Dennise Cox
Rice University
Fundamental Issues in Bayesian Functional Data Analysis
We will introduce the basic notion of Functional
Data Analysis (FDA) - that the observed data are
functions of a continuous variable. Practical FDA
requires finite dimensional representation.
We argue that a foundational requirement
of FDA is the Grid Refinement Invariance Principle:
as the funite dimensional representation becomes
more accurate, any statistical inferences should
converge to the equivalent inference on the idealized
functional observations. For Bayesians, the easiest
way to achieve this is to put a prior on the
infinite dimensional function space, which can be
challenging. We shall consider a Gaussian sampling model for
functional data and discuss the challenges of
creating a prior for the unknown covariance of
the Gaussian measure. We will give a practical
prior which can be used and give some numerical
results. We will also present preliminary work on
priors obtained by limits of finite dimensional
inverted Wishart distributions. This is joint work
with Hong Xiao Zhu.