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

TL;DR

bssm is an R package enabling Bayesian inference for complex non-linear, non-Gaussian state space models using approximate methods like Laplace and Kalman filters, with advanced MCMC techniques.

Contribution

It introduces an easy-to-use R package that supports flexible Bayesian inference for non-linear, non-Gaussian models, including diffusion processes, with automatic MCMC and bias correction.

Findings

Supports Gaussian approximations like Laplace and extended Kalman filter.

Includes adaptive MCMC with importance sampling for bias correction.

Provides an Rcpp interface for custom model specification.

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.