2020 | STOCHNUM | Stochastic Numerics Research Group

Articles

Chernov, A., Hoel, H., Law, K. J. H., Nobile, F., & Tempone, R. (2020). Multilevel ensemble Kalman filtering for spatio-temporal processes. Numerische Mathematik. doi:10.1007/s00211-020-01159-3

Piazzola, C., Tamellini, L., & Tempone, R. (2020). A note on tools for prediction under uncertainty and identifiability of SIR-like dynamical systems for epidemiology. Mathematical Biosciences, 108514. doi:10.1016/j.mbs.2020.108514

Keywords: Dynamical Systems, Mathematical Epidemiology, Uncertainty Quantification, Model Identifiability, Bayesian Inversion, Fisher Approximation

Bayer, C., Tempone, R., & Wolfers, S. (2020). Pricing American options by exercise rate optimization. Quantitative Finance, 1–12. doi:10.1080/14697688.2020.1750678

Keywords: Computational finance, American option pricing, Stochastic optimization problem, Monte Carlo, Multivariate approximation, Rough volatility

Bayer, C., Hammouda, C. B., & Tempone, R. (2020). Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model. Quantitative Finance, 1–17. doi:10.1080/14697688.2020.1744700

Keywords: Rough volatility, Monte Carlo, Adaptive sparse grids, Quasi-Monte Carlo, Brownian bridge construction, Richardson extrapolation.

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Beck, J., Mansour Dia, B., Espath, L., & Tempone, R. (2020). Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design. International Journal for Numerical Methods in Engineering. doi:10.1002/nme.6367

Keywords: Electrical impedance tomography, Expected information gain, Importance sampling, Multilevel, Stochastic collocation

Haji-Ali, A.-L., Nobile, F., Tempone, R., & Wolfers, S. (2020). Multilevel weighted least squares polynomial approximation. ESAIM: Mathematical Modelling and Numerical Analysis, 54(2), 649–677. doi:10.1051/m2an/2019045

Keywords: Multilevel methods, Least-squares approximation, Multivariate approximation, Polynomial approximation, Convergence rates, Error analysis

Litvinenko, A., Logashenko, D., Tempone, R., Wittum, G., & Keyes, D. (2020). Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability. GEM - International Journal on Geomathematics, 11(1). doi:10.1007/s13137-020-0147-1

Keywords: Uncertainty quantiﬁcation, ug4, Multigrid, Density-driven ﬂow, Reservoir, Groundwater, Salt formations

Carlon, A. G., Dia, B. M., Espath, L., Lopez, R. H., & Tempone R. (2020). Nesterov-aided stochastic gradient methods using Laplace approximation for Bayesian design optimization. Computer Methods in Applied Mechanics and Engineering, Volume 363, doi:10.1016/j.cma.2020.112909

Keywords: Optimal experimental design, Bayesian inference, Laplace approximation, Stochastic optimization, Accelerated gradient descent, Importance sampling

Rached, N. B., MacKinlay, D., Botev, Z., Tempone, R., & Alouini, M.-S. (2020). A Universal Splitting Estimator for the Performance Evaluation of Wireless Communications Systems. IEEE Transactions on Wireless Communications, 1–1. doi:10.1109/twc.2020.2982649

Keywords: Rare event, Performance evaluation, Multilevel splitting algorithm, Variance reduction

Rached, N. B., Kammoun, A., Alouini, M.-S., & Tempone, R. (2020). An Accurate Sample Rejection Estimator of the Outage Probability with Equal Gain Combining. IEEE Open Journal of the Communications Society, 1–1. doi:10.1109/ojcoms.2020.3010649

Keywords: Outage probability, Equal gain combining, Importance sampling, Sample rejection, Generalised selection combining, Bounded relative error.

Issaid, C. B., Alouini, M.-S., & Tempone, R. (2020). Efficient Importance Sampling for the Left Tail of Positive Gaussian Quadratic Forms. IEEE Wireless Communications Letters, 1–1. doi:10.1109/lwc.2020.3036588

Keywords: Importance sampling, left tail, positive quadratic forms, Gaussian random vectors, bounded relative error.

Hoel, H., Shaimerdenova, G., & Tempone, R. (2020). Multilevel Ensemble Kalman Filtering based on a sample average of independent EnKF estimators. Foundations of Data Science, 2(4), 351–390. doi:10.3934/fods.2020017

Keywords: Monte Carlo, Multilevel, Convergence rates, Kalman filter, Ensemble Kalman filter

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Hammouda, C. B., Rached, N. B., & Tempone, R. (2020). Importance sampling for a robust and efficient multilevel Monte Carlo estimator for stochastic reaction networks, Statistics and Computing, 30:1665–1689. doi:10.1007/s11222-020-09965-3

Keywords: Multilevel Monte Carlo. Continuous-time Markov chains. Stochastic reaction networks. Stochastic biological systems. Importance sampling

Carlon, A. G., Torii, A. J., Lopez, R. H., & de Cursi, J. E. S. (2020). Stochastic Gradient Descent for Risk Optimization. Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling, 424–435 [conference paper]. doi:10.1007/978-3-030-53669-5_31

Keywords: Risk optimization, Stochastic gradient descent, Chernoff bound, Stochastic optimization

Manuscripts

Carlon, A. G., Espath, L., Lopez, R. H., & Tempone, R. Multi-Iteration Stochastic Optimizers. arXiv preprint, arXiv:2011.01718, 2020

Keywords: Stochastic Optimization; Monte Carlo; Multilevel Monte Carlo; Variance Reduc- tion; Control Variates; Machine Learning

Kammonen, A., Kiessling, J., Plechac, P., Sandberg, M., Szepessy, A., & Tempone, R. Smaller generalization error derived for deep compared to shallow residual neural networks. arXiv preprint, arXiv:2010.01887, 2020

Keywords: residual network, deep random feature, supervised learning, error estimates, layer by layer algorithm.

Bayer, C., Hall, E. J., & Tempone, R. Weak error rates for option pricing under the rough Bergomi model. arXiv preprint, arXiv:2009.01219, 2020

Keywords: Rough Bergomi, Weak error rate

Caballero, R., Kebaier, A., Scavino, M., & Tempone, R. A Derivative Tracking Model for Wind Power Forecast Error. arXiv preprint, arXiv:2006.15907, 2020

Keywords: Wind power, probabilistic forecasting, stochastic differential equations, Lamperti transform, numerical optimization, model selection, time-inhomogeneous Jacobi diffusion

Bayer, C., Hammouda, C. B., & Tempone, R. Numerical smoothing and hierarchical approximations for efficient option pricing and density estimation. arXiv preprint, arXiv:2003.05708, 2020

Keywords: Deterministic quadrature methods, Hierarchical variance reduction methods, Multilevel Monte Carlo, Numerical smoothing, Adaptive sparse grids quadrature, Brownian bridge, Richardson extrapolation, Option pricing, Monte Carlo

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