Nested smoothing algorithms for inference and tracking of heterogeneous multi-scale state-space systems

by   Sara Pérez-Vieites, et al.

Multi-scale problems, where variables of interest evolve in different time-scales and live in different state-spaces. can be found in many fields of science. Here, we introduce a new recursive methodology for Bayesian inference that aims at estimating the static parameters and tracking the dynamic variables of these kind of systems. Although the proposed approach works in rather general multi-scale systems, for clarity we analyze the case of a heterogeneous multi-scale model with 3 time-scales (static parameters, slow dynamic state variables and fast dynamic state variables). The proposed scheme, based on nested filtering methodology of Pérez-Vieites et al. (2018), combines three intertwined layers of filtering techniques that approximate recursively the joint posterior probability distribution of the parameters and both sets of dynamic state variables given a sequence of partial and noisy observations. We explore the use of sequential Monte Carlo schemes in the first and second layers while we use an unscented Kalman filter to obtain a Gaussian approximation of the posterior probability distribution of the fast variables in the third layer. Some numerical results are presented for a stochastic two-scale Lorenz 96 model with unknown parameters.


page 1

page 2

page 3

page 4


Nested Gaussian filters for recursive Bayesian inference and nonlinear tracking in state space models

We introduce a new sequential methodology to calibrate the fixed paramet...

A probabilistic scheme for joint parameter estimation and state prediction in complex dynamical systems

Many problems in the geophysical sciences demand the ability to calibrat...

A Kalman particle filter for online parameter estimation with applications to affine models

In this paper we address the problem of estimating the posterior distrib...

Model uncertainty estimation in data assimilation for multi-scale systems with partially observed resolