This example uses particle marginal Metropolis Hastings to estimate
the standard deviation of the evolution and observation noise in the following
non-linear state space model:
\(x(n) = 0.5 x(n-1) + 25 x(n-1) / (1+x(n-1)^2) + 8 cos(1.2n)+ e(n)\) and
\(y(n) = x(n)^2 / 20 + f(n)\)
where e(n) and f(n) are mutually-independent normal random
variables of variances var_evol and var_obs, respectively,
and \(x(0) ~ N(0,5)\).
Following Andrieu, Doucet and Holenstein (2010), the priors are
\(var_evol ~ IG(0.01,0.01)\) and \(var_obs ~ IG(0.01,0.01)\) where IG
is the inverse gamma distribution.
Data can be simulated from the model using simNonlin
.