2.3. Observations¶
For simplicity, we assume that both the prey and predator populations — \(x(t)\) and \(y(t)\) — are directly observed, and that the observation error is distributed normally with zero mean and a known standard deviation \(\sigma_\mathrm{obs}\).
\[\begin{split}\mathbf{x_t} &= [x, y, \alpha, \beta, \delta, \gamma]^T \\ \mathcal{L}(x(t) \mid \mathbf{x_t}) &\sim \mathcal{N}(\mu=x, \sigma=\sigma_\mathrm{obs}) \\ \mathcal{L}(y(t) \mid \mathbf{x_t}) &\sim \mathcal{N}(\mu=y, \sigma=\sigma_\mathrm{obs})\end{split}\]
These observation models are implemented by
pypfilt.examples.predation.ObsModel
, and are used to update our
beliefs about how well each particle \(\mathbf{x_t}\) explains each of the
provided observations (shown below).
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