We present the effect of using the Metropolis-Hastings algorithm for sampling the integrand on the accuracy of calculating the value of the integral. In addition, a hybrid method for sampling the integrand is proposed, in which part of the training sample is generated by applying the Metropolis-Hastings algorithm, and the other part includes points of a uniform grid. Numerical experiments show that when integrating in high-dimensional domains, sampling of integrands both by the Metropolis-Hastings algorithm and by a hybrid method is more efficient with respect to the points of a uniform grid.
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