  We propose a Bayesian approach to estimating parameters in multiclass
functional models. Unordered multinomial probit, ordered multinomial probit and
multinomial logistic models are considered. We use finite random series priors
based on a suitable basis such as B-splines in these three multinomial models,
and classify the functional data using the Bayes rule. We average over models
based on the marginal likelihood estimated from Markov Chain Monte Carlo (MCMC)
output. Posterior contraction rates for the three multinomial models are
computed. We also consider Bayesian linear and quadratic discriminant analyses
on the multivariate data obtained by applying a functional principal component
technique on the original functional data. A simulation study is conducted to
compare these methods on different types of data. We also apply these methods
to a phoneme dataset.
