6,064 research outputs found
Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate models
Global sensitivity analysis aims at quantifying the impact of input
variability onto the variation of the response of a computational model. It has
been widely applied to deterministic simulators, for which a set of input
parameters has a unique corresponding output value. Stochastic simulators,
however, have intrinsic randomness due to their use of (pseudo)random numbers,
so they give different results when run twice with the same input parameters
but non-common random numbers. Due to this random nature, conventional Sobol'
indices, used in global sensitivity analysis, can be extended to stochastic
simulators in different ways. In this paper, we discuss three possible
extensions and focus on those that depend only on the statistical dependence
between input and output. This choice ignores the detailed data generating
process involving the internal randomness, and can thus be applied to a wider
class of problems. We propose to use the generalized lambda model to emulate
the response distribution of stochastic simulators. Such a surrogate can be
constructed without the need for replications. The proposed method is applied
to three examples including two case studies in finance and epidemiology. The
results confirm the convergence of the approach for estimating the sensitivity
indices even with the presence of strong heteroskedasticity and small
signal-to-noise ratio
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
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