The Poisson-Binomial Model for Fish Abundance Estimation: With Applications to Northeast Arctic cod

• Main Author: Moss, Kjersti
• Format: Master Thesis
• Language: English
• Published: 2015
• Subjects: Importance; sampling; Monte; Carlo; methods; Identifiability; Poisson; binomial; model; Bayesian; state; space; Abundance; estimation; Population; dynamics; Arctic; Arctic cod; Northeast Arctic cod; Skrei
• Online Access: http://hdl.handle.net/10852/49341; http://urn.nb.no/URN:NBN:no-53206

The Institute of Marine Research collects data from different sources for the estimation of fish abundance. These data can be divided into two groups: 1) Data from research surveys. 2) Fishery based data. In this thesis, we aim to utilize both data sets to estimate the abundance of fish, along with the catch. In addition to a point estimate, we wish to assess the uncertainty in these estimates. More formally, we hope to find quantiles of the simultaneous distribution p(N,C|Data,parameters), that is, the distribution of the abundances and catches, given both data sources. On the way towards this goal, we need to specify a model for the abundance, the catch, and the data. The model for the abundance and catch is what we call the Poisson-binomial model. This model is the central theme of the thesis. We explore the properties of the model, and derive conditions for when it is identifiable. Furthermore, we investigate both a frequentistic and a Bayesian method to estimate the model parameters. It turns out that we are not able to describe the simultaneous distribution p(N,C|Data,parameters) analytically, and we can neither sample directly from it. However, we can obtain Monte Carlo samples of this distribution through importance sampling techniques, and thereby calculate approximate quantiles. The methods we develop are applied to data on Northeast Arctic cod (Skrei in Norwegian), from the years 1985-2003.