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- Ian H. Sloan, Frances Y. Kuo, Stephen Joe
- SIAM J. Numerical Analysis
- 2002

Shifted rank-1 lattice rules, a special class of quasi-Monte Carlo methods, have recently been proposed by the present authors for the integration of functions belonging to certain “weighted” Sobolev… (More)

- Stephen Joe, Frances Y. Kuo
- ACM Trans. Math. Softw.
- 2003

An algorithm to generate Sobol' sequences to approximate integrals in up to 40 dimensions has been previously given by Bratley and Fox in Algorithm 659. Here, we provide more primitive polynomials… (More)

- Ian H. Sloan, Frances Y. Kuo, Stephen Joe
- Math. Comput.
- 2002

We develop and justify an algorithm for the construction of quasi– Monte Carlo (QMC) rules for integration in weighted Sobolev spaces; the rules so constructed are shifted rank-1 lattice rules. The… (More)

- Stephen Joe, Frances Y. Kuo
- SIAM J. Scientific Computing
- 2008

Direction numbers for generating Sobol′ sequences that satisfy the so-called Property A in up to 1111 dimensions have previously been given in Joe and Kuo [ACM Trans. Math. Software, 29 (2003), pp.… (More)

- G. Thomson, Wendy P. Robinson, +7 authors Max P. Baur
- American journal of human genetics
- 1988

From 11 studies, a total of 1,792 Caucasian probands with insulin-dependent diabetes mellitus (IDDM) are analyzed. Antigen genotype frequencies in patients, transmission from affected parents to… (More)

Rank-1 lattice rules based on a weighted star discrepancy with weights of a product form have been previously constructed under the assumption that the number of points is prime. Here, we extend… (More)

- Haydeh Payami, Stephen Joe, +5 authors G. Thomson
- American journal of human genetics
- 1989

A method is described to reveal the relative predispositional effects (RPEs) (predisposing, protective, or neutral) of the HLA alleles or of any other marker system that is associated with a disease.… (More)

- Stephen Joe
- 1997

For a d-dimensional quasi-Monte Carlo method with n points, calculating the weighted L 2 discrepancy using a formula obtained directly from its deenition requires O(2 d?1 dn 2) operations. Here we… (More)

- Frances Y. Kuo, Stephen Joe
- SIAM J. Numerical Analysis
- 2003

It is known that the generating vector of a rank-1 lattice rule can be constructed component-by-component to achieve strong tractability error bounds in both weighted Korobov spaces and weighted… (More)