Hierarchical Bayesian strategy for modeling correlated compositional data with observed zero counts

This article proposes a hierarchical multivariate conditional autoregressive model applied to a compositional response vector. We particularly focus on situations when the composition is discrete occurring when observations are based on small multinomial counts. We address drawbacks that exist in current modeling approaches for such data. Our hierarchical model will be demonstrated with data used to help manage a commercial sockeye salmon fishery in the Fraser River of British Columbia.