Birch implementation of the ecological model.
x[t] = x[t-1] + b0 + b2 exp(b3 x[t-1]) + w[t]
y[t] = x[t] + v[t]
Where w[t] ~ N(0, Q) and v[t] ~ N(0, R).
We use conjugate priors for b0, b2, Q, and R. The parameter b3 has a
normal prior:
R ~ InverseGamma(α_R, β_R)
Q ~ InverseGamma(α_Q, β_Q)
[b0, b2] ~ Gaussian(μ, S*Q)
b3 ~ Gaussian(μ3, s2)
x[t] ~ Gaussian(x[t-1] + b0 + b2 exp(b3 x[t-1]), Q)
y[t] ~ Gaussian(x[t], R)
Build and install
birch build
birch install
The file input/observation_data.json contains data from observations of song
birds between 1976 and 1998 (extracted from Saether et al., "Estimating the time to Extinction
in an island population of song sparrows", Proc. Biol. Sci., Vol. 267, No. 1443
(2000), pp. 621-626).
The model has a proposal function that can be use together with the
ParticleMarginalMetropolisHasting sampler in the metropolis-hastings branch
of the Birch standard library. Note that you need to use commit 55a047c of the
Birch language to run the simulation.