spatio-temporal modeling for estimation of bigeye tuna catch in the presence of pandemic-related data loss using parametric adjacency structures

Conditionally autoregressive (CAR) space-time models have wide applicability because spatial association structure can be captured through an adjacency matrix, without expressly relying on distance information. However, in the traditional spatio-temporal CAR (STCAR), the adjacency matrix is based on adjacency relationships, which can be problematic in practical applications where those relationships are dependent on non-spatial considerations. A new formulation of a parametric structure for the adjacency structure was developed, offering a functional and flexible solution to this problem. This method is applied to estimate bigeye tuna catch for the purse-seine fishery in the eastern Pacific Ocean for 2020–2021. During the COVID-19 pandemic, collection of some data types for this fishery was severely negatively impacted, resulting in non-random loss of data. To mitigate this, a STCAR model was developed, combining multiple sources of spatio-temporal data to obtain enhanced prediction results. The objective was to produce statistically similar catch estimates to the historical time series on which current fisheries management is based, thereby minimizing bias due to a change in estimation methodology. The traditional CAR formulation assumes uniform weight in defining spatial dependence between neighboring areas when they share boundaries or corners, and no weight when the areal units do not share boundaries or corners. The new parametric approach uses expert opinions to define weighted adjacency in the formulation where the ‘weight’ is based on how substitutions rules apply when data is missing and areas can be ‘adjacent’ in terms of characteristics rather than simply spatially. The new parametric formulation of the adjacency matrix performed best, as compared to traditional formulations, was asymptotic as the parameter got smaller. This parametric specification of the adjacency matrix, along with an AR (1) structure in the STCAR, performed robustly when a sensitivity analysis was carried out by simulating non-random pandemic-like data-loss for pre-pandemic years.