Related papers: MCMC for State Space models
In the case of a linear state space model, we implement an MCMC sampler with two phases. In the learning phase, a self-tuning sampler is used to learn the parameter mean and covariance structure. In the estimation phase, the parameter mean…
We consider the challenge of estimating the model parameters and latent states of general state-space models within a Bayesian framework. We extend the commonly applied particle Gibbs framework by proposing an efficient particle generation…
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…
We describe a Markov latent state space (MLSS) model, where the latent state distribution is a decaying mixture over multiple past states. We present a simple sampling algorithm that allows to approximate such high-order MLSS with fixed…
State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time…
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
State space models are well-known for their versatility in modeling dynamic systems that arise in various scientific disciplines. Although parametric state space models are well studied, nonparametric approaches are much less explored in…
Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions…
Non-linear state space models are a widely-used class of models for biological, economic, and physical processes. Fitting these models to observed data is a difficult inference problem that has no straightforward solution. We take a…
We introduce state-space models where the functionals of the observational and the evolutionary equations are unknown, and treated as random functions evolving with time. Thus, our model is nonparametric and generalizes the traditional…
We present a scalable approach to performing approximate fully Bayesian inference in generic state space models. The proposed method is an alternative to particle MCMC that provides fully Bayesian inference of both the dynamic latent states…
Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…
Particle MCMC is a class of algorithms that can be used to analyse state-space models. They use MCMC moves to update the parameters of the models, and particle filters to propose values for the path of the state-space model. Currently the…
State-space models (SSMs) are commonly used to model time series data where the observations depend on an unobserved latent process. However, inference on the model parameters of an SSM can be challenging, especially when the likelihood of…
We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…
State space models contain time-indexed parameters, termed states, as well as static parameters, simply termed parameters. The problem of inferring both static parameters as well as states simultaneously, based on time-indexed observations,…
We investigate nonlinear state-space models without a closed-form transition density, and propose reformulating such models over their latent noise variables rather than their latent state variables. In doing so the tractable noise density…
Hidden Markov models (HMMs) offer a robust and efficient framework for analyzing time series data, modelling both the underlying latent state progression over time and the observation process, conditional on the latent state. However, a…
State-space models effectively model multivariate time series by updating over time a representation of the system state from which predictions are made. The state representation is usually a vector without any explicit structure.…