My primary area of research interest is the numerical computation of multiple integrals. These integrals arise in a wide variety application areas that include electromagnetics, chemistry, physics and statistics. I have developed and implemented many different types of algorithms for the computation of multiple integrals. I am also interested in related problems in multivariate approximation theory.

• Alan Genz and Frank Bretz: Computation of Multivariate Normal and t Probabilities, Lecture Notes in Statistics 195, 2009, Springer-Verlag, New York.
• Alan Genz: Numerical Computation of Rectangular Bivariate and Trivariate Normal and t Probabilities (PDF, Postscript ), revised version published in Statistics and Computing, 14 (2004), pp. 151-160.
• Alan Genz, Frank Bretz and Yosef Hochberg: Approximations to Multivariate t Integrals with Application to Multiple Comparison Procedures (PDF, Postscript ), revised version in Recent Developments in Multiple Comparison Procedures, Institute of Mathematical Statistics LNMS 47, 2004, pp. 24-32.
• Alan Genz: Fully Symmetric Interpolatory Rules for Multiple Integrals over Hyper-Spherical Surfaces (PDF, Postscript ), revised version published in J. Comp. Appl. Math. 157 (2003), pp. 187-195
• Alan Genz and Ronald Cools: An Adaptive Numerical Cubature Algorithm for Simplices (PDF, Postscript ), revised version published in ACM Trans. Math. Soft. 29 (2003), pp. 297-308.
• Alan Genz and Frank Bretz: Methods for the Computation of Multivariate t-Probabilities (PDF, Postscript ), revised version publisehd in J. Comp. Graph. Stat. 11 (2002), pp. 950-971.
• Alan Genz and Frank Bretz: Numerical Computation of Critical Values for Multiple Comparison Problems (PDF, Postscript ), in 2000 Proceedings of the Statistical Computing Section, American Statistical Association, Alexandria, VA, pp. 84-87.
• Alan Genz and Koon-Shing Kwong: Numerical Evaluation of Singular Multivariate Normal Distributions (PDF, Postscript, ); revised version published in J. Stat. Comp. Simul. 68 (2000), pp. 1-21.
• Alan Genz: Finding Critical Values Using Numerical Integration (Postscript); revised version published in Computing Science and Statistics 31 (1999), pp. 263-266.
• Alan Genz and Frank Bretz: Numerical Computation of Multivariate t-Probabilities with Application to Power Calculation of Multiple Contrasts (PDF, Postscript ); revised version published in J. Stat. Comp. Simul. 63 (1999), pp. 361-378.
• Alan Genz: Methods for Generating Random Orthogonal Matrices (Postscript); revised version published in Monte Carlo and Quasi-Monte Carlo Methods 1998, H. Niederreiter and J. Spanier (Eds.), Springer-Verlag, Berlin, (1999), pp. 199-213.
• Alan Genz and John Monahan: A Stochastic Algorithm for High Dimensional Multiple Integrals over Unbounded Regions with Gaussian Weight (PDF); revised version published in J. Comp. Appl. Math. 112 (1999), pp. 71-81.
• Alan Genz: Stochastic Methods for Multiple Integrals over Unbounded Regions (PDF); revised version published in Mathematics and Computers in Simulation} 47 (1998), pp. 287-298.
• Alan Genz and John Monahan: Stochastic Integration Rules for Infinite Regions (Postscript, PDF); revised version published in SIAM J. Sci. Com. 19 (1998), pp. 426-439.
• John Monahan and Alan Genz: Spherical-Radial Integration Rules for Bayesian Computation (Postscript); revised version published in JASA 92 (1997), pp. 664--674.
• Alan Genz and Robert Kass: Subregion Adaptive Integration of Functions Having a Dominant Peak (Postscript, PDF); revised version published in J. Comp. Graph. Stat. 6 (1997), pp. 92-111.
• Alan Genz and Bradley Keister: Fully Symmetric Interpolatory Rules for Multiple Integrals over Infinite Regions with Gaussian Weight (PDF); revised version published in J. Comp. Appl. Math. 71 (1996), pp. 299-309.
• Alan Genz: Comparison of Methods for the Computation of Multivariate Normal Probabilities (Postscript) revised version published in Computing Science and Statistics 25 (1993), pp. 400-405.
• Alan Genz: Numerical Computation of Multivariate Normal Probabilities (PDF, Postscript ); revised version published in J. Comp. Graph Stat. 1 (1992), pp. 141-149.
• Alan Genz: An Adaptive Numerical Integration Algorithm for Simplices (Postscript); revised version published in Computing in the 90s, Proceedings of the First Great Lakes Computer Science Conference, N. A. Sherwani, E. de Doncker and J. A. Kapenga (Eds.), Lecture Notes in Computer Science Volume 507, Springer--Verlag, New York (1991), pp. 279-292.
• Jarle Berntsen, Terje O. Espelid and Alan Genz, : An Adaptive Algorithm for the Approximate Calculation of Multiple Integrals (PDF or Postscript); revised version published in ACM Trans. Math. Softw. 17 (1991), pp. 437-451.
• Jarle Berntsen, Terje O. Espelid and Alan Genz, : An Adaptive Multidimensional Integration Routine for a Vector of Integrals. (PDF); revised version published in ACM Trans. Math. Softw. 17 (1991), pp. 452-456.