Approximating Multivariate Normal Orthant Probabilities Using the Clark Algorithm.
Technical rept. 1 Aug 85-1 Jan 87,
ILLINOIS STATE PSYCHIATRIC INST CHICAGO BIOMETRIC LAB
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The probability of m correlated random variables is drawn from a multivariate normal distribution being non-negative. Exact results for this probability integral are unavailable for m 3. Approximations for higher dimensional problems have generally yielded poor results except for special cases, such as compound symmetry, which is of limited value in practice. The purpose of this paper is to present a general approximation of this probability integral. The algorithm developed here is computationally tractable for m 50 and accurate for very general correlational structures. The performance of this algorithm is compared to results based on Clarks 1961 original approximation, Gaussian quadrature formulae, and Monte Carlo simulation methods. Application of this approximation to problems of conditional dependence in IRT estimation problems is discussed.
- Statistics and Probability