Postdoctoral Fellow Seminars: Fall 2018

September 19, 2018, 1:15pm – 2:15pm

Special Guest Lecture: Where You Gonna Go When the Volcano Blows?

Location: SAMSI Classroom
Speaker: Bruce Pitman, University of Buffalo

Abstract

We discuss one approach to determining the hazard threat to a locale due to a large volcanic avalanche. The methodology employed includes large-scale numerical simulations, field data reporting the volume and run out of flow events, and a detailed statistical analysis of uncertainties in the modeling and data. The probability of a catastrophic event impacting a single location is calculated, together with a estimate of the uncertainty in that calculation. By a careful use of simulation and emulation, a hazard map for an entire region can be determined. This calculation can be turned around quickly, so hazard maps can be updated as conditions evolve.The methodology can be applied to other hazard scenarios.

References

No references provided at this time


September 26, 2018, 1:15pm – 2:15pm

Lecture: Fine-scale Spatio-temporal Air Pollution Analysis Using Mobile mMnitors on Google Street View vehicles

Location: SAMSI Classroom
Speaker: Yawen Guan, Second-Year SAMSI Postdoctoral Fellow

Abstract

People are increasingly concerned with understanding their personal environment, including possible exposure to harmful air pollutants. In order to make informed decisions on their day-to-day activities, they are interested in real-time information on a localized scale. Publicly available, fine-scale, high-quality air pollution measurements acquired using mobile monitors represent a paradigm shift in measurement technologies. A methodological framework utilizing these increasingly fine-scale measurements to provide real-time air pollution maps as well as short-term air quality forecasts on a fine-resolution spatial scale could prove to be instrumental in increasing public awareness and understanding. The Google Street View study provides a unique source of data with spatial and temporal complexities, with the potential to provide information about commuter exposure and hot spots within city streets with high traffic. We develop a computationally-efficient spatio-temporal model for these data and use the model to make high-resolution maps of current air pollution levels and short-term forecasts. We also show via an experiment that mobile networks are far more informative than an equally-sized fixed-location networks. This modeling framework has important real-world implications in understanding citizens’ personal environments, as data production and real-time availability continue to be driven by the ongoing development and improvement of mobile measurement technologies.

References

No references provided at this time


October 3, 2018, 1:15pm – 2:15pm

Special Guest Lecture: Short-term Probabilistic Hazard Mapping — Forecasting Catastrophe without Stationary Assumptions

Location: SAMSI Classroom
Speaker: Elaine Spiller, Marquette University

Abstract

Geophysical hazards — landslides, tsunamis, volcanic avalanches, etc. — which lead to catastrophic inundation are rare yet devastating events for surrounding communities. The rarity of these events poses two significant challenges. First, there are limited data to inform aleatoric scenario models, how frequent, how big, where. Second, such hazards often follow heavy-tailed distributions resulting in a significant probability that a larger-than-recorded catastrophe might occur. To overcome this second challenge, we must rely on physical models of these hazards to “probe” the tail for these catastrophic events. Typically these physical models are computationally intensive to exercise and a probabilistic hazard map relies on an expensive Monte Carlo simulation which samples the scenario model. This approach forces one to focus resources on a single scenario model based on one set of assumptions. We will present a surrogate-based strategy that allows great speed-up in Monte Carlo simulations and hence the flexibility to explore the impact of non-stationary scenario modelling on short term forecasts. Additionally, this approach provides a platform to perform uncertainty quantification on hazard forecasts.

References

No references provided at this time


October 10, 2018, 1:15pm – 2:15pm

Lecture: New Approaches in Sea Ice Modeling

Location: SAMSI Classroom
Speaker: Christian Sampson, Second-Year SAMSI Postdoctoral Fellow

Abstract

Sea ice is a critical component of Earth’s climate whose dynamics is driven by processes operating at a variety of spatio-temporal scales. As a result, accurate modeling and even observation of the polar ice packs is difficult to say the least. In this talk I will out line some new approaches being investigated which aim to find ways to better include important driving processes in sea ice models and improve observations or the assimilation of observations in to sea ice models. In particular, I will discuss new bounds for the effective viscoelastity parameter of an ice covered ocean needed for wave propagation models ,reduced order modeling for fluid flow through the porous structure of sea ice tied to sea ice crystallographic structure, methods for generating microstructural geometries consistent with coarse scale information, a proposed approach for the assimilation of sea ice concentration derived from passive microwave satellites, and a framework for a reduced order model of the climate for use in the prediction of sea ice loss reversibility.

