A new reconstruction of multivariate normal orthant probabilities

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 70, Issue 1, 2008, Pages 227-243

  Craig, Peter ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Cumulative distribution function; Fractional fast Fourier transform; Multivariate normal distribution; Multivariate probit model; Orthant probabilities; Orthoscheme; Polyhedral cones

Indexed keywords

EID: 37849034387     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2007.00625.x     Document Type: Article

References (20)

1. Abrahamson, I. G. (1964) Orthant probabilities for the quadrivariate normal distribution. Ann. Math. Statist., 35, 1685 1703.
2. Armitage, P., McPherson, C. K. Rowe, B. C. (1969) Repeated significance tests on accumulating data. J. R. Statist. Soc. A, 132, 235 244.
3. Bailey, D. H. Swarztrauber, P. N. (1991) The fractional Fourier transform and applications. SIAM Rev., 33, 389 404.
4. Chib, S. Greenberg, E. (1998) Analysis of multivariate probit models. Biometrika, 85, 347 361.
5. Chib, S. Jeliazkov, I. (2001) Marginal likelihood from the Metropolis-Hastings output. J. Am. Statist. Ass., 96, 270 281.
6. Chib, S. Jeliazkov, I. (2006) Inference in semiparametric dynamic models for binary longitudinal data. J. Am. Statist. Ass., 101, 685 700.
7. Craig, P. (2007) Orthants: multivariate normal orthant probabilities. University of Durham, Durham. (Available from http://www.maths.dur.ac.uk/ ∼dma0psc/orthants/ 47.
8. Gassmann, H. I., Deák, I. Szántai, T. (2002) Computing multivariate normal probabilities: a new look. J. Computnl Graph. Statist., 11, 920 949.
9. Genz, A. (1992) Numerical computation of multivariate normal probabilities. J. Computnl Graph. Statist., 1, 141 150.
10. Genz, A. (1993) Comparison of methods for the computation of multivariate normal probabilities. Comput. Sci. Statist., 25, 400 405.
11. Genz, A. Bretz, F. (2002) Comparison of methods for the computation of multivariate t probabilities. J. Computnl Graph. Statist., 11, 950 971.
12. Genz, A., Bretz, F. Torsten Hothorn, R. (2005) mvtnorm: multivariate normal and t distribution. Friedrich- Alexander-Universität, Erlangen-Nürnberg. (Available from http://cran.r-project.org/src/contrib/ Descriptions/mvtnorm.html Agresti, A. (2001) A correlated probit model for joint modeling of clustered binary and continuous responses. J. Am. Statist. Ass., 96, 1102 1112.
13. Hayter, A. J. (2006) Recursive integration methodologies with statistical applications. J. Statist. Planng Inf., 136, 2284 2296.
14. Hirotsu, C., Kuriki, S. Hayter, A. J. (1992) Multiple comparison procedures based on the maximal component of the cumulative chi-squared statistic. Biometrika, 79, 381 392.
15. Miwa, T., Hayter, A. J. Kuriki, S. (2003) The evaluation of general non-centred orthant probabilities. J. R. Statist. Soc. B, 65, 223 234.
16. Papathomas, M. O'Hagan, A. (2005) Updating beliefs for binary variables. J. Statist. Planng Inf., 135, 324 338.
17. Press, W. H., Flannery, B. P., Teukolsky, S. A. Vetterling, W. T. (1993) Numerical Recipes in C: the Art of Scientific Computing, 2nd edn. Cambridge : Cambridge University Press.
18. R Development Core Team (2006) R: a Language and Environment for Statistical Computing. Vienna : R Foundation for Statistical Computing.
19. 2<1. Q. J. Pure Appl. Math., 2, 269 301.
20. Williams, D. (1971) A test for differences between treatment means when several dose levels are compared with a zero dose control. Biometrics, 27, 103 117.