Postdoctoral Fellows Seminars – Fall 2012

How to give a research presentation

September 5, 2012, 1:15pm – 2:15pm
SAMSI, Room 150
Speaker: Richard L. Smith (SAMSI and UNC-Chapel Hill)


Note: This is a professional development talk, rather than a scientific report.

Dimension reduced modeling of space-time processes with application to statistical downscaling

September 26, 2012, 1:15pm – 2:15pm
SAMSI, Room 150
Speaker: Jenny Brynjarsdottir, SAMSI and Duke University


The field of spatial and spatio-temporal statistics is increasingly faced with the challenge of very large datasets. The classical approach to spatial and spatio-temporal modeling is extremely computationally expensive when the datasets are large. Dimension-reduced modeling approach has proved to be effective in such situations. In this talk we focus on the problem of modeling two spatio-temporal processes where the primary goal is to predict one process from the other and where the datasets for both processes are large. We outline a general dimension-reduced Bayesian hierarchical approach where the spatial structures of both processes are modeled in terms of a low number of basis vectors, hence reducing the spatial dimension of the problem. The temporal evolution of the spatio-temporal processes and their dependence is then modeled through the coefficients (also called amplitudes) of the basis vectors. We present a new method of obtaining data-dependent basis vectors that are geared to the goal of predicting one process from the other: (Orthogonal) Maximum Covariance Patterns. We apply these methods to a statistical downscaling example, where surface temperatures on a coarse grid over the Antarctic are downscaled onto a finer grid.

Postdoc Lunch – The paper review process

October 3, 2012 – 12:30pm – 2:00pm
SAMSI Commons Room


Note: This is a professional development activity, in lieu of this week’s.

Data sketches, online nonlinear dimension reduction, and astrophysical inference

October 10, 2012, 1:15pm – 2:15pm
SAMSI, Room 150
Speaker: David Lawlor, SAMSI


As the size of data collected by telescopes grows, the need for computationally efficient inferential methods increases. Two strains of recent astrostatistical research have approached this problem in different ways. On the one hand, there has been an effort to devise streaming (or online) algorithms to incrementally update a low-dimensional (linear) approximation of the data, thus avoiding storing the entire data set in memory. At the same time, others have begun applying non-linear dimension reduction techniques — in particular, diffusion maps — to the data, which better capture its intrinsic variations.

In this exploratory talk, I propose combining these two approaches in an online nonlinear dimension reduction technique. Existing research focuses on incremental updates to nonlinear low-dimensional approximations, while I will argue that maintaining an efficient sketch of the data — from which quantities of interest can be derived — is computationally more efficient.

Estimating optimal nitrogen fertilization rate for grafted tomato field production: moving from parametric models to semiparametric models

October 24, 2012, 1:15pm – 2:15pm
SAMSI, Room 150
Speaker: Kenny Lopiano, SAMSI


Given the expected increase in demand for agricultural products, agricultural experts are seeking innovative ways to increase yield. One such innovation is the practice of grafting. Grafting plants to vigorous, interspecific, hybrid rootstocks has shown great potential for enhancing growth. Because grafted plants are fundamentally different than non-grafted plants, nitrogen input recommendations for non-grafted plants are not necessarily equivalent for grafted plants. In practice, optimal nitrogen input recommendations are derived from linear and nonlinear models of yield as a function of applied nitrogen. Here we investigate the performance of five different parametric models for grafted and ungrafted tomato plants grown in Florida. Although the five models result in almost equivalent measures of goodness-of-fit, the derived optimal nitrogen values are quite different. Because the choice of model is inherently subjective, we are currently considering semiparametric models and assessing the ability of such models to provide point and interval estimates of optimal nitrogen values. In this talk, we review our work on parametric models relating yield and nitrogen and discuss future directions based on semiparametric models. This research is joint with Desire Djidonou (Department
of Horticultural Sciences, University of Florida).

Dimension reduction for diffusion tensor images

October 31, 2012, 1:15pm – 2:15pm
SAMSI, Room 150
Speaker: Dan Yang, SAMSI


Diffusion Tensor Imaging (DTI) data can be used to understand the brain structure and connectivity. It is intrinsically large dimensional, which requires dimension reduction. But it has its own feature, namely, for each voxel in a three dimensional space, there a symmetric positive definite matrix associated with it. How to reduce the dimensionality of this type of data to visualize and improve our understanding is an interesting problem. The past work in this direction essentially is a variant of nonnegative matrix factorization by flattening the three dimensional object into a vector, which neglects the spatial structure and results in a solution that is of lower dimension than the original data, but still large. We would like to approach the problem through tensor perspective, which keeps the spatial information and has the potential of further dimension reduction. The challenge is the combination of tensor decomposition method with symmetric positive definite and non-negative constraints. We are trying to develop efficient algorithms that scale with large data, incorporate the smooth structure, and have nice statistical properties. In the end, we hope the methodology, when applied to real data, can help discover more about brain functionality.

The equations of landscape formation: review and a new model

November 7, 2012, 1:15pm – 2:15pm
SAMSI, Room 150
Speaker: Alex Chen, UNC and SAMSI


In this talk, we start by reviewing some models for landscape evolution, many of which are hybrid models, combining fundamental physical laws with empirical modeling. Such models can be valid near equilibrium. Nevertheless, this situation is not satisfactory from the mathematical standpoint, since such models will be valid only for a given landscape or class of landscapes.

We propose a simple landscape model, deduced from mathematical principles, coping with the main features of all models. This model singles out three spatially distributed scalar state variables, namely the landscape elevation, water elevation, and sediment concentration in water. These state variables are linked by three partial differential equations. Two of these equations are mere conservation laws. A third equation copes with the three main features identified in the literature as the main phenomena shaping a landscape: erosion, sedimentation and creep.

Numerical results show that a variety of common landscape features can be reproduced. Furthermore, changing various parameters in the model can alter the morphology of the landscape and the various features observed, even for the same initial landscape. The conjectured mathematical instability and non-uniqueness of landscape evolution is illustrated numerically. On the other hand numerical stability of real landscape topographies under realistic values for their evolution is also observed. Lastly, the model presented also shows promise in the field of channel network restoration, as river networks tend to become sharper with the proper choice of parameters in the erosion model.

Seasonal tropical cyclone forecast

November 14, 2012, 1:15pm – 2:15pm
SAMSI, Room 150
Speaker: Dorit Hammerling, SAMSI


Tropical cyclones such as Hurricane Sandy are events of high societal relevance, causing large damage. The formation of tropical cyclones is inherently a chaotic phenomenon, and predicting a specific occurrence more than weeks ahead will likely remain elusive. There is, however, the possibility to conduct seasonal forecasts, which are typically based on annually or decadally varying climatic modes and patterns.

In a joint effort between the Department of Marine, Earth, and Atmospheric Sciences and the Department of Statistics, a team at NC State has been working and providing such seasonal recasts of tropical cyclones for the Atlantic basin. The forecasts are based on a log-linear regression model. As part of my research, I will work on this forecasting challenge, but I will also be part of the team conducting the operational portion of the 2013 forecast, which is due in April 2013.

In this talk, I will provide an overview of the formation of tropical cyclones, discuss the current forecast model, and present ideas for potentially improving the approach. These ideas are still in brain-storming stage, so I will solicit input and feedback on the short- and long-term improvement ideas.

Implicit regularization by sub-sampling

November 28, 2012, 1:15pm – 2:15pm
SAMSI, Room 150
Speaker: Garvesh Raskutti , SAMSI


Sub-sampling is a very popular technique for data compression and is especially useful for data storage and processing of massive datasets. A central question when using sub-sampling schemes is how much is lost or gained by doing inference on the sub-sample and which sub-sampling schemes lead to the best inference. In this talk, I attempt to address this question by putting sub-sampling into a regularization framework in the case of linear regression. The underlying goal is to use the regularization framework to determine good sub-sampling schemes in terms of leverage scores and relate to existing methods that do sub-sampling based on leverage scores. Preliminary ideas and thoughts are presented.

Mathematics Meets Art: Image Analysis of Paintings

December 5, 2012, 1:15pm – 2:15pm
SAMSI, Room 150
Speaker: Yi Grace Wang, SAMSI


Science has been playing a role to provide art historians with new insights on paintings. Until recently, this research starts to involve image analysis. For the problems of forgery detection and under drawing identification, could image analysis and machine learning be used to assist art experts, especially on disputed paintings and how? This presentation will give you a review of the history in the area as well as bring the challenges and problems for future study.