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Abstract:
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Integral population models are a method used to describe the change in population over time for a specific species when the metric used to measure an individual's size is assumed to be continuous. Typically, elements of the integral projection model such as fecundicity, growth rates, and size at recruitment are modeled separately, irrespective of the other components, and then combined. Under a Bayesian framework, the parameters of an integral projection model can be learned using complete conditionals. Additionally, the discretized grid typically used to evaluate the integral is replaced with a finite sum of basis coefficients derived from expanding the kernel of the integral population model and the population density with orthonormal basis functions. This allows the estimated population density function to be continuous, which is a motivating condition of integral population models to begin with. Using an integral population model as the process level and a poisson process as the observation level we treat the model as a nonlinear and non-Gaussian dynamic model, which will be estimated using sequential Monte Carlo steps.
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