosmology likelihood modules are implemented, and new modules can be added easily. The importance-sampling algorithm is written in C, and fully parallelised using the Message Passing Interface (MPI). Due to very little overhead, the wall-clock time required for sampling scales approximately with the number of CPUs. The CosmoPMC package contains post-processing and plotting programs, and in addition a Monte-Carlo Markov chain (MCMC) algorithm. The sampling engine is implemented in the library pmclib, and can be used independently. The software is available for download at http://www.cosmopmc.info.
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We use Bayesian model selection techniques to test extensions of the standard flat LambdaCDM paradigm. Dark-energy and curvature scenarios, and primordial perturbation models are considered. To that end, we calculate the Bayesian evidence in favour of each model using Population Monte Carlo (PMC), a new adaptive sampling technique which was recently applied in a cosmological context. The Bayesian evidence is immediately available from the PMC sample used for parameter estimation without further computational effort, and it comes with an associated error evaluation. Besides, it provides an unbiased estimator of the evidence after any fixed number of iterations and it is naturally parallelizable, in contrast with MCMC and nested sampling methods. By comparison with analytical predictions for simulated data, we show that our results obtained with PMC are reliable and robust. The variability in the evidence evaluation and the stability for various cases are estimated both from simulations and from data. For the cases we consider, the log-evidence is calculated with a precision of better than 0.08. Using a combined set of recent CMB, SNIa and BAO data, we find inconclusive evidence between flat LambdaCDM and simple dark-energy models. A curved Universe is moderately to strongly disfavoured with respect to a flat cosmology. Using physically well-motivated priors within the slow-roll approximation of inflation, we find a weak preference for a running spectral index. A Harrison-Zeldovich spectrum is weakly disfavoured. With the current data, tensor modes are not detected; the large prior volume on the tensor-to-scalar ratio r results in moderate evidence in favour of r=0. [Abridged]
Monte Carlo methods are widely used for approximating complicated, multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC) is an important class of Monte Carlo methods, which utilizes a population of proposals to generate weighted samples that approximate the target distribution. The generic PMC framework iterates over three steps: samples are simulated from a set of proposals, weights are assigned to such samples to correct for mismatch between the proposal and target distributions, and the proposals are then adapted via resampling from the weighted samples. When the target distribution is expensive to evaluate, the PMC has its computational limitation since the convergence rate is $mathcal{O}(N^{-1/2})$. To address this, we propose in this paper a new Population Quasi-Monte Carlo (PQMC) framework, which integrates Quasi-Monte Carlo ideas within the sampling and adaptation steps of PMC. A key novelty in PQMC is the idea of importance support points resampling, a deterministic method for finding an optimal subsample from the weighted proposal samples. Moreover, within the PQMC framework, we develop an efficient covariance adaptation strategy for multivariate normal proposals. Lastly, a new set of correction weights is introduced for the weighted PMC estimator to improve the efficiency from the standard PMC estimator. We demonstrate the improved empirical convergence of PQMC over PMC in extensive numerical simulations and a friction drilling application.
Weak lensing by large-scale structure is a powerful probe of cosmology and of the dark universe. This cosmic shear technique relies on the accurate measurement of the shapes and redshifts of background galaxies and requires precise control of systematic errors. The Monte Carlo Control Loops (MCCL) is a forward modelling method designed to tackle this problem. It relies on the Ultra Fast Image Generator (UFig) to produce simulated images tuned to match the target data statistically, followed by calibrations and tolerance loops. We present the first end-to-end application of this method, on the Dark Energy Survey (DES) Year 1 wide field imaging data. We simultaneously measure the shear power spectrum $C_{ell}$ and the redshift distribution $n(z)$ of the background galaxy sample. The method includes maps of the systematic sources, Point Spread Function (PSF), an Approximate Bayesian Computation (ABC) inference of the simulation model parameters, a shear calibration scheme, and the fast estimation of the covariance matrix. We find a close statistical agreement between the simulations and the DES Y1 data using an array of diagnostics. In a non-tomographic setting, we derive a set of $C_ell$ and $n(z)$ curves that encode the cosmic shear measurement, as well as the systematic uncertainty. Following a blinding scheme, we measure the combination of $Omega_m$, $sigma_8$, and intrinsic alignment amplitude $A_{rm{IA}}$, defined as $S_8D_{rm{IA}} = sigma_8(Omega_m/0.3)^{0.5}D_{rm{IA}}$, where $D_{rm{IA}}=1-0.11(A_{rm{IA}}-1)$. We find $S_8D_{rm{IA}}=0.895^{+0.054}_{-0.039}$, where systematics are at the level of roughly 60% of the statistical errors. We discuss these results in the context of earlier cosmic shear analyses of the DES Y1 data. Our findings indicate that this method and its fast runtime offer good prospects for cosmic shear measurements with future wide-field surveys.
Population annealing is a recent addition to the arsenal of the practitioner in computer simulations in statistical physics and beyond that is found to deal well with systems with complex free-energy landscapes. Above all else, it promises to deliver unrivaled parallel scaling qualities, being suitable for parallel machines of the biggest calibre. Here we study population annealing using as the main example the two-dimensional Ising model which allows for particularly clean comparisons due to the available exact results and the wealth of published simulational studies employing other approaches. We analyze in depth the accuracy and precision of the method, highlighting its relation to older techniques such as simulated annealing and thermodynamic integration. We introduce intrinsic approaches for the analysis of statistical and systematic errors, and provide a detailed picture of the dependence of such errors on the simulation parameters. The results are benchmarked against canonical and parallel tempering simulations.
In order to understand the dynamical and chemical evolution of our Galaxy it is of fundamental importance to study the local neighborhood. White dwarf stars are ideal candidates to probe the history of the solar neighborhood, since these ``fossil stars have very long evolutionary time-scales and, at the same time, their evolution is relatively well understood. In fact, the white dwarf luminosity function has been used for this purpose by several authors. However, a long standing problem arises from the relatively poor statistics of the samples, especially at low luminosities. In this paper we assess the statistical reliability of the white dwarf luminosity function by using a Monte Carlo approach.
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