TY - JOUR AU - Fábián, Csaba AU - Gurka Dezsőné Csizmás, Edit Margit AU - Drenyovszki, Rajmund AU - Wim, van Ackooij AU - Vajnai, Tibor AU - Kovács, Lóránt AU - Szántai, Tamás TI - Probability maximization by inner approximation JF - ACTA POLYTECHNICA HUNGARICA J2 - ACTA POLYTECH HUNG VL - 15 ET - 0 PY - 2018 IS - 1 SP - 105 EP - 125 PG - 21 SN - 1785-8860 DO - 10.12700/APH.15.1.2018.1.7 UR - https://m2.mtmt.hu/api/publication/3323588 ID - 3323588 AB - We solve probability maximization problems using an approximation scheme that is analogous to the classic approach of p-efficient points, proposed by Prékopa to handle chance constraints. But while p-efficient points yield an approximation of a level set of the probabilistic function, we approximate the epigraph. The present scheme is easy to implement and is immune to noise in gradient computation. © 2018, Budapest Tech Polytechnical Institution. All rights reserved. LA - English DB - MTMT ER - TY - JOUR AU - Nesterov, Yurii AU - Vial, J.-Ph. TI - Confidence level solutions for stochastic programming JF - AUTOMATICA J2 - AUTOMATICA VL - 44 PY - 2008 IS - 6 SP - 1559 EP - 1568 PG - 10 SN - 0005-1098 DO - 10.1016/j.automatica.2008.01.017 UR - https://m2.mtmt.hu/api/publication/34729741 ID - 34729741 LA - English DB - MTMT ER - TY - JOUR AU - Gassmann, H I AU - Deák, István AU - Szántai, Tamás TI - Computing multivariate normal probabilities: A new look JF - JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS J2 - J COMPUT GRAPH STAT VL - 11 PY - 2002 IS - 4 SP - 920 EP - 949 PG - 30 SN - 1061-8600 DO - 10.1198/106186002321018876 UR - https://m2.mtmt.hu/api/publication/1999178 ID - 1999178 AB - This article describes and compares several numerical methods for finding multivariate probabilities over a rectangle. A large computational study shows how the computation times depend on the problem dimensions, the correlation structure, the magnitude of the sought probability, and the required accuracy. No method is uniformly best for all problems and-unlike previous work-this article gives some guidelines to help establish the most promising method a priori. Numerical tests were conducted on approximately 3,000 problems generated randomly in up to 20 dimensions. Our findings indicate that direct integration methods give acceptable results for up to 12-dimensional problems, provided that the probability mass of the rectangle is not too large (less than about 0.9). For problems with small probabilities (less than 0.3) a crude Monte Carlo method gives reasonable results quickly, while bounding procedures perform best on problems with large probabilities (> 0.9). For larger problems numerical integration with quasirandom Korobov points may be considered, as may a decomposition method due to Deák. The best method found four-digit accurate probabilities for every 20-dimensional problem in less than six minutes on a 533MHz Pentium III computer. LA - English DB - MTMT ER - TY - JOUR AU - Szántai, Tamás TI - Improved bounds and simulation procedures on the value of the multivariate normal probability distribution function JF - ANNALS OF OPERATIONS RESEARCH J2 - ANN OPER RES VL - 100 ET - 0 PY - 2000 IS - 1-4 SP - 85 EP - 101 PG - 17 SN - 0254-5330 DO - 10.1023/A:1019211000153 UR - https://m2.mtmt.hu/api/publication/2617024 ID - 2617024 N1 - Cited By :17 Export Date: 31 October 2018 AB - Improved bounds and simulation procedures on the value of the multivariate normal probability distribution function value are given in the paper. The authors variance reduction technique was based on the Bonferroni bounds involving the first two binomial moments only. The new variance reduction technique is adapted to the most refined new bounds developed in the last decade for the estimation the probability of union respectively intersection of events. Numerical test results prove the efficiency of the simulation procedures described in the paper. LA - English DB - MTMT ER - TY - JOUR AU - Bukszár, József AU - Szántai, Tamás TI - Hipercseresznyefákkal adott valószínűségi korlátok. Probability bounds given by hypercherry trees TS - Probability bounds given by hypercherry trees JF - ALKALMAZOTT MATEMATIKAI LAPOK J2 - ALK MAT LAP VL - 19 PY - 1999 IS - 1 SP - 69 EP - 85 PG - 17 SN - 0133-3399 UR - https://m2.mtmt.hu/api/publication/2654382 ID - 2654382 LA - Hungarian DB - MTMT ER - TY - CONF AU - Szántai, Tamás ED - Yu, Ermoliev ED - R J-B, Wets TI - A computer code for solution of probabilistic constrained stochastic programming problems T2 - Numerical Techniques for Stochastic Programming Problems, Springer Series in Computational Mathematics PB - Springer Netherlands C1 - Heidelberg ET - 0 PY - 1988 SP - 229 EP - 235 PG - 7 UR - https://m2.mtmt.hu/api/publication/2694566 ID - 2694566 LA - English DB - MTMT ER - TY - JOUR AU - Deák, István TI - Computing probabilities of rectangles in case of multinormal distribution JF - JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION J2 - J STAT COMPUT SIM VL - 26 PY - 1986 IS - 1-2 SP - 101 EP - 114 PG - 14 SN - 0094-9655 DO - 10.1080/00949658608810951 UR - https://m2.mtmt.hu/api/publication/2002241 ID - 2002241 LA - English DB - MTMT ER - TY - THES AU - Szántai, Tamás TI - Többdimenziós valószínűség-eloszlásokkal kapcsolatos valószínűségek numerikus meghatározásáról PY - 1985 SP - 122 UR - https://m2.mtmt.hu/api/publication/2617134 ID - 2617134 N1 - Source: PublEx LA - Hungarian DB - MTMT ER - TY - JOUR AU - Deák, István TI - Three digit accurate multiple normal probabilities JF - NUMERISCHE MATHEMATIK J2 - NUMER MATH VL - 35 PY - 1980 IS - 4 SP - 369 EP - 380 PG - 12 SN - 0029-599X DO - 10.1007/BF01399006 UR - https://m2.mtmt.hu/api/publication/2008597 ID - 2008597 AB - Computer algorithms are presented for evaluating the multidimensional normal distribution function by Monte Carlo techniques. The computation of such probabilities is frequently required in stochastic programming models and in multivariate statistical problems. Using a medium size computer, three significant digits can be obtained up to ten dimensions in five seconds, up to twenty dimensions in one minute and up to fifty dimensions in ten minutes. Results of the detailed computer experiences are also reported together with some numerical examples. © 1980 Springer-Verlag. LA - English DB - MTMT ER - TY - JOUR AU - Szántai, Tamás TI - Egy eljárás a többdimenziós normális eloszlásfüggvény és gradiense értékeinek meghatározására JF - ALKALMAZOTT MATEMATIKAI LAPOK J2 - ALK MAT LAP VL - 2 PY - 1976 IS - 1-2 SP - 27 EP - 39 PG - 13 SN - 0133-3399 UR - https://m2.mtmt.hu/api/publication/2617117 ID - 2617117 N1 - Source: PublEx LA - Hungarian DB - MTMT ER -