Past Working Groups

Description: The “microbiome” group studied and developed models and methods for effective analysis of microbiome data in the context of predicting health outcomes and inferring the underlying biological processes. Some problems to be investigated include modeling the latent structure in compositional data, integrating microbiome data with other “-omics” data, and modeling dynamics of microbiome data.

Description: Neural networks, deep and otherwise, have recently set the standard for performance in a number of challenging tasks in the disciplines of computer vision, natural language processing, speech recognition, and so on. These highly expressive, graphical models have also proven effective in a range of tasks in biology and medicine. Despite the many application successes of neural networks, theory and even empirical best practices for specification and selection of these models is still under development. Current practices in the field, while effective, could be (and in some cases have already been) enhanced with a statistical approach. We believe there is an opportunity for researchers from statistical and mathematical disciplines to contribute and adapt their perspectives and techniques for model specification, estimation of predictive uncertainty, incorporation of prior/domain information and other common statistical tasks to the field of neural networks. This working group aimed at creating an updated (Cheng and Titterington did it back in 1994), open, and community-driven review article that bridged exciting recent developments in statistical and neural network modeling as well as at their interface. The review highlighted state-of-the-art statistics-based neural network models, developed rough guidelines for carrying out routine statistical tasks in the neural network context, and listed software and data resources for the development and application of neural network models in biomedical research. The working group leveraged this knowledge to develop and evaluate neural network models for detection of structural abnormalities in a publicly available set of musculo-skeletal radiographs.

Description: A goal of developing personalized medicine changes the focus in clinical trials to decision making for the individual, or subgroups, rather than more traditional treatment comparison via average response. This change of focus has implications for all aspects of clinical trials. The group focused on the study of the role of heterogeneity/subgroups in clinical trials in three ways: (1) prepare a review paper(s) on methods for identification of subgroups, beginning with analysis of existing clinical trials data (where a drug may have “failed” at the population level), then exploring the design of clinical trials for the purpose of identifying subgroups (“responders”), and potentially also studying methods for shrinkage over subgroups such as are used in basket trials. (2) The group studied the implications of heterogeneity/subgroups in resource allocation in clinicals, specifically the influence on decision making at interim analysis points. (3) The group attempted to quantify the contribution of a single agent in trials that evaluate sequence of agents (such as SMART studies). A 4th area of strong interest was handling multiple, competing utilities in clinical trial design, particularly incorporating patient-specific utility functions.

This course provided a comprehensive introduction to methodology for data-based development and evaluation of dynamic treatment regimes. A dynamic treatment regime is a set of sequential decision rules, each corresponding to a key point in a disease or disorder process at which a decision on the next treatment action must be made. Each rule takes patient information to that point as input and returns the treatment s/he should receive from among the available options, thus tailoring treatment decisions to a patient’s individual characteristics. Methods will be motivated and developed through a formal time-dependent causal inference framework. Examples were drawn from cancer and other chronic disease research and research in the behavioral, educational, and other sciences.

Schedule: January 9 – April 24, 2019 / Wednesdays at 4:30PM – 7:00PM

Description: The group sought to quantify faithfulness/accuracy of reduced order models to the science. We further seek methods for the development/creation of reduced order models that leverage scientific knowledge. The theoretical and practical advancements in reduced order models should be applicable to modern scientific settings.

Description: This research thrust sought to develop methods and case studies for developing physically motivated error models to account for the discrepancy between computational model and reality, resulting in more reliable prediction uncertainties. This thrust considered a number of applications and activities that motivated new modeling approaches, helped to determine overarching principles for identifying settings in which reliable prediction uncertainties can be developed.

Potential projects included:

• discrepancy models for OCO-2 or simpler test model
• discovering pde structure to better characterize discrepancy between model and reality
• use of stochastic “emulators” to better capture the link between model and reality
• Discrepancy models in rich/structured design space
• Designing model runs and physical experiments in additive manufacturing
• Potential workshop on agent-based models in November

Description:
Integration of multiple data sources to:
1. Infer upon the parameters/inputs to a computer model (data fusion in the UQ world)
2. Obtain improved inference/predictions on process (data fusion of model outputs and observations)
3. Deal with datasets of varying qualities

This course introduced statistical and mathematical sensitivity analysis and uncertainty quantification techniques for large-scale models arising in current applications. This included the construction and verification of surrogate models and emulators for complex simulation models, frequentist and Bayesian inference techniques, and techniques to quantify uncertainties associated with statistical quantities of interest. Examples were drawn from applications in materials science, biology and biomedical sciences, and nuclear engineering.

