  We present an R package bssm for Bayesian non-linear/non-Gaussian state space
modelling. Unlike the existing packages, bssm allows for easy-to-use
approximate inference for the latent states based on Gaussian approximations
such as the Laplace approximation and the extended Kalman filter. The package
accommodates also discretised diffusion latent state processes. The inference
is based on fully automatic, adaptive Markov chain Monte Carlo (MCMC) on the
hyperparameters, with optional importance sampling post-correction to eliminate
any approximation bias. The package implements also a direct pseudo-marginal
MCMC or a delayed acceptance pseudo-marginal MCMC using the approximations. The
package supports directly models with linear-Gaussian state dynamics (but with
non-Gaussian observation models), and has an Rcpp interface for specifying
custom non-linear models.
