In the need for low assumption inferential methods in infinite-dimensional settings, Bayesian adaptive estimation via a prior distribution that does not depend on the regularity of the function to be estimated nor on the sample size is valuable.
Lu, J; Vanden-Eijnden, E, Methodological and Computational Aspects of Parallel Tempering Methods in the Infinite Swapping Limit, Journal of Statistical Physics, vol. 174 no. 3 (February, 2019), pp. 715-733 [abs] [abs].
Numerical examples show that the DtN condition for multiple scattering is as accurate as the well-known DtN condition for single scattering problems [J. Comput. Phys. 82 (1989) 172; Numerical Methods for Problems in Infinite Domains, Elsevier, Amsterdam, 1992], while being more efficient due to the reduced size of the computational domain.
Martinsson, A; Lu, J; Leimkuhler, B; Vanden-Eijnden, E, The simulated tempering method in the infinite switch limit with adaptive weight learning, Journal of Statistical Mechanics: Theory and Experiment, vol. 2019 no. 1 (January, 2019), pp. 013207-013207, IOP Publishing [doi] [abs].
As applications of our results, we give strong convergence theorems as regards the split feasibility problem with modified CQ method, strong convergence theorem as regards the lasso problem, and strong convergence theorems for the mathematical programming with a modified proximal point algorithm and a modified gradient-projection method in the infinite dimensional Hilbert space.
15.099, Special Seminar in Operations Research: Computational Methods for Infinite Dimensional Optimization, Spring 2019.
We also provide detailed asymptotic expansions by a method of stationary phase in infinite dimensions, with convergence and estimates for the remainder provided by a strong control on finite dimensional approximations.
Well test interpretation methods for a single well in infinite reservoirs may not be suitable for those wells when their pressure is affected by other wells operating in the same reservoir.
In his proofs, he used Fermat's method of infinite descent.
The associated modal analysis is the only widely applicable approximate method for computing the response without discretizing the continuous system by methods such as the finite element method, in which the infinite n.d.o.f. is not retained.
