@article{saibaba_hart_bloemen waanders_2021, title={Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis}, volume={28}, ISSN={["1099-1506"]}, DOI={10.1002/nla.2364}, abstractNote={Abstract}, number={4}, journal={NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS}, author={Saibaba, Arvind K. and Hart, Joseph and Bloemen Waanders, Bart}, year={2021}, month={Aug} }
 @article{hart_bessac_constantinescu_2019, title={Global Sensitivity Analysis for Statistical Model Parameters}, volume={7}, ISSN={["2166-2525"]}, DOI={10.1137/17M1161397}, abstractNote={Global sensitivity analysis (GSA) is frequently used to analyze the influence of uncertain parameters in mathematical models. In principle, tools from GSA may be extended to analyze the influence of parameters in statistical models. Such analyses may enable parsimonious modeling and greater predictive capability. However, difficulties such as parameter correlation, model stochasticity, and multivariate model output prohibit a direct extension of GSA tools to statistical models. We introduce a novel framework that addresses these difficulties and enables GSA for statistical model parameters. Theoretical and computational properties are considered and illustrated on a synthetic example. The framework is applied to a Gaussian process model that depends on 95 parameters from the literature. Non-influential parameters are discovered through GSA and a reduced model with equal or stronger predictive capability is constructed by using only 79 parameters.}, number={1}, journal={SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION}, author={Hart, Joseph L. and Bessac, Julie and Constantinescu, Emil M.}, year={2019}, pages={67–92} }
 @article{hart_gremaud_david_2019, title={Global Sensitivity Analysis of High-Dimensional Neuroscience Models: An Example of Neurovascular Coupling}, volume={81}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-019-00578-0}, abstractNote={The complexity and size of state-of-the-art cell models have significantly increased in part due to the requirement that these models possess complex cellular functions which are thought—but not necessarily proven—to be important. Modern cell models often involve hundreds of parameters; the values of these parameters come, more often than not, from animal experiments whose relationship to the human physiology is weak with very little information on the errors in these measurements. The concomitant uncertainties in parameter values result in uncertainties in the model outputs or quantities of interest (QoIs). Global sensitivity analysis (GSA) aims at apportioning to individual parameters (or sets of parameters) their relative contribution to output uncertainty thereby introducing a measure of influence or importance of said parameters. New GSA approaches are required to deal with increased model size and complexity; a three-stage methodology consisting of screening (dimension reduction), surrogate modeling, and computing Sobol’ indices, is presented. The methodology is used to analyze a physiologically validated numerical model of neurovascular coupling which possess 160 uncertain parameters. The sensitivity analysis investigates three quantities of interest, the average value of $$\hbox {K}^{+}$$ in the extracellular space, the average volumetric flow rate through the perfusing vessel, and the minimum value of the actin/myosin complex in the smooth muscle cell. GSA provides a measure of the influence of each parameter, for each of the three QoIs, giving insight into areas of possible physiological dysfunction and areas of further investigation.}, number={6}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Hart, J. L. and Gremaud, P. A. and David, T.}, year={2019}, month={Jun}, pages={1805–1828} }
 @article{hart_gremaud_2019, title={ROBUSTNESS OF THE SOBOL' INDICES TO DISTRIBUTIONAL UNCERTAINTY}, volume={9}, ISSN={["2152-5099"]}, DOI={10.1615/Int.J.UncertaintyQuantification.2019030553}, abstractNote={Global sensitivity analysis (GSA) is used to quantify the influence of uncertain variables in a mathematical model. Prior to performing GSA, the user must specific a probability distribution to model the uncertainty, and possibly statistical dependencies, of the variables. Determining this distribution is challenging in practice as the user has limited and imprecise knowledge of the uncertain variables. This article analyzes the robustness of the Sobol' indices, a commonly used tool in GSA, to changes in the distribution of the uncertain variables. A method for assessing such robustness is developed which requires minimal user specification and no additional evaluations of the model. Theoretical and computational aspects of the method are considered and illustrated through examples.}, number={5}, journal={INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION}, author={Hart, Joseph and Gremaud, Pierre}, year={2019}, pages={453–469} }
