Statistical Models for Dependent High-Dimensional Data


Statistical Models for Dependent High-Dimensional Data

These researchers are involved in several projects using MSI.

  • Statistical Methods for Spatial Data: This research on spatial models has focused on regression inference for areal, i.e., spatially aggregated, data. Areal data are common in many fields, including forestry, marketing, epidemiology, image analysis, and ecology. Since investigators in these fields are often interested in scientific explanations rather than, or in addition to, predictions, spatial regression is important.
  • Spatiotemporal Inference for fMRI Data: Typical fMRI experiments generate large datasets that exhibit complex spatial and temporal dependence. Fitting a full statistical model to such data can be so computationally burdensome that many practitioners resort to fitting oversimplified models, which can lead to lower quality inference. These researchers have developed a full statistical model that permits efficient computation.
  • Joint Models for Longitudinal Data: The researchers have developed semiparametric and nonparametric joint models for multidimensional longitudinal outcomes. Although they focus on revealing time-varying dependence relationships, the frameworks accommodate all manner of time- varying parameters for the coordinate processes: regression coefficients, variances, etc. These methods will allow researchers to reveal complex dynamic patterns of dependence and response–predictor relationships.
  • Piecewise Growth Mixture Models: This project focused on piecewise growth mixture models (PGMM), a special case of the finite mixture of multinormals. The researchers investigated Bayesian inference for PGMMs and maximum likelihood inference by expectation maximization.
  • Bayesian Inference for Gaussian Copula Regression Models: Gaussian copula regression models (GCRM) provide a flexible, intuitive framework for modeling high- dimensional dependent outcomes. When such outcomes are discrete, the likelihood is computationally intractable because the running time grows exponentially in the sample size. These researchers developed three computationally feasible approaches to Bayesian inference for GCRMs with discrete outcomes.

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