Registered Data

[CT089]

  • Session Time & Room
    • CT089 (1/1) : 5B @E505 [Chair: Shanyin Tong]
  • Classification
    • CT089 (1/1) : Probabilistic methods, stochastic differential equations (65C)

[00694] Large deviation theory-based adaptive importance sampling for rare events in high dimensions

  • Session Time & Room : 5B (Aug.25, 10:40-12:20) @E505
  • Type : Contributed Talk
  • Abstract : I will discuss our proposed method for estimating rare event probabilities for expensive-to-evaluate numerical models in high dimensions. The approach combines ideas from large deviation theory and adaptive importance sampling. Large deviation theory is used to find a good initial biasing distribution and to identify a low-dimensional subspace that is most informative of the rare event probability. We compare the method with a state-of-the-art cross-entropy-based importance sampling scheme.
  • Classification : 65C05, 60F10, 62L12, 65F15, 65K10
  • Format : Talk at Waseda University
  • Author(s) :
    • Shanyin Tong (Columbia University)
    • Georg Stadler (New York University)

[00832] Monte Carlo estimation of equity measures for apportionment problem

  • Session Time & Room : 5B (Aug.25, 10:40-12:20) @E505
  • Type : Contributed Talk
  • Abstract : A Markov chain Monte Carlo method is devised for the computation of several equity measures for the apportionment problem of assembly seats to electoral districts. Seat bias and Gini mean difference is of our primary interest in computing. Generating a random walk in the high-dimensional simplex is the key to our algorithm. It is helpful to estimate the mean and several quantiles of the target statistics.
  • Classification : 65C05, 91G60, 60J22
  • Format : Talk at Waseda University
  • Author(s) :
    • Hozumi Morohosi (National Graduate Institute for Policy Studies)

[01001] Recent developments on low-discrepancy point sets for Markov chain quasi-Monte Carlo

  • Session Time & Room : 5B (Aug.25, 10:40-12:20) @E505
  • Type : Contributed Talk
  • Abstract : We consider the problem of estimating expectations by using Markov chain Monte Carlo methods and improving the accuracy by replacing IID uniform random points with quasi-Monte Carlo (QMC) points. In this talk, we present short-period Tausworthe generators for Markov chain QMC optimized in terms of the $t$-value, which is a criterion of uniformity widely used in the study of QMC methods. In addition, we show the effectiveness in some numerical examples using Gibbs sampling.
  • Classification : 65C10, 11K45, 65C05
  • Format : Talk at Waseda University
  • Author(s) :
    • Shin Harase (Ritsumeikan University)

[00396] A Stochastic Approach for the Computation of Large-Scale Matrix Functions

  • Session Time & Room : 5B (Aug.25, 10:40-12:20) @E505
  • Type : Contributed Talk
  • Abstract : Although many scientific problems can be described in term of functions over matrices, their high computational cost and the lack of parallel and scalable numerical tools propel scientists to seek alternative solutions. In this talk, we will introduce a Monte Carlo method that is capable of computing matrix functions for large-scale datasets and in particular present how it can be used to solve time-fractional differential equations.
  • Classification : 65C05, 35R11, 33E12, 60Gxx, 60K50
  • Format : Talk at Waseda University
  • Author(s) :
    • Nicolas Guidotti (INESC-ID, Instituto Superior Técnico, Lisboa)

[00476] Hierarchical Sampling Techniques and Goal-Oriented Adaptive Finite Element for Elliptic PDE with Lognormal Coefficients

  • Session Time & Room : 5B (Aug.25, 10:40-12:20) @E505
  • Type : Contributed Talk
  • Abstract : We propose our Adaptive Multilevel Monte Carlo (AMLMC) method to solve an elliptic partial differential equation with lognormal random input data where the PDE model has geometry-induced singularities. This work combines (MLMC) and the dual-weighted-residual goal-oriented adaptive finite element. Specifically, for a given input coefficient realization and an accuracy level, the (AMLMC) constructs its approximate sample as the ones using the first mesh in the sequence of pre-generated, non-uniform meshes satisfying the sample-dependent bias constraint.
  • Classification : 65C05, 65N50, 65N22, 35R60
  • Format : Talk at Waseda University
  • Author(s) :
    • Joakim Beck (King Abdullah University of Science and Technology)
    • Yang Liu (King Abdullah University of Science and Technology)
    • Erik von Schwerin (King Abdullah University of Science and Technology)
    • Raul Tempone (King Abdullah University of Science and Technology)