First by truncating the sampling expansion (4) and then by approximating the samples, using standard methods of solving ordinary differential equations.
These quantities can be related to the scalar outputs from the MC simulations defined in Section 2.1 by approximating the effective sampling volume as (7) 〈 V 〉 ≈ A 1 〈 Z M C 〉 d f 2 with 〈 Z MC〉 the effective sampling depth and A1 a proportionality factor that depends on the geometrical shape of the effective volume.
In practice, we first construct the proximity graph by searching for the nearest k-neighbors of each sample using the new metric based on their spatial relationship and function values, and then projecting the samples onto the contour tree by approximating the distance between every pair of sample points.
In this paper, an extended MVU (EMVU) method is proposed, extending the utilization of MVU to new samples by approximating the nonlinear mapping between the input space and the output space with a Gaussian process model.
In practice, the ERLE is computed by approximating the expectation operator with the current sample value.
In the texture-mapping procedure, we begin by approximating the target surface with an approximating cylinder.
Because the ratio of sample size to population size was small, we approximated the sample design by a "with-replacement" design for purposes of variance estimation in SUDAAN.
The calculation of a 95% confidence interval, as described above, relies on two assumptions: that the distribution of sample means is approximately Normal and that the population SD can be approximated by the sample SD.
In practice, the statistical covariance matrix can only be computed using a limited number of signal samples, where can be approximated by the sample covariance matrix defined as (32).
