In recent years, new, intelligent and efficient sampling techniques for Monte Carlo simulation have been developed. However, when such new techniques are introduced, they are compared to one or two existing techniques, and their performance is evaluated over two or three problems. A literature survey shows that benchmark studies, comparing the performance of several techniques over several problems, are rarely found. This article presents a benchmark study, comparing Simple or Crude Monte Carlo with four modern sampling techniques: Importance Sampling Monte Carlo, Asymptotic Sampling, Enhanced Sampling and Subset Simulation; which are studied over six problems. Moreover, these techniques are combined with three schemes for generating the underlying samples: Simple Sampling, Latin Hypercube Sampling and Antithetic Variates Sampling. Hence, a total of fifteen sampling strategy combinations are explored herein. Due to space constrains, results are presented for only three of the six problems studied; conclusions, however, cover all problems studied. Results show that Importance Sampling using design points is extremely efficient for evaluating small failure probabilities; however, finding the design point can be an issue for some problems. Subset Simulation presented very good performance for all problems studied herein. Although similar, Enhanced Sampling performed better than Asymptotic Sampling for the problems considered: this is explained by the fact that in Enhanced Sampling the same set of samples is used for all support points; hence a larger number of support points can be employed without increasing the computational cost. Finally, the performance of all the above techniques was improved when combined with Latin Hypercube Sampling, in comparison to Simple or Antithetic Variates sampling.
Objective: To develop a joint time-frequency analysis technique based on generalized harmonic wavelets (GHWs) for dynamic cerebral autoregulation (DCA) performance quantification. Approach: We considered two groups of human subjects to develop and validate the method: 55 healthy volunteers and 35 stroke-free subjects with unilateral internal carotid artery stenosis (CAS). We determined the mean and coherence-weighted average of the phase shift (PS) of appropriately defined GHW-based transfer functions, based on data points over the joint time-frequency domain. We compared agreement of standard transfer function analysis (TFA) and GHW analyses in healthy subjects using Bland-Altman plots. We assessed sensitivity of each metric to detect the presumed side-to-side difference in DCA function in CAS subjects (with decreased PS on the occluded side), using McNemar’s chi square test to compare each metric to the standard TFA approach. An alternative Morlet wavelet-based approach was also considered. Main results: The GHW and TFA methods exhibited strong agreement in healthy subjects. Among CAS subjects, GHW metrics outperformed TFA and Morlet wavelet-based approaches in identifying expected side-to-side differences: TFA sensitivity was 40.0% (95%CI 23.9–57.9), Morlet 60.0% (95%CI 42.1–76.1), and GHW >70% for both metrics (GHW mean PS sensitivity 74.3, 95%CI 56.7–87.5, p = 0.0027 versus TFA; GHW coherence-weighted PS sensitivity 71.4, 95%CI 53.7–85.4, p = 0.0009 versus TFA). Significance: In comparison to the widely used stationary Fourier transform-based TFA and to Morlet wavelet-based analysis, our data suggest that the GHW-based analysis performs better in identifying DCA asymmetry between the two cerebral hemispheres in patients with high grade unilateral carotid stenosis. Our method may provide enhanced confidence in employing DCA metrics as a sensitive diagnostic tool for detecting impaired DCA function in a variety of pathological settings.
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