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Modelling hierarchy

Bayesian inference is not the epidemic simulator

Let D be access-period data and Theta the transmission-rate vector. EpiPvr estimates

\[ p(\Theta\mid D). \]

This is uncertainty about biological parameters.

Branching process

EpiPvr can then combine transmission and local field parameters in a multitype branching process to estimate an early invasion probability

\[ P_{\mathrm{est}}=1-q. \]

That calculation concerns stochastic extinction versus establishment when infection is rare.

Mean field

The meanfield mixture model provides deterministic population-average dynamics. Cropmix generalizes the SPT form to an arbitrary number of varieties and uses it as a consistency reference.

Spatial Gillespie CTMC

Cropmix explicitly tracks plant states and virus-bearing vector counts at planting locations. The Gillespie algorithm generates complete stochastic field trajectories conditional on parameters.

Two sources of uncertainty

Cropmix distinguishes:

  • parameter uncertainty from p(Theta | D);
  • process stochasticity from the finite epidemic CTMC.

The full predictive target is

\[ p(\mathcal O\mid D,z) = \int p_{\mathrm{CTMC}}(\mathcal O\mid z,\Theta) p(\Theta\mid D)\,d\Theta. \]

Version 0.1 exposes EpiPvr posterior draws and can accept coherent TransmissionDraw objects. Full Bayesian optimization across many varieties is a planned extension.