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Verkaik, Jarno (author), Sutanudjaja, Edwin H. (author), Oude Essink, Gualbert H.P. (author), Lin, H.X. (author), Bierkens, Marc F.P. (author)We discuss the various performance aspects of parallelizing our transient global-scale groundwater model at 30′′ resolution (30arcsec; °1/41km at the Equator) on large distributed memory parallel clusters. This model, referred to as GLOBGM, is the successor of our 5′ (5arcmin; °1/410km at the Equator) PCR-GLOBWB 2 (PCRaster Global Water...journal article 2024
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Pengel, A.L. (author), Bierkens, G.N.J.C. (author)Strong invariance principles describe the error term of a Brownian approximation to the partial sums of a stochastic process. While these strong approximation results have many applications, results for continuous-time settings have been limited. In this paper, we obtain strong invariance principles for a broad class of ergodic Markov...journal article 2024
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van Leer, Martijn D. (author), Zaadnoordijk, Willem (author), Zech, Alraune (author), Buma, Jelle (author), Harting, Ronald (author), Bierkens, Marc F.P. (author), Griffioen, Jasper (author)Aquitards are common hydrogeological features and their hydraulic conductivity is an important property for various groundwater management issues. Predicting their hydraulic conductivity proves challenging, given its dependence on numerous variables. In this study, the dominant factors for predicting aquitard hydraulic conductivity are...journal article 2023
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van Leer, Martijn D. (author), Zaadnoordijk, Willem (author), Zech, Alraune (author), Griffioen, Jasper (author), Bierkens, Marc F.P. (author)Aquitards are common hydrogeological features in the subsurface. Typically, pumping tests are used to parameterize the hydraulic conductivity of heterogeneous aquitards. However, they do not take spatial variability and uncertainty into account. Alternatively, core-scale measurements of hydraulic conductivity are used in geostatistical...journal article 2023
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Dobson, P. (author), Bierkens, G.N.J.C. (author)In this paper we aim to construct infinite dimensional versions of well established Piecewise Deterministic Monte Carlo methods, such as the Bouncy Particle Sampler, the Zig-Zag Sampler and the Boomerang Sampler. In order to do so we provide an abstract infinite dimensional framework for Piecewise Deterministic Markov Processes (PDMPs) with...journal article 2023
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Bierkens, G.N.J.C. (author), Grazzi, S. (author), van der Meulen, F.H. (author), Schauer, M.R. (author)We construct a new class of efficient Monte Carlo methods based on continuous-time piecewise deterministic Markov processes (PDMPs) suitable for inference in high dimensional sparse models, i.e. models for which there is prior knowledge that many coordinates are likely to be exactly 0. This is achieved with the fairly simple idea of endowing...journal article 2023
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Bierkens, G.N.J.C. (author), Kamatani, Kengo (author), Roberts, Gareth O. (author)Piecewise deterministic Markov processes are an important new tool in the design of Markov chain Monte Carlo algorithms. Two examples of fundamental importance are the bouncy particle sampler (BPS) and the zig–zag process (ZZ). In this paper scaling limits for both algorithms are determined. Here the dimensionality of the space tends towards...journal article 2022
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Bertazzi, A. (author), Bierkens, G.N.J.C. (author), Dobson, P. (author)Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modelling of physical phenomena to computational methods. A PDMP is specified by three characteristic quantities: the deterministic motion, the law of the random event times...journal article 2022
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Bertazzi, A. (author), Bierkens, G.N.J.C. (author)The Bouncy Particle sampler (BPS) and the Zig-Zag sampler (ZZS) are continuous time, non-reversible Monte Carlo methods based on piecewise deterministic Markov processes. Experiments show that the speed of convergence of these samplers can be affected by the shape of the target distribution, as for instance in the case of anisotropic targets....journal article 2022
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Bierkens, G.N.J.C. (author), Verduyn Lunel, Sjoerd M. (author)The zigzag process is a variant of the telegraph process with position dependent switching intensities. A characterization of the L2-spectrum for the generator of the one-dimensional zigzag process is obtained in the case where the marginal stationary distribution on R is unimodal and the refreshment intensity is zero. Sufficient conditions...journal article 2022
