Seminar by Kartik Waghmare

Conditional Independence in Continuous Domain

The concept of conditional independence allows us to distinguish between direct and indirect associations in data and thus has a long history in statistics. Its application to statistical modeling and inference in the context of continuous time stochastic processes or random fields, however, has been obstructed by technical difficulties arising from working with infinite-dimensional function spaces. In a second-order or Gaussian setting, we show how the theory of reproducing kernels allows us to fruitfully study conditional independence in a continuous context by circumventing these difficulties and how the insights it furnishes can be applied to the problems of (a) covariance estimation for partially observed functional data with application to longitudinal studies in medicine and (b) modeling stochastic processes as graphical models corresponding to continuous graphs with application to fMRI studies of brain functional networks.