page_title: Variance-based sensitivity analysis
section_title: Sampling sequences
hierarchical_section_title: Variance-based sensitivity analysis / Calculation of indices / Sampling sequences
caption_attribution_description: English: Construction of ABi matrices in monte carlo estimation of sensitivity indices.
context_page_description: Variance-based sensitivity analysis is a form of global sensitivity analysis. Working within a probabilistic framework, it decomposes the variance of the output of the model or system into fractions which can be attributed to inputs or sets of inputs. For example, given a model with two inputs and one output, one might find that 70% of the output variance is caused by the variance in the first input, 20% by the variance in the second, and 10% due to interactions between the two. These percentages are directly interpreted as measures of sensitivity. Variance-based measures of sensitivity are attractive because they measure sensitivity across the whole input space, they can deal with nonlinear responses, and they can measure the effect of interactions in non-additive systems.
context_section_description: The Monte Carlo approach involves generating a sequence of randomly distributed points inside the unit hypercube (strictly speaking these will be pseudorandom). In practice, it is common to substitute random sequences with low-discrepancy sequences to improve the efficiency of the estimators. This is then known as the quasi-Monte Carlo method. Some low-discrepancy sequences commonly used in sensitivity analysis include the Sobol sequence and the Latin hypercube design.
caption: An example of construction of ABi matrices with d=3 and N=4.
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