Probabilistic modeling provides the capability to represent and manipulateuncertainty in data, models, predictions and decisions. We are concerned withthe problem of learning probabilistic models of dynamical systems from measureddata. Specifically, we consider learning of probabilistic nonlinear state-spacemodels. There is no closed-form solution available for this problem, implyingthat we are forced to use approximations. In this tutorial we will provide aself-contained introduction to one of the state-of-the-art methods---theparticle Metropolis--Hastings algorithm---which has proven to offer a practicalapproximation. This is a Monte Carlo based method, where the particle filter isused 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 itis guaranteed to converge to the "true solution" under mild assumptions,despite being based on a particle filter with only a finite number ofparticles. We will also provide a motivating numerical example illustrating themethod using a modeling language tailored for sequential Monte Carlo methods.The intention of modeling languages of this kind is to open up the power ofsophisticated Monte Carlo methods---including particleMetropolis--Hastings---to a large group of users without requiring them to knowall the underlying mathematical details.
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