  We propose a Bayesian method to detect change points for functional data. We
extract the features of a sequence of functional data by the discrete wavelet
transform (DWT), and treat each sequence of feature independently. We believe
there is potentially a change in each feature at possibly different time
points. The functional data evolves through such changes throughout the
sequences of observations. The change point for this sequence of functional
data is the cumulative effect of changes in all features. We assign the
features with priors which incorporate the characteristic of the wavelet
coefficients. Then we compute the posterior distribution of change point for
each sequence of feature, and define a matrix where each entry is a measure of
similarity between two functional data in this sequence. We compute the ratio
of the mean similarity between groups and within groups for all possible
partitions, and the change point is where the ratio reaches the minimum. We
demonstrate this method using a dataset on climate change.
