  We investigate nonlinear state-space models without a closed-form transition
density, and propose reformulating such models over their latent noise
variables rather than their latent state variables. In doing so the tractable
noise density emerges in place of the intractable transition density. For
importance sampling methods such as the auxiliary particle filter, this enables
importance weights to be computed where they could not be otherwise. As case
studies we take two multivariate marine biogeochemical models and perform state
and parameter estimation using the particle marginal Metropolis-Hastings
sampler. For the particle filter within this sampler, we compare several
proposal strategies over noise variables, all based on lookaheads with the
unscented Kalman filter. These strategies are compared using conventional means
for assessing Metropolis-Hastings efficiency, as well as with a novel metric
called the conditional acceptance rate for assessing the consequences of using
an estimated, and not exact, likelihood. Results indicate the utility of
reformulating the model over noise variables, particularly for fast-mixing
process models.
