bssm: Bayesian Inference of Non-linear and Non-Gaussian State Space Models in R

Abstract

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 based on Gaussian approximations such as the Laplace approximation and the extended Kalman filter. The package accommodates also discretely observed latent diffusion 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 and a delayed acceptance pseudo-marginal MCMC using intermediate approximations. The package offers an easy-to-use interface to define models with linear-Gaussian state dynamics with non-Gaussian observation models, and has an Rcpp interface for specifying custom non-linear and diffusion models.