Filters

2020 - 20213

More filters

2022 - 20233
Reset filters

Settings

Start date: 2020 × DDC: 310 ×

Search Results

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Gaussian processes with multidimensional distribution inputs via optimal transport and Hilbertian embedding
    (Ithaca, NY : Cornell University Library, 2020) Bachoc, François; Suvorikova, Alexandra; Ginsbourger, David; Loubes, Jean-Michel; Spokoiny, Vladimir
    In this work, we propose a way to construct Gaussian processes indexed by multidimensional distributions. More precisely, we tackle the problem of defining positive definite kernels between multivariate distributions via notions of optimal transport and appealing to Hilbert space embeddings. Besides presenting a characterization of radial positive definite and strictly positive definite kernels on general Hilbert spaces, we investigate the statistical properties of our theoretical and empirical kernels, focusing in particular on consistency as well as the special case of Gaussian distributions. A wide set of applications is presented, both using simulations and implementation with real data.
  • Thumbnail Image
    Item
    Convergence analysis of Tikhonov regularization for non-linear statistical inverse problems
    (Ithaca, NY : Cornell University Library, 2020) Rastogi, Abhishake; Blanchard, Gilles; Mathé, Peter
    We study a non-linear statistical inverse problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of regularization) approach to estimate the quantity for the non-linear ill-posed inverse problem. The estimator is defined as the minimizer of a Tikhonov functional, which is the sum of a data misfit term and a quadratic penalty term. We develop a theoretical analysis for the minimizer of the Tikhonov regularization scheme using the concept of reproducing kernel Hilbert spaces. We discuss optimal rates of convergence for the proposed scheme, uniformly over classes of admissible solutions, defined through appropriate source conditions.
  • Thumbnail Image
    Item
    The future of Swiss hydropower: how to distribute the risk and the profits?
    (Cham, Switzerland : Springer Nature Switzerland AG, 2021) Kosch, Mirjam; Betz, Regina; Geissmann, Thomas; Schillinger, Moritz; Weigt, Hannes
    Low electricity prices put economic pressure on hydropower companies. A more flexible water fee design can counteract this pressure and support hydropower companies during times when market revenues are low. However, this comes at the cost of lower revenues for resource owners. Using a sample of cost data for 62 companies and revenue data derived from an electricity market model, we have quantified this trade-off for the case of Switzerland. We found that electricity market price developments dominate changes in water fees and that for the profitability of hydropower, electricity prices are more important than water fee levels. However, with electricity prices of around CHF 40 per MWh, water fees can make the difference between profit and loss. Therefore, while flexible water fee regimes shift the market risk from producers to resource owners to some extent, the extent of this risk shift depends on the detailed design of the flexible regime.