 @article{hart_gremaud_2019, title={Robustness of the Sobol' Indices to Marginal Distribution Uncertainty}, volume={7}, ISSN={["2166-2525"]}, DOI={10.1137/18M123387X}, abstractNote={Global sensitivity analysis (GSA) quantifies the influence of uncertain variables in a mathematical model. The Sobol' indices, a commonly used tool in GSA, seek to do this by attributing to each variable its relative contribution to the variance of the model output. In order to compute Sobol' indices, the user must specify a probability distribution for the uncertain variables. This distribution is typically unknown and must be chosen using limited data and/or knowledge. The usefulness of the Sobol' indices depends on their robustness to this distributional uncertainty. This article presents a novel method which uses "optimal perturbations" of the marginal probability density functions to analyze the robustness of the Sobol' indices. The method is illustrated through synthetic examples and a model for contaminant transport.}, number={4}, journal={SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION}, author={Hart, Joseph L. and Gremaud, Pierre A.}, year={2019}, pages={1224–1244} }
 @article{hart_gremaud_2018, title={AN APPROXIMATION THEORETIC PERSPECTIVE OF SOBOL' INDICES WITH DEPENDENT VARIABLES}, volume={8}, ISSN={["2152-5099"]}, DOI={10.1615/Int.J.UncertaintyQuantification.2018026498}, abstractNote={The Sobol' indices are a recognized tool in global sensitivity analysis. When the uncertain variables in a model are statistically independent, the Sobol' indices may be easily interpreted and utilized. However, their interpretation and utility is more challenging with statistically dependent variables. This article develops an approximation theoretic perspective to interpret Sobol' indices in the presence of variable dependencies. The value of this perspective is demonstrated in the context of dimension reduction, a common application of the Sobol' indices. Theoretical analysis and illustrative examples are provided.}, number={6}, journal={INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION}, author={Hart, J. L. and Gremaud, P. A.}, year={2018}, pages={483–493} }
 @article{hart_alexanderian_gremaud_2017, title={EFFICIENT COMPUTATION OF SOBOL' INDICES FOR STOCHASTIC MODELS}, volume={39}, ISSN={["1095-7197"]}, DOI={10.1137/16m106193x}, abstractNote={Stochastic models are necessary for the realistic description of an increasing number of applications. The ability to identify influential parameters and variables is critical to a thorough analysis and understanding of the underlying phenomena. We present a new global sensitivity analysis approach for stochastic models, i.e., models with both uncertain parameters and intrinsic stochasticity. Our method relies on an analysis of variance through a generalization of Sobol' indices and on the use of surrogate models. We show how to efficiently compute the statistical properties of the resulting indices and illustrate the effectiveness of our approach by computing first order Sobol' indices for two stochastic models.}, number={4}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Hart, J. L. and Alexanderian, A. and Gremaud, P. A.}, year={2017}, pages={A1514–A1530} }
 @article{hart_novak_saunders_gremaud_2016, title={Transcranial Doppler-Based Surrogates for Cerebral Blood Flow: A Statistical Study}, volume={11}, ISSN={["1932-6203"]}, DOI={10.1371/journal.pone.0165536}, abstractNote={It is commonly assumed that perfusion in a given cerebral territory can be inferred from Blood Flow Velocity (BFV) measurements in the corresponding stem artery. In order to test this hypothesis, we construct a cerebral blood flow (CBF) estimator based on transcranial Doppler (TCD) blood flow velocity and ten other easily available patient characteristics and clinical parameters. A total of 261 measurements were collected from 88 older patients. The estimator is based on local regression (Random Forest). Its performance is analyzed against baseline CBF from 3-D pseudocontinuous arterial spin labeling (pCASL) magnetic resonance imaging (MRI). Patient specific CBF predictions are of poor quality (r = 0.41 and p-value = 4.5 × 10−12); the hypothesis is thus not clearly supported by evidence.}, number={11}, journal={PLOS ONE}, author={Hart, Joseph and Novak, Vera and Saunders, Charles and Gremaud, Pierre A.}, year={2016}, month={Nov} }