blowflies1 and blowflies2 are pomp objects encoding stochastic delay-difference models.
The models are discrete delay equations:
$$R(t+1) \sim \mathrm{Poisson}(P N(t-\tau) \exp{(-N(t-\tau)/N_{0})} e(t+1) {\Delta}t)$$
$$S(t+1) \sim \mathrm{binomial}(N(t),\exp{(-\delta \epsilon(t+1) {\Delta}t)})$$
$$N(t) = R(t)+S(t)$$
where $e[t]$ and $eps[t]$ are Gamma-distributed i.i.d. random variables with mean 1 and variances $sigma.p^2/dt$, $sigma.d^2/dt$, respectively.
blowflies1 has a timestep ($dt$) of 1 day, and blowflies2 has a timestep of 2 days.
The process model in blowflies1 thus corresponds exactly to that studied by Wood (2010).
The measurement model in both cases is taken to be
$$y(t) \sim \mathrm{negbin}(N(t),1/\sigma_y^2)$$, i.e., the observations are assumed to be negative-binomially distributed with mean $N[t]$ and variance $N[t]+(sigma.y N[t])^2$.
Do
pompExample(blowflies,show=TRUE)to view the code that constructs these pomp objects.
E. L. Ionides (2011) Discussion of ``Feature Matching in Time Series Modeling'' by Y. Xia and H. Tong. Statistical Science 26, 49--52.
S. N. Wood (2010) Statistical inference for noisy nonlinear ecological dynamic systems. Nature 466, 1102--1104. W. S. C. Gurney, S. P. Blythe, and R. M. Nisbet (1980) Nicholson's blowflies revisited. Nature 287, 17--21.
D. R. Brillinger, J. Guckenheimer, P. Guttorp and G. Oster (1980) Empirical modelling of population time series: The case of age and density dependent rates. in G. Oster (ed.), Some Questions in Mathematical Biology, vol. 13, pp. 65--90. American Mathematical Society, Providence.
pomppompExample(blowflies)
plot(blowflies1)
plot(blowflies2)
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