No Arabic abstract
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.
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.
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.
Population annealing Monte Carlo is an efficient sequential algorithm for simulating k-local Boolean Hamiltonians. Because of its structure, the algorithm is inherently parallel and therefore well suited for large-scale simulations of computationally hard problems. Here we present various ways of optimizing population annealing Monte Carlo using 2-local spin-glass Hamiltonians as a case study. We demonstrate how the algorithm can be optimized from an implementation, algorithmic accelerator, as well as scalable parallelization points of view. This makes population annealing Monte Carlo perfectly suited to study other frustrated problems such as pyrochlore lattices, constraint-satisfaction problems, as well as higher-order Hamiltonians commonly found in, e.g., topological color codes.
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.
Gaia-DR2 has provided an unprecedented number of white dwarf candidates of our Galaxy. In particular, it is estimated that Gaia-DR2 has observed nearly 400,000 of these objects and close to 18,000 up to 100 pc from the Sun. This large quantity of data requires a thorough analysis in order to uncover their main Galactic population properties, in particular the thin and thick disk and halo components. Taking advantage of recent developments in artificial intelligence techniques, we make use of a detailed Random Forest algorithm to analyse an 8-dimensional space (equatorial coordinates, parallax, proper motion components and photometric magnitudes) of accurate data provided by Gaia-DR2 within 100 pc from the Sun. With the aid of a thorough and robust population synthesis code we simulated the different components of the Galactic white dwarf population to optimize the information extracted from the algorithm for disentangling the different population components. The algorithm is first tested in a known simulated sample achieving an accuracy of 85.3%. Our methodology is thoroughly compared to standard methods based on kinematic criteria demonstrating that our algorithm substantially improves previous approaches. Once trained, the algorithm is then applied to the Gaia-DR2 100 pc white dwarf sample, identifying 12,227 thin disk, 1,410 thick disk and 95 halo white dwarf candidates, which represent a proportion of 74:25:1, respectively. Hence, the numerical spatial densities are $(3.6pm0.4)times10^{-3},{rm pc^{-3}}$, $(1.2pm0.4)times10^{-3},{rm pc^{-3}}$ and $(4.8pm0.4)times10^{-5},{rm pc^{-3}}$ for the thin disk, thick disk and halo components, respectively. The populations thus obtained represent the most complete and volume-limited samples to date of the different components of the Galactic white dwarf population.