Highly efficient stochastic approaches for multidimensional integrals in biology for access control

  • 1 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Department of Information Modeling, Sofia, Bulgaria; Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Department of Parallel Algorithms, Sofia, Bulgaria
  • 2 Rousse Univers ity ”Angel Kanchev”


Monte Carlo methods have become popular computational device for problems in biology. In this work we implement and analyze the computational complexity of the Latin hypercube sampling algorithm. We compare the results with Importance sampling algorithm which is the most widely used variance reduction Monte Carlo method. We show that the Latin hypercube sampling has some advantageous over the importance sampling technique



  1. Caflisch, R. E.: Monte Carlo and quasi-Monte Carlo methods. Acta Numerica, 7 (1998) 149.
  2. Davis P. and Rabinowitz. P.: Methods of Numerical Integration. Academic Press, London, 2nd edition, (1984).
  3. Dimov I., Atanassov E.: What Monte Carlo models can do and cannot do efficiently?, Applied Mathematical Modelling 32 (2007) 1477–1500.
  4. Dimov I.: Monte Carlo Methods for Applied Scientists, New Jersey, London, Singapore, World Scientific, (2008), 291p.
  5. Dimov I., Karaivanova A., Georgieva R., Ivanovska S.: Parallel Importance Separation and Adaptive Monte Carlo Algorithms for Multiple Integrals, 5th Int. conf. on NMA, August, 2002, Borovets, Bulgaria, Springer Lecture Notes in Computer Science, 2542, (2003), Springer-Verlag, Berlin, Heidelberg, New York, pp. 99- 107.
  6. Hesterberg, T.: Weighted average importance sampling and defensive mixture distributions. Technometrics, 37(2) (1995) 185194.
  7. Jarosz, W.: Efficient Monte Carlo Methods for Light Transport in Scattering Media, PhD dissertation, UCSD, (2008)
  8. McKay, M.D., Beckman, R.J., Conover, W.J.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2), 23945 (1979)
  9. Michael I. Jordan, Stat260: Bayesian Modeling and Inference- Monte Carlo sampling, (2010).
  10. Owen, A. and Zhou, Y.: Safe and effective importance sampling. Technical report, Stanford University, Statistics Department (1999)
  11. Vose, D.: The pros and cons of Latin Hypercube sampling, (2014)
  12. ~mh2078/MCS04/MCS_var_red2.pdf

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