|A Flexible Approach to Bayesian Multiple Curve Fitting
Carsten Botts, Ph.D.,Williams College/ColoradoState University
Monday, October 13, 2008
4:00 p.m. 223 Weber
We model sparse functional data from multiple subjects with a mixed-effects regression spline. In this model, the expected values for any subject (conditioned on the random effects) can be written as the sum of a population curve and a subject-specific deviate from this population curve. The population curve and the subject-specific deviates are both modeled as free-knot b-splines with an unknown number of knots. To identify the number and location of the ``free'' knots, we sample from the posterior distribution of knots using reversible jump MCMC methods. Sampling from this posterior distribution is complicated, however, by the flexibility we allow for the model's covariance structure. No restrictions (other than positive definiteness) are placed on the covariance parameters and, as a result, no analytical form for the appropriate likelihood exists. In this talk, two approximations to the likelihood are considered. We sample from the corresponding posterior distributions and compare these posterior samples.