Markov chain Monte Carlo (MCMC) methods have found widespread use in many fields of study to estimate the average properties of complex systems, and for posterior inference in a Bayesian framework. Existing theory and experiments prove convergence of well-constructed MCMC schemes to the appropriate limiting distribution under a variety of different conditions. In practice, however this convergence is often observed to be disturbingly slow. This is frequently caused by an inappropriate selection of the proposal distribution used to generate trial moves in the Markov Chain. Here we show that significant improvements to the efficiency of MCMC simulation can be made by using a self-adaptive Differential Evolution learning strategy within a population-based evolutionary framework. This scheme, entitled Differential Evolution Adaptive Metropolis or DREAM, runs multiple different chains simultaneously for global exploration, and automatically tunes the scale and orientation of the proposal distribution in randomized subspaces during the search. Ergodicity of the algorithm is proved, and various examples involving nonlinearity, highdimensionality, and multimodality show that DREAM is generally superior to other adaptive MCMC sampling approaches. The DREAM scheme significantly enhances the applicability of MCMC simulation to complex, multi-modal search problems.

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Near-future cosmological observations targeted at investigations of dark energy pose stringent requirements on the accuracy of theoretical predictions for the nonlinear clustering of matter. Currently, N-body simulations comprise the only viable approach to this problem. In this paper we study various sources of computational error and methods to control them. By applying our methodology to a large suite of cosmological simulations we show that results for the (gravity-only) nonlinear matter power spectrum can be obtained at 1% accuracy out to k ∼ 1 h Mpc −1 . The key components of these high accuracy simulations are: precise initial conditions, very large simulation volumes, sufficient mass resolution, and accurate time stepping. This paper is the first in a series of three; the final aim is a high-accuracy prediction scheme for the nonlinear matter power spectrum that improves current fitting formulae by an order of magnitude. Subject headings: methods: N-body simulations -cosmology: large-scale structure of universe 1

Modern sky surveys are returning precision measurements of cosmological statistics such as weak lensing shear correlations, the distribution of galaxies, and cluster abundance. To fully exploit these observations, theorists must provide predictions that are at least as accurate as the measurements, as well as robust estimates of systematic errors that are inherent to the modeling process. In the nonlinear regime of structure formation, this challenge can only be overcome by developing a large-scale, multi-physics simulation capability covering a range of cosmological models and astrophysical processes. As a first step to achieving this goal, we have recently developed a prediction scheme for the matter power spectrum (a so-called emulator), accurate at the 1% level out to k ∼ 1 Mpc −1 and z = 1 for wCDM cosmologies based on a set of high-accuracy N-body simulations. It is highly desirable to increase the range in both redshift and wavenumber and to extend the reach in cosmological parameter space. To make progress in this direction, while minimizing computational cost, we present a strategy that maximally reuses the original simulations. We demonstrate improvement over the original spatial dynamic range by an order of magnitude, reaching k ∼ 10 h Mpc −1 , a four-fold increase in redshift coverage, to z = 4, and now include the Hubble parameter as a new independent variable. To further the range in k and z, a new set of nested simulations run at modest cost is added to the original set. The extension in h is performed by including perturbation theory results within a multi-scale procedure for building the emulator. This economical methodology still gives excellent error control, ∼5% near the edges of the domain of applicability of the emulator. A public domain code for the new emulator is released as part of the work presented in this paper.

The power spectrum of density fluctuations is a foundational source of cosmological information. Precision cosmological probes targeted primarily at investigations of dark energy require accurate theoretical determinations of the power spectrum in the nonlinear regime. To exploit the observational power of future cosmological surveys, accuracy demands on the theory are at the one percent level or better. Numerical simulations are currently the only way to produce sufficiently error-controlled predictions for the power spectrum. The very high computational cost of (precision) N-body simulations is a major obstacle to obtaining predictions in the nonlinear regime, while scanning over cosmological parameters. Near-future observations, however, are likely to provide a meaningful constraint only on constant dark energy equation of state, 'wCDM', cosmologies. In this paper we demonstrate that a limited set of only 37 cosmological models -the "Coyote Universe" suite -can be used to predict the nonlinear matter power spectrum to one percent over a prior parameter range set by current cosmic microwave background observations. This paper is the second in a series of three, with the final aim to provide a high-accuracy prediction scheme for the nonlinear matter power spectrum for wCDM cosmologies. Subject headings: methods: statistical -cosmology: large-scale structure of the universe