  This tutorial provides a gentle introduction to the particle
Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear
state-space models together with a software implementation in the statistical
programming language R. We employ a step-by-step approach to develop an
implementation of the PMH algorithm (and the particle filter within) together
with the reader. This final implementation is also available as the package
pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some
intuition as to how the algorithm operates and discuss some solutions to
problems that might occur in practice. To illustrate the use of PMH, we
consider parameter inference in a linear Gaussian state-space model with
synthetic data and a nonlinear stochastic volatility model with real-world
data.
