Frequency behaviour for multinomial counts of fisheries discards via a nested wavelet zero and N inflated binomial model

TL;DR

This paper models the changing frequency patterns of fish discard counts in the Irish Sea using a Bayesian hierarchical wavelet approach with a nested ZaNI binomial distribution, revealing irregular seasonal behaviors.

Contribution

It introduces a novel Bayesian hierarchical model combining wavelet basis functions and a nested ZaNI binomial distribution for efficient and flexible analysis of multinomial count data.

Findings

Seasonal discard patterns are irregular and occur at multiple frequencies.

The nested ZaNI binomial model fits multinomial count data effectively.

Wavelet-based shrinkage captures dynamic frequency changes in the data.

Abstract

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.