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Verkaik, J. (author), van Engelen, J. (author), Huizer, S. (author), Bierkens, Marc F.P. (author), Lin, H.X. (author), Oude Essink, G.H.P. (author)Fresh groundwater reserves, being of vital importance for more than a billion of people living in the coastal zone, are being threatened by saltwater intrusion due to anthropogenic activities and climate change. High resolution three-dimensional (3D), variable-density (VD), groundwater flow and salt transport (FT) numerical models are...journal article 2021
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Bierkens, G.N.J.C. (author), Nyquist, Pierre (author), Schlottke, Mikola C. (author)The zig-zag process is a piecewise deterministic Markov process in position and velocity space. The process can be designed to have an arbitrary Gibbs type marginal probability density for its position coordinate, which makes it suitable for Monte Carlo simulation of continuous probability distributions. An important question in assessing the...journal article 2021
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Verkaik, J. (author), Hughes, J.D. (author), van Walsum, P.E.V. (author), Oude Essink, G. H. P. (author), Lin, H.X. (author), Bierkens, M.F.P. (author)Worldwide, billions of people rely on fresh groundwater reserves for their domestic, agricultural and industrial water use. Extreme droughts and excessive groundwater pumping put pressure on water authorities in maintaining sustainable water usage. High-resolution integrated models are valuable assets in supporting them. The Netherlands...journal article 2021
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Bierkens, G.N.J.C. (author), Grazzi, S. (author), van der Meulen, F.H. (author), Schauer, M.R. (author)We introduce the use of the Zig-Zag sampler to the problem of sampling conditional diffusion processes (diffusion bridges). The Zig-Zag sampler is a rejection-free sampling scheme based on a non-reversible continuous piecewise deterministic Markov process. Similar to the Lévy–Ciesielski construction of a Brownian motion, we expand the...journal article 2021
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Bierkens, G.N.J.C. (author), Grazzi, S. (author), Kamatani, K. (author), Roberts, G. O. (author)This paper introduces the boomerang sampler as a novel class of continuous-time non-reversible Markov chain Monte Carlo algorithms. The methodology begins by representing the target density as a density, e(−U), with respect to a prescribed (usually) Gaussian measure and constructs a continuous trajectory consisting of a piecewise circular path....conference paper 2020
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Bierkens, G.N.J.C. (author), van der Meulen, F.H. (author), Schauer, M.R. (author)Suppose X is a multidimensional diffusion process. Assume that at time zero the state of X is fully observed, but at time 0$ ]]> only linear combinations of its components are observed. That is, one only observes the vector for a given matrix L. In this paper we show how samples from the conditioned process can be generated. The main...journal article 2020
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Zaadnoordijk, Willem (author), Booltink, Wim (author), Oudega, Mathijs (author), Gunnink, Jan (author), Bierkens, Marc F.P. (author)The Geological Survey of the Netherlands (TNO-GSN) provides public information on the subsurface (http://www.dinoloket.nl). Among this information are (hydro)geological models with hydraulic parametrization. GeoTOP is a voxel model of the upper 50 meters with voxels of 100m x 100m x 0.5m. The basis of the hydraulic parametrisation is a large...poster 2019
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Bierkens, G.N.J.C. (author), Fearnhead, Paul (author), Roberts, Gareth (author)Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational burden, but with the drawback that these algorithms no longer target the true posterior distribution. We...journal article 2019
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Blöschl, Günter (author), Bierkens, Marc F.P. (author), Savenije, Hubert (author), Bogaard, T.A. (author), Hrachowitz, M. (author), Kolechkina, A.G. (author), Pande, S. (author), van der Ent, R.J. (author), van Nooijen, R.R.P. (author)This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through online media, followed by two workshops through which a large number of potential science questions were collated,...journal article 2019
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Huizer, S. (author), Luijendijk, Arjen (author), Bierkens, M. F.P. (author), Oude Essink, G. H.P. (author)Whether a coastal area is suitable for beach nourishments and can induce a growth in fresh groundwater resources depends on the appropriateness of the intended site for beach nourishments, and the attainable growth in fresh groundwater resources. In this study we presume that all eroding sandy beaches are suitable for large beach nourishments,...journal article 2019
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