  Probabilistic (or Bayesian) modeling and learning offers interesting
possibilities for systematic representation of uncertainty using probability
theory. However, probabilistic learning often leads to computationally
challenging problems. Some problems of this type that were previously
intractable can now be solved on standard personal computers thanks to recent
advances in Monte Carlo methods. In particular, for learning of unknown
parameters in nonlinear state-space models, methods based on the particle
filter (a Monte Carlo method) have proven very useful. A notoriously
challenging problem, however, still occurs when the observations in the
state-space model are highly informative, i.e. when there is very little or no
measurement noise present, relative to the amount of process noise. The
particle filter will then struggle in estimating one of the basic components
for probabilistic learning, namely the likelihood $p($data$|$parameters$)$. To
this end we suggest an algorithm which initially assumes that there is
substantial amount of artificial measurement noise present. The variance of
this noise is sequentially decreased in an adaptive fashion such that we, in
the end, recover the original problem or possibly a very close approximation of
it. The main component in our algorithm is a sequential Monte Carlo (SMC)
sampler, which gives our proposed method a clear resemblance to the SMC^2
method. Another natural link is also made to the ideas underlying the
approximate Bayesian computation (ABC). We illustrate it with numerical
examples, and in particular show promising results for a challenging
Wiener-Hammerstein benchmark problem.
