Dissertation
COMPUTATION OF MULTIVARIATE NORMAL PROBABILITIES USING BIVARIATE CONDITIONING WITH SIMULATION
Doctor of Philosophy (PhD), Washington State University
01/2013
Handle:
https://hdl.handle.net/2376/4733
Abstract
We introduce algorithms for block LDL^{t} decompositions of positive definite covariance matrices. These are extensions of the LDL^t decomposition which requires D to be a diagonal matrix. We make use of these algorithms to represent the mutivariate normal (MVN) probability as a bivariate-iterated, trivariate-iterated and multivariate-iterated integrals. From there, we introduce a new method of approximating and simulating MVN probabilities using bivariate conditioning with simulation. Basic algorithms for bivariate, trivariate, multivariate conditioning are derived. A new approximate formula for multivariate normal probabilities which uses a product of bivariate normal probabilities is derived and considered with different variance reduction techniques. The new method is compared with approximation methods based on products of univariate normal probabilities. The new method uses conditioning with a sequence of truncated bivariate probabilites. Simulation methods which use Monte Carlo, and quasi-Monte Carlo point sets are developed.
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Details
- Title
- COMPUTATION OF MULTIVARIATE NORMAL PROBABILITIES USING BIVARIATE CONDITIONING WITH SIMULATION
- Creators
- GIANG TRINH
- Contributors
- ALAN GENZ (Advisor)ROBERT H DILLON (Committee Member)FRANCIS PASCUAL (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 124
- Identifiers
- 99900581651301842
- Language
- English
- Resource Type
- Dissertation