Postdoctoral Fellow Seminars: Spring 2020

January 8, 2020

Lecture: Kriging: Beyond Matérn

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

Abstract

Satellite instruments and computer models that simulate physical processes of interest often lead to massive amount of data with complicated structures. Statistical analysis of such data needs to deal with a wide range of challenging problems such as high-dimensionality and nonstationarity. To understand and predict real-world processes, kriging, originated in geostatistics in the 1960s, has been widely used for prediction in spatial statistics and uncertainty quantification (UQ). In the first part of my talk, I shall give a brief overview of my research related to kriging or Gaussian process regression to tackle these challenging issues in various real-world applications. In the second part of my talk, I shall introduce a new family of covariance functions to perform kriging. Over the past several decades, the Matérn covariance function has been a popular choice to model dependence structures. A key benefit of the Matérn class is that it is possible to get precise control over the degree of differentiability of the process realizations. However, the Matérn class possesses exponentially decaying tails, and thus may not be suitable for modeling long range dependence. This problem can be remedied using polynomial covariances; however, one loses control over the degree of differentiability of the process realizations, in that the realizations using polynomial covariances are either infinitely differentiable or not differentiable at all. To overcome this dilemma, a new family of covariance functions is constructed using a scale mixture representation of the Matérn class where one obtains the benefits of both Matérn and polynomial covariances. The resultant covariance contains two parameters: one controls the degree of differentiability near the origin and the other controls the tail heaviness, independently of each other. This new covariance function also enjoys nice theoretical properties under infill asymptotics including equivalence measures, asymptotic behavior of the maximum likelihood estimators, and asymptotically efficient prediction under misspecified models. The improved theoretical properties in predictive performance of this new covariance class are verified via extensive simulations. Application using NASA’s Orbiting Carbon Observatory-2 satellite data confirms the advantage of this new covariance class over the Matérn class, especially in extrapolative settings. This talk concludes with discussions on extrapolation in UQ studies.

References

No references provided at this time


January 15, 2020

Lecture: Multi-Resolution Functional ANOVA (MRFA) Emulation

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

Abstract

Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. In this talk, a multi-resolution functional ANOVA model will be introduced as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input non-linear regression problems.

References

No references provided at this time


January 22, 2020

Lecture: Data-driven Methods for Multi-scale Models of Cell Migration

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

Abstract

Human skin cells collectively migrate into a wound area for healthy wound repair; failure of this process leads to so-called non-healing wounds. There is little consensus on why non-healing wounds occur, but they are a significant burden to the US Healthcare system, as they occur in up to 2% of the population and cost $18 billion annually.

In this talk, I will discuss the derivation and analysis of multi-scale mathematical models that can be used to better understand the wound healing process. These modeling formulations include a biochemically-stage structured reaction diffusion equation to incorporate how biochemical signaling pathways may alter cell behavior and a nonlinear diffusion equation model to capture the effects of cell-cell interactions on population-wide migration. Analysis of these equations allows for insight into both healthy and impaired wound dynamics and comparison of these models to biological data allows for parameterization of the models to ensure they are biologically realistic. I will also present some results on how machine learning can aid us in the model development process with either continuum or agent-based models.

References

No references provided at this time


January 29, 2020

Lecture: To be determined

Location: SAMSI Classroom
Speaker: To be determined

Abstract

To be determined

References

No references provided at this time


Feburary 5, 2020

Lecture: To be determined

Location: SAMSI Classroom
Speaker: To be determined

Abstract

To be determined

References

No references provided at this time


Feburary 12, 2020

Lecture: To be determined

Location: SAMSI Classroom
Speaker: To be determined

Abstract

To be determined

References

No references provided at this time


Feburary 19, 2020

Lecture: To be determined

Location: SAMSI Classroom
Speaker: To be determined

Abstract

To be determined

References

No references provided at this time


Feburary 26, 2020

Lecture: To be determined

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

Abstract

To be determined

References

No references provided at this time


March 4, 2020

Lecture: To be determined

Location: SAMSI Classroom
Speaker: Deborshee Sen, First-Year SAMSI Postdoctoral Fellow

Abstract

To be determined

References

No references provided at this time


March 11, 2020

** SPRING BREAK – No Seminar Scheduled **


March 18, 2020

Lecture: To be determined

Location: SAMSI Classroom
Speaker: Mamadou Yauck, First-Year SAMSI Postdoctoral Fellow

Abstract

To be determined

References

No references provided at this time


March 25, 2020

Lecture: To be determined

Location: SAMSI Classroom
Speaker: Jaffer Zaidi, First-Year SAMSI Postdoctoral Fellow

Abstract

To be determined

References

No references provided at this time


April 1, 2020

Lecture: To be determined

Location: SAMSI Classroom
Speaker: Ruda Zhang, First-Year SAMSI Postdoctoral Fellow

Abstract

To be determined

References

No references provided at this time


April 8, 2020

Lecture: To be determined

Location: SAMSI Classroom
Speaker: Maggie Mao, First-Year SAMSI Postdoctoral Fellow

Abstract

To be determined

References

No references provided at this time


April 15, 2020

Lecture: To be determined

Location: SAMSI Classroom
Speaker: Jason Poulos, First-Year SAMSI Postdoctoral Fellow

Abstract

To be determined

References

No references provided at this time


April 22, 2020

Lecture: To be determined

Location: SAMSI Classroom
Speaker: To be determined

Abstract

To be determined

References

No references provided at this time