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Phương pháp tính tích phân Monte Carlo và ứng dụng
Abtract
Effective integration methods are very necessary for taking inferences in statistics. These methods can compute approximations for intractable integrals to calculate for probabilities, expectations, variances, et al. For deterministic numerical methods, quadrature forms are used to approximate for the region beneath the functions. These methods depend on the number of partitions and the finite of the integrated regions. Monte Carlo (MC) integration methods can solve for this problem and provide accurate approximations using generating random sample techniques in statistics. The aims of this paper are to weaken assumptions of the deterministic numerical methods for infinite integrated regions by using the MC integration method. The way to control the accuracy of the MC integration method is also proposed. This MC integration method has been implemented for particular examples with finite and infinite integrated regions.
Keyword: MC integration, Bayesian statistics, infinite integrated regions, random generation, modification of MC integration.
