Efficient cosmological parameter sampling using sparse grids

We present a novel method to significantly speed up cosmological parameter sampling. The method relies on constructing an interpolation of the CMB-log-likelihood based on sparse grids, which is used as a shortcut for the likelihood-evaluation. We obtain excellent results over a large region in parameter space, comprising about 25 log-likelihoods around the peak, and we reproduce the one-dimensional projections of the likelihood almost perfectly. In speed and accuracy, our technique is competitive to existing approaches to accelerate parameter estimation based on polynomial interpolation or neural networks, while having some advantages over them. In our method, there is no danger of creating unphysical wiggles as it can be the case for polynomial fits of a high degree. Furthermore, we do not require a long training time as for neural networks, but the construction of the interpolation is determined by the time it takes to evaluate the likelihood at the sampling points, which can be parallelised to an arbitrary degree. Our approach is completely general, and it can adaptively exploit the properties of the underlying function. We can thus apply it to any problem where an accurate interpolation of a function is needed.Comment: Submitted to MNRAS, 13 pages, 13 figure

Methodologies for Assessment of Building's Energy Efficiency and Conservation: A Policy-Maker View

Recent global peer-review reports have concluded on importance of buildings in tacking the energy security and climate change challenges. To integrate the buildings energy efficiency into the policy agenda, significant research efforts have been recently done. More specifically, the public domain provides a bulk of literature on the application of buildings-related efficiency technologies and behavioural patterns, barriers to penetration of these practices, policies to overcome these barriers. From the policy-making perspective it is useful to understand how far our understanding of building energy efficiency goes and the approaches and methodologies are behind such assessment

Fully Discrete Multiscale Galerkin BEM

We analyze multiscale Galerkin methods for strongly elliptic boundary integral equations of order zero on closed surfaces in lR 3 . Piecewise polynomial, discontinuous multiwavelet bases of any polynomial degree are constructed explicitly. We show that optimal convergence rates in the boundary energy norm and in certain negative norms can be achieved with "compressed" stiffness matrices containing O(N (log N) 2 ) nonvanishing entries where N denotes the number of degrees of freedom on the boundary manifold. We analyze a quadrature scheme giving rise to fully discrete methods. We show that the fully discrete scheme preserves the asymptotic accuracy of the scheme and that its overall computational complexity is O(N (log N) 4 ) kernel evaluations. The implications of the results for the numerical solution of elliptic boundary value problems in or exterior to bounded, three-dimensional domains are discussed. AMS(MOS) subject classifications (1991): Primary: 65N38 Secondary: 65N55 1 ..

Fast Deterministic Pricing of Options on Lévy Driven Assets

A partial integro-dierential equation (PIDE) @ t u + A[u] = 0 for European contracts on assets with general jump-diusion price process of Levy type is derived. The PIDE is localized to bounded domains and the error due to this localization is estimated. The localized PIDE is discretized by the -scheme in time and a wavelet Galerkin method with N degrees of freedom in space. The full Galerkin matrix for A can be replaced with a sparse matrix in the wavelet basis, and the linear systems for each time step are solved approximatively with GMRES in linear complexity. The total work of the algorithm for M time steps is bounded by O(MN(lnN) ) operations and O(N ln(N)) memory. The deterministic algorithm gives optimal convergence rates (up to logarithmic terms) for the computed solution in the same complexity as nite dierence approximations of the standard Black-Scholes equation. Computational examples for various Levy price processes (VG, CGMY) are presented.