  In this paper we identify the changing frequency behaviour of multinomial
counts of fish species discarded by vessels in the Irish Sea. We use a Bayesian
hierarchical model which captures dynamic frequency changes via a shrinkage
model applied to wavelet basis functions. Wavelets are known for capturing data
features at different temporal scales; we use a recently-proposed shrinkage
prior from the factor analysis literature so that features at the finest levels
of detail exhibit the greatest shrinkage. Rather than using a multinomial
distribution for monitoring the changes in discards over time, which can be
slow to fit and inflexible, we use a nested zero-and-N inflated (ZaNI) binomial
distribution which enables much faster computation with no obvious
deterioration in model flexibility. Our results show that seasonal behaviour in
these data are not regular and occur at different frequencies. We also show
that the nested ZaNI binomial distribution is a good fit to multinomial count
data of this sort when an informative nested structure is applied.
