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Abstract:
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Modeling nonlinear processes, such as population dynamics, has been given much attention in mathematics. For example, species competition has been extensively modeled by differential equations. It is of both scientific and mathematical interest to utilize such models in a statistical framework. This incorporation allows one to quantify uncertainty associated with random effects, such as demographic and environmental stochasticity, and thus assess the accuracy of deterministic model components. In this pursuit, parameters of the process models are characterized in a Bayesian hierarchical context, using discretizations with varying levels of precision to assess the necessity of higher-order approximations.
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