Related papers: Getting Started with Particle Metropolis-Hastings …

In this tutorial we consider the non-linear Bayesian filtering of static parameters in a time-dependent model. We outline the theoretical background and discuss appropriate solvers. We focus on particle-based filters and present Sequential…

We propose a moving horizon estimation scheme for estimating the states and time-varying parameters of nonlinear systems. We consider the case where observability of the parameters depends on the excitation of the system and may be absent…

Traditional MCMC algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis-Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each…

This work develops a powerful and versatile framework for determining acceptance ratios in Metropolis-Hastings type Markov kernels widely used in statistical sampling problems. Our approach allows us to derive new classes of kernels which…

Estimating the parameters of nonlinear block-oriented state-space models from input-output data typically involves solving a highly non-convex optimization problem, which is prone to poor local minima and slow convergence. This paper…

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…

The multiple-try Metropolis (MTM) algorithm is an extension of the Metropolis-Hastings (MH) algorithm by selecting the proposed state among multiple trials according to some weight function. Although MTM has gained great popularity owing to…

The Metropolis algorithm is a Markov chain Monte Carlo (MCMC) algorithm used to simulate from parameter distributions of interest, such as generalized linear model parameters. The "Metropolis step" is a keystone concept that underlies…

Traditional methods for unsupervised learning of finite mixture models require to evaluate the likelihood of all components of the mixture. This becomes computationally prohibitive when the number of components is large, as it is, for…

Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…

Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data.…

This article addresses the problem of efficient Bayesian inference in dynamic systems using particle methods and makes a number of contributions. First, we develop a correlated pseudo-marginal (CPM) approach for Bayesian inference in state…

We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…

Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distributions. For models that…

Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…

Particle MCMC involves using a particle filter within an MCMC algorithm. For inference of a model which involves an unobserved stochastic process, the standard implementation uses the particle filter to propose new values for the stochastic…

The classical Metropolis-Hastings (MH) algorithm can be extended to generate non-reversible Markov chains. This is achieved by means of a modification of the acceptance probability, using the notion of vorticity matrix. The resulting Markov…

Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps…

Particle learning (PL) provides state filtering, sequential parameter learning and smoothing in a general class of state space models. Our approach extends existing particle methods by incorporating the estimation of static parameters via a…

Probabilistic programming uses programs to express generative models whose posterior probability is then computed by built-in inference engines. A challenging goal is to develop general purpose inference algorithms that work out-of-the-box…