Probabilistic learning of nonlinear dynamical systems using sequential Monte Carlo
  Probabilistic modeling provides the capability to represent and manipulate
uncertainty in data, models, predictions and decisions. We are concerned with
the problem of learning probabilistic models of dynamical systems from measured
data. Specifically, we consider learning of probabilistic nonlinear state-space
models. There is no closed-form solution available for this problem, implying
that we are forced to use approximations. In this tutorial we will provide a
self-contained introduction to one of the state-of-the-art methods---the
particle Metropolis--Hastings algorithm---which has proven to offer a practical
approximation. This is a Monte Carlo based method, where the particle filter is
used to guide a Markov chain Monte Carlo method through the parameter space.
One of the key merits of the particle Metropolis--Hastings algorithm is that it
is guaranteed to converge to the "true solution" under mild assumptions,
despite being based on a particle filter with only a finite number of
particles. We will also provide a motivating numerical example illustrating the
method using a modeling language tailored for sequential Monte Carlo methods.
The intention of modeling languages of this kind is to open up the power of
sophisticated Monte Carlo methods---including particle
Metropolis--Hastings---to a large group of users without requiring them to know
all the underlying mathematical details.