References

No references provided at this time


October 17, 2018, 12:00pm – 1:00pm

Lecture: Phaseless sampling and reconstruction of signals of finite rate of innovation

Location: SAMSI Classroom
Speaker: Cheng Cheng, Second-Year SAMSI Postdoctoral Fellow

Abstract

In this talk, we consider the stable reconstruction of real-valued signals with finite rate of innovations (FRI), up to a sign, from their magnitude measurements on the whole domain or their phaseless samples on a discrete subset. FRI signals appear in many engineering applications such as magnetic resonance spectrum, ultra wide-band communication and electrocardiogram. For an FRI signal, we introduce an undirected graph to describe its topological structure. We establish the equivalence between the graph connectivity and phase retrievability of FRI signals, and we apply the graph connected component decomposition to find all FRI signals that have the same magnitude measurements as the original FRI signal has. We also propose a stable algorithm with linear complexity to reconstruct FRI signals from their phaseless samples on the above phaseless sampling set.

References

No references provided at this time


October 17, 2018, 1:15pm – 2:15pm

Lecture: Scalable Markov chain Monte Carlo methods via generalized Langevin equations

Location: SAMSI Classroom
Speaker: Matthias Sachs, Second-Year SAMSI Postdoctoral Fellow

Abstract

We discuss the design of numerical methods to solve the generalized Langevin equation (GLE) focusing on canonical sampling properties of numerical integrators. For this purpose, we cast the GLE in an extended phase space formulation and derive a family of splitting methods which generalize existing Langevin dynamics integration methods. We show that the dynamics of a suggested integration scheme is consistent with asymptotic limits of the exact dynamics and can reproduce (in the short memory limit) a superconvergence property for the analogous splitting of Langevin dynamics. We apply our proposed integration scheme to several model systems, including a simple Bayesian inference problem. Using a parameterization of the memory kernel in the GLE as proposed by Ceriotti et al [1], we find that our proposed integration scheme outperforms other previously proposed GLE integration schemes in terms of the accuracy of sampling. Moreover, our experiments indicate the potential benefits of a GLE-based method in comparison to other white noise Langevin dynamics integration schemes in terms of robustness and efficiency.

References

[1] M. Ceriotti, G. Bussi, and M. Parrinello, “Colored-noise thermostats àla Carte,” J. Chem. Theory Comput., vol. 6, no. 4, pp. 1170–1180, 2010.
[2] B. Leimkuhler and M. Sachs, “Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise,” 2018.


October 31, 2018, 1:15pm – 2:15pm

Lecture: Sparse Learning for Image-on-Scalar Regression with Application to Imaging Genetics Studies

Location: SAMSI Classroom
Speaker: Xinyi Li, First-Year SAMSI Postdoctoral Fellow

Abstract

Motivated by recent advances in technology for medical imaging and high-throughput genotyping, we consider an imaging genetics approach to discover relationships between the interplay of genetic variation and environmental factors and measurements from imaging phenotypes. We propose an image-on-scalar regression method, in which the spatial heterogeneity of gene-environment interactions on imaging responses is investigated via an ultra-high-dimensional spatially varying coefficient model (SVCM). Bivariate splines on triangulations are used to represent the coefficient functions over an irregular two-dimensional (2D) domain of interest. For the proposed SVCMs, we further develop a unified approach for simultaneous sparse learning (i.e., G×E interaction identification) and model structure identification (i.e., determination of spatially varying vs. constant coefficients). Our method can identify zero, nonzero constant and spatially varying components correctly and efficiently. The estimators of constant coefficients and varying coefficient functions are consistent and asymptotically normal. The performance of the method is evaluated by Monte Carlo simulation studies and a brain mapping study based on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) data.

