Institut für Mathematik
Refine
Has Fulltext
- no (1612) (remove)
Year of publication
Document Type
- Article (1030)
- Monograph/Edited Volume (420)
- Doctoral Thesis (87)
- Other (46)
- Review (16)
- Conference Proceeding (6)
- Preprint (4)
- Part of a Book (3)
Is part of the Bibliography
- yes (1612)
Keywords
- data assimilation (8)
- Bayesian inference (5)
- discrepancy principle (5)
- ensemble Kalman filter (5)
- linear term (5)
- Cauchy problem (4)
- Data assimilation (4)
- Earthquake interaction (4)
- Elliptic complexes (4)
- Fredholm property (4)
Institute
- Institut für Mathematik (1612)
- Department Psychologie (4)
- Institut für Geowissenschaften (3)
- Institut für Umweltwissenschaften und Geographie (3)
- Extern (2)
- Institut für Biochemie und Biologie (2)
- Institut für Physik und Astronomie (2)
- Department Linguistik (1)
- Department Sport- und Gesundheitswissenschaften (1)
- Fakultät für Gesundheitswissenschaften (1)
This paper reports on the historical development of the Runge-Kutta methods beginning with the simple Euler method up to an embedded 13-stage method. Moreover, the design and the use of those methods under error order, stability and computation time conditions is edited for students of numerical analysis at undergraduate level. The second part presents applications in natural sciences, compares different methods and illustrates some of the difficulties of numerical solutions.
The estimation of a log-concave density on R is a canonical problem in the area of shape-constrained nonparametric inference. We present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet process mixture prior and show that the posterior distribution converges to the log-concave truth at the (near-) minimax rate in Hellinger distance. Our proof proceeds by establishing a general contraction result based on the log-concave maximum likelihood estimator that prevents the need for further metric entropy calculations. We further present computationally more feasible approximations and both an empirical and hierarchical Bayes approach. All priors are illustrated numerically via simulations.