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.
Highlights
State space models (SSM) are a flexible class of latent variable models commonly used in analyzing time series data
There are several packages available for state space modeling for R, especially for two special cases: a linear-Gaussian SSM (LGSSM) where both the observation and state densities are Gaussian with linear relationships with the states, and an SSM with discrete state space, which is sometimes called a hidden Markov model (HMM)
The joint posterior is typically very high dimensional, and due to the strong autocorrelation structures of the state densities, the efficiency of such methods can be relatively poor. Another asymptotically exact approach is based on the pseudo-marginal particle Markov chain Monte Carlo (MCMC) approach (Andrieu et al, 2010), where the likelihood function and the state distributions are estimated using sequential Monte Carlo (SMC), i.e., the particle filter (PF) algorithm
Summary
State space models (SSM) are a flexible class of latent variable models commonly used in analyzing time series data (cf. Durbin and Koopman, 2012). The present R package bssm is designed for Bayesian inference of general state space models with non-Gaussian and/or non-linear observational and state equations. The joint posterior is typically very high dimensional, and due to the strong autocorrelation structures of the state densities, the efficiency of such methods can be relatively poor Another asymptotically exact approach is based on the pseudo-marginal particle MCMC approach (Andrieu et al, 2010), where the likelihood function and the state distributions are estimated using sequential Monte Carlo (SMC), i.e., the particle filter (PF) algorithm. A general state space model consists of two parts: observation level densities gt(θ)(yt|αt) and latent state transition densities μ(t θ ) (αt+1 |αt ) Both gt(θ) and (θ) μt depend on unknown parameter vector θ for which we can define arbitrary prior p(θ).
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