We provide a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state space models (SSMs) together with a software implementation in the statistical programming language R. Throughout this tutorial, we develop an implementation of the PMH algorithm (and the integrated particle filter ), which is distributed as the package pmhtutorial available from the CRAN repository. Moreover , we provide the reader with some intuition for how the algorithm operates and discuss some solutions to numerical problems that might occur in practice. To illustrate the use of PMH, we consider parameter inference in a linear Gaussian SSM with synthetic data and a nonlinear stochastic volatility model with real-world data . We conclude the tutorial by discussing important possible improvements to the algorithm and we also list suitable references for further study .
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 on 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 .
R
We provide
This tutorial provides
R
state space models (SSMs)
state-space models
R
Throughout this tutorial, we
We employ a step-by-step approach to
R
integrated particle filter ), which is distributed
particle filter within) together with the reader. This final implementation is also available
R
available from
on
R
Moreover
Throughout the tutorial
R
the reader with some intuition for
some intuition as to
D
numerical
R
SSM
state-space model
D
. We conclude the tutorial by discussing important possible improvements to the algorithm and we also list suitable references for further study