References

No references provided at this time


November 7, 2018, 1:15pm – 2:15pm

Lecture: Parameter Estimation, Uncertainty Quantificaiton, and numerical methods for advective PDE models

Location: SAMSI Classroom
Speaker: John Nardini, First-Year SAMSI Postdoctoral Fellow

Abstract

The inverse problem methodology is a commonly-used framework in the sciences for parameter estimation and inference. It is typically performed by fitting a mathematical model to noisy experimental data. There are two significant sources of error in the process: 1. Noise from the measurement and collection of experimental data and 2. numerical error in approximating the solution to the mathematical model. Little attention has been paid to how this second source of error alters parameter estimation using frequentist techniques. To better understand of this problem, we present a modeling and simulation study using a simple advection-driven PDE model. We present both analytical and computational results concerning how the different sources of error impact the least squares cost function as well as parameter estimation and uncertainty quantification. We investigate residual patterns to derive an autocorrelative statistical model that can improve parameter estimation and confidence interval computation for first order methods. We ultimately use these observations to provide guidelines for practitioners on how to determine if numerical error is inhibiting the results of their inverse problem.

References

No references provided at this time


November 14, 2018, 1:15pm – 2:15pm

Special Guest Lecture: Validation of computer models via Bayesian model selection

Location: SAMSI Classroom
Speaker: Pierre Barbillon, Agro Paris Tech

Abstract

Complex physical systems are increasingly modeled by computer codes which aim at predicting the reality as accurately as possible. During the last decade, code validation has benefited from a large interest within the scientific community (Bayarri et al., 2007) because of the requirement to assess the uncertainty affecting the code outputs. Inspiring from past contributions to this task, two testing procedures are proposed to decide whether the code needs to be corrected by a discrepancy term or not. We resort first to the intrinsic Bayes Factor (Berger and Perrichi 1996) to compare the two models. Using the intrinsic Bayes Factor limits the dependency on the prior distribution chosen in each model. We propose also to deal with the model selection problem as the estimation of the weights in a mixture model following the approach of Kamary et al. (2014). The two methods are illustrated on synthetic examples and applied to real case studies.

References

  • Bayarri, M. J., Berger, J. O., Paulo, R., Sacks, J., Cafeo, J. A., Cavendish, J., Lin. C.-H. & Tu, J. (2007). A framework for validation of computer models. Technometrics, 49(2), 138-154.
  • Berger, J. O., & Pericchi, L. R. (1996). The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association, 91(433), 109-122.
  • Kaniav Kamary, Kerrie Mengersen, Christian P. Robert and Judith Rousseau, (2014), “Testing hypotheses as a mixture estimation model’’, arXiv preprint arXiv:1412.2044.

November 28, 2018, 1:15pm – 2:15pm

Lecture: Statistical Emulation for Expensive Simulators: An Application to Storm Surge

Location: SAMSI Classroom
Speaker: Pulong Ma, First-Year SAMSI Postdoctoral Fellow

Abstract

Uncertainty Quantification (UQ) has grown rapidly over the last several decades. Complex computer models of real-world processes (or simulators) are an essential ingredient to carry out UQ in virtually every field of science and engineering. In coastal emergency risks assessment, storm surge is one of the most severe natural disasters that attracts ever-increasing attentions in UQ, and it can lead to significant flooding in coastal areas and severely damages life and property from hurricanes. Quantifying the risk to storm surge hazard requires large-scale numerical simulations of hurricanes from storm surge modeling systems. In the United States, the Advanced Circulation (ADCIRC) model is one of the primary storm surge models used to predict storm surge and control the impact of storm damage. Each run of the ADCIRC model requires a large amount of computing resources. A crucial need is the development of an emulator, i.e., a fast simulator approximation. In this presentation, I will highlight several challenges in building a statistical emulator for the ADCIRC model, and show some preliminary results based on this on-going project. In the end, I will discuss a few future directions.

References

No references provided at this time


December 5, 2018, 1:15pm – 2:15pm

Lecture: Smoothness Estimation and Adaptive Kernel Ridge Regression

Location: SAMSI Classroom
Speaker: Wenjia Wang, First-Year SAMSI Postdoctoral Fellow

Abstract

We propose a new method to identify the smoothness of an underlying function, by employing the idea from the maximum likelihood estimation for Gaussian process models. This maximum likelihood approach is widely used in estimating the smoothness parameter in practice, but a rigorous study of its theoretical properties is lacking. We propose a modified maximum likelihood method to estimate the underlying function as well as its smoothness based on its noisy evaluations. Under certain conditions, we prove the consistency of the smoothness estimator and that the function estimator achieves a nearly optimal rate of convergence for all degrees of smoothness.

References

No references provided at this time