Abstract
Abstract A Bayesian hierarchical model was applied to acoustic backscattering data collected on Mysis relicta (opossum shrimp) populations in Lake Ontario in 2005 to estimate the combined uncertainty in mean density estimates as well as the individual contributions to that uncertainty from the various information sources involved in the calculation including calibration, target strength determination, threshold specification and survey sampling design. Traditional estimation approaches often only take into account the variability associated with the survey design, while assuming that all other intermediate parameter estimates used in the calculations are fixed and known. Unfortunately, unaccounted for variation in the steps leading up to the global density estimate may make significant contributions to the uncertainty of density estimates. While other studies have used sensitivity analyses to demonstrate the degree to which uncertainty in the various input parameters can influence estimates, including the uncertainty directly as demonstrated here using a Bayesian hierarchical approach allows for a more transparent representation of the true uncertainty and the mechanisms needed for its reduction. A Bayesian analysis of the mysid data examined here indicates that increasing the sample size of biological collections used in the target strength regression prove to be a more direct and practical way of reducing the overall variation in mean density estimates than similar steps employed to increase the number of transects surveyed. A doubling of target strength net tow samples resulted in a 23% reduction in variance relative to an 11% reduction that resulted from doubling the number of survey transects. This is an important difference as doubling the number of survey transects would add 5 days to the survey whereas doubling the number of net tows would add only one day. Although these results are specific to this particular data set, the method described is general.
Highlights
Assessment scientists engaged in conducting acoustic surveys of marine and freshwater populations have long recognized that there are several sources of variation contributing to the overall uncertainty in population estimates (Simmonds et al, 1992; Simmonds and MacLennan, 2005)
The posterior density estimates of mysid abundance from the fully parameterized Bayesian model can be compared to a t distribution parameterized using the mean and variance derived from the classical cluster sampling analysis, where the only variation explicitly included is that due to the sampling design (Figure 5)
Other techniques have been used to examine which components in the process are the most likely to influence estimates, but the Bayesian hierarchical framework provides a relatively straightforward mechanism for directly including auxiliary information and appropriately characterizing the uncertainty in the estimation process
Summary
Assessment scientists engaged in conducting acoustic surveys of marine and freshwater populations have long recognized that there are several sources of variation contributing to the overall uncertainty in population estimates (Simmonds et al, 1992; Simmonds and MacLennan, 2005). Once such approach is Bayesian hierarchical modelling (Gelman et al, 2014) This statistical method often uses Markov Chain Monte Carlo (MCMC) simulation to create a posterior distribution of the probability that the population density is at a particular level and does so by combining all the different contributing sources of information (e.g. data, expert information, or sampling design) into a single hierarchical framework. The architecture of the MCMC algorithm typically allows the complex contribution of all of these pieces of information to come together into a single cohesive probability distribution even when no theoretical distribution can be analytically derived Such estimates could be derived using other statistical frameworks, such as penalized likelihood methods, the Bayesian approach results in estimates that can be more interpreted as probabilities of a population being at a certain level, which assists in determining risk in a straightforward manner
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