Schedule: August 28 – December 4, 2018 / Tuesdays at 4:30PM – 7:00PM

• Time series methods and assessments of trends in climatological data
• Analysis of large spatial datasets in climate research
• Methods based on Empirical Orthogonal Functions
• Climate Informatics: the application of machine learning methods and high-performance computing in climate research
• Statistics for climate extremes
• Climate and Health

Schedule: August 29 – December 5, 2017 / Tuesdays at 4:30PM – 7:00PM

Description: The accuracy and robustness of numerical predictions that are based on mathematical models depend critically upon the construction of accurate discrete approximations to key quantities of interest. The exact error due to approximation will be unknown to the analyst, but worst-case upper bounds can often be obtained. This working group aims, instead, to develop Probabilistic Numerical Methods, which provide the analyst with a richer, probabilistic quantification of the numerical error in their output, thus providing better tools for reliable statistical inference.

Description: In recent years, several algorithms, based on interacting samplers, have been proposed and further advanced; such algorithms have been used in various settings, including high dimensional Bayesian sampling, particle filtering, computational physics, etc. This working group plans to explore the connections between various ideas proposed in different communities and try to advance the theoretical understanding of efficiency and design principle for such sampling algorithms.

Description: Representative points, which compact a probability distribution into a finite point set, are useful for a wide array of “small-data” and “big-data” problems. Small-data problems arise naturally in many engineering applications, where a key challenge is to allocate limited experimental runs for performing functional approximation, uncertainty propagation or design optimization. Similarly, given the massive volume, variety and velocity of big-data (particularly in Bayesian problems), the reduction of such datasets using representative points allows for meaningful and timely analysis. This working group aims to investigate the theory and application of representative points to the aforementioned small-data and big-data problems, with an emphasis on engineering applications and Bayesian computation.

Description: For some problems, generating observations (multivariate function values) is expensive, such as running a time-consuming computer code or conducting a real-world experiment. This can result in having only a few samples for high-dimensional input variables. These samples can be noisy and may not be available for some important ranges of the parameters. Examples include medical trials, large-scale computer simulations, such as climate models, and financial market data. This working group will study how to best use the available small samples and how strategically guide picking future samples. The group will consider algorithms based on assumptions about the underlying input-output relationship to improve the effectiveness of the statistical analysis under these difficult constraints. The assumption will be that the cost of the observations will far exceed the computational cost of the post-processing algorithms.

Description: High dimensional numerical integration problems can often be solve efficiently using algorithms devised for weighted Sobolev spaces. A given black box function may belong to all of the spaces people use. That raises the question of which weights to be used. This WG looks at methods to select weights using ideas from global sensitivity analysis and active subspaces.

Description: The multivariate decomposition method allows us to approximate infinite-dimensional problems by a sum of finite-dimensional subproblems in the “active set” whose size depends on the requested error demand. The weight structure imposed on these finite-dimensional subspaces often implies that the maximum number of variables in each subspace grows very slowly in terms of the requested error demand. Thus we only need to solve many low-dimensional problems (say, 1, 2, 3 dimensional) and a few medium-dimensional problems (say, up to 10 dimensions) to reach a reasonable error demand. These problems can be solved in parallel. The working group will develop efficient implementation of the MDM and consider its application to PDE problems with random coefficients as well as other potential applications.

Description: Quasi-Monte Carlo methods have recently been successfully used in calculating expected values of quantities of interests which depend on the solutions of PDEs with random coefficients, for so-called “uniform” and “lognormal” random fields. The construction of “randomly shifted lattice rules” and “interlaced polynomial lattice rules” based on decay properties of the random field has been implemented in the QMC4PDE software package.

The working group will extend the theory and implementation of these methods in various directions: for example, to generate lognormal random fields by the circulant embedding technique, to stochastic wave propagation, to neutron diffusion, to Bayesian inverse problems in uncertainty quantification, and more.

Description: The working group studies multivariate algorithms for numerical integration and function approximation in the context of Information-Based Complexity (IBC). Apart from deriving error bounds for these algorithms, we are particularly interested in studying how much information about a given problem is needed to solve it to within a given error bound.

Description: Lattice rules are normally applied in the context of integrating periodic functions. There are however several results known in which lattice rules can be used in the context of non-periodic function spaces. We are interested in obtaining higher-order convergence for such non-periodic function spaces.

As a first wild idea, inspired by an interpretation of tent-transormed lattice rules as trapezoidal rules over a billiard ball trajectory, we might look at a fractal-transform which generates a Simpson’s rule. We are then interested in deriving worst-case error bounds which show higher-order convergence.

The dynamics of networks working group is exploring a variety of mathematical and statistical approaches for describing and understanding the changing connection topology of networks over time, the interplay of these network dynamics with other dynamic processes on the network, and the connections between these different mathematical and statistical methodologies.

Random graphs are useful models of social and technological networks. To date most of the research in this area has concerned geometric properties of the graphs. This working group will focus on processes taking place ON the network. In particular we are interested in how their behavior on networks differs from  that in homogeneously mixing populations or on regular lattices of the type commonly used in ecology and physics.