Activity Number:

253
 Contributed Poster Presentations: Section on Statistical Computing

Type:

Contributed

Date/Time:

Monday, July 30, 2018 : 2:00 PM to 3:50 PM

Sponsor:

Section on Statistical Computing

Abstract #329084


Title:

HierarchicalBlock Conditioning Approximations for HighDimensional Multivariate Normal Probabilities

Author(s):

Jian Cao* and Marc G Genton and David E Keyes and George Turkiyyah

Companies:

King Abdullah University of Science and Technology and King Abdullah University of Science and Technology and King Abdullah University of Science and Technology and King Abdullah University of Science and Technology

Keywords:

Block reordering;
ddimensional conditioning;
Hierarchical representation;
Spatial covariance functions;
Univariate reordering

Abstract:

This paper presents a new method to estimate largescale multivariate normal probabilities. The approach combines a hierarchical representation with processing of the covariance matrix that decomposes the ndimensional problem into a sequence of smaller mdimensional ones. It also includes a ddimensional conditioning method that further decomposes the mdimensional problems into smaller ddimensional problems. The resulting twolevel hierarchicalblock conditioning method requires Monte Carlo simulations to be performed only in d dimensions, with d < < n, and allows the complexity of the algorithm's major cost to be O(nlog n). We also introduce an inexpensive block reordering strategy to provide improved accuracy in the overall probability computation. Numerical simulations on problems from 2D spatial statistics with dimensions up to 16384 indicate that the algorithm achieves a 1% error level and improves the run time over a onelevel hierarchical QuasiMonte Carlo method by a factor between 10 and 15.
