parus: POMPs for time series of Parus major population counts from...
In kingaa/pompExamples: Additional POMP Examples

Description State process Measurement process See Also Examples

pompExample(parus) constructs a function that constructs pomp objects implementing each of several population-dynamics models and abundance data from Parus major in Wytham Wood.

The model has one state variable, N_t, the true abundance. There is one observable, \mathrm{pop}_t.

The function defined is:

1 2	parus(proc = c("Gompertz", "Ricker"), meas = c("lognormal","Poisson","negbin"))

If proc="Gompertz", the state process is the stochastic Gompertz model

N_{t} = K^{1-S}\,N_{t-1}^S\,ε_t,

where S=e^r and ε_t\sim\mathrm{Lognormal}(0,σ) i.i.d.

If proc="Ricker", the state process is the stochastic Ricker model

N_{t} = N_{t-1}\,\exp≤ft(r\,≤ft(1-\frac{N_{t-1}}{K}\right)\right)\,ε_t,

where, again, ε_t\sim\mathrm{Lognormal}(0,σ) i.i.d.

There are three alternative measurement models.

If meas="Poisson", the measurement process is

\mathrm{pop}_{t} \sim \mathrm{Poisson}(N_t).

If meas="negbin", the measurement process is

\mathrm{pop}_{t} \sim \mathrm{Negbin}(N_t,θ),

i.e., \mathrm{pop}_t has mean N_t and variance N_t+\frac{N_t^2}{θ}.

If meas="lognormal", the measurement process is

\mathrm{pop}_{t} \sim \mathrm{Lognormal}(\log(N_t),θ).

vignette("parus")

pompExample(parus)
p1 <- parus(proc="Ricker",meas="negbin") 
plot(p1)
plot(simulate(p1))

p2 <- parus(proc="Gompertz",meas="lognormal")
plot(simulate(p2))
pf <- pfilter(p2,Np=1000)