About Research The Stochastic Processes and Mathematical Statistics group, led by Prof. David Bolin, develops methodology for statistical models involving stochastic processes and random fields. A main focus is the development of statistical methods based on stochastic partial differential equations. This exciting line of research combines methods from statistics and applied mathematics in order to construct flexible and physically interpretable statistical models, and efficient computational methods for statistical inference. Current areas of focus include the following: Random fields on metric graphs Many
excursions Research Resources latent Gaussian models spatial statistics applied statistics bayesian inference R-INLA Gaussian random fields excursion sets excursions: A Framework for Probabilistic Excursion Sets and Contour Inference
MetricGraph Research Resources spatial statistics applied statistics bayesian analysis Bayesian and computational Statistics Bayesian Statistics Log-Gaussian Cox process latent Gaussian models Gaussian processes INLA MetricGraph Metric graphs MetricGraph: A Statistical Framework for Modeling Gaussian Fields on Metric Graphs
rSPDE Research Resources spatial statistics applied statistics Gaussian random fields SPDEs bayesian inference geostatistics rSPDE: A Computational Framework for Rational Approximations of Fractional Stochastic Partial Differential Equations
excursions Research Resources latent Gaussian models spatial statistics applied statistics bayesian inference R-INLA Gaussian random fields excursion sets excursions: A Framework for Probabilistic Excursion Sets and Contour Inference
MetricGraph Research Resources spatial statistics applied statistics bayesian analysis Bayesian and computational Statistics Bayesian Statistics Log-Gaussian Cox process latent Gaussian models Gaussian processes INLA MetricGraph Metric graphs MetricGraph: A Statistical Framework for Modeling Gaussian Fields on Metric Graphs
rSPDE Research Resources spatial statistics applied statistics Gaussian random fields SPDEs bayesian inference geostatistics rSPDE: A Computational Framework for Rational Approximations of Fractional Stochastic Partial Differential Equations
Older publications and technical reports Publications Peer-reviewed Publications before 2019 P. Sidén, F. Lindgren, D. Bolin, M. Villani (2018), Efficient Covariance Approximations for Large Sparse Precision Matrices, Journal of Computational and Graphical Statistics, 27:4, 898-909 J. Wallin and D. Bolin (2018), Efficient adaptive MCMC through precision estimation, Journal of Computational and Graphical Statistics, 27:4, 887-897 D. Bolin, K. Kirchner, M. Kovács (2018), Weak convergence of Galerkin approximations for fractional elliptic stochastic PDEs with spatial white noise, BIT Numerical Mathematics, 58:4, 881-906. A. Hildeman, D. Bolin, J
Stochastic Processes and Mathematical Statistics Front Page Led by Prof. David Bolin, the Stochastic Processes and Mathematical Statistics research group develops methodology for statistical models involving stochastic processes and random fields. A main focus is the development of statistical methods based on stochastic partial differential equations (SPDEs), and current main areas of research are random fields on metric graphs and networks, stochastic processes formulated through fractional-order SPDEs, and non-Gaussian random fields. More details on our work can be found in the About section, and details on the software we develop can be found in
Recent Publications Preprints Finite element and box-method discretizations for fractional elliptic problems with quadrature and mass lumping Authors: Kelvin J. R. Almeida-Sousa, David Bolin, Alexandre B. Simas Full text A Unified and Computationally Efficient Non-Gaussian Statistical Modeling Framework Authors: David Bolin, Xiaotian Jin, Alexandre B. Simas, Jonas Wallin Full text Whittle-Matérn Fields with Variable Smoothness Authors: Hamza Ruzayqat, Wenyu Lei, David Bolin, George Turkiyyah, Omar Knio Full text Geometric ergodicity of Gibbs samplers for linear latent models with GIG variance mixtures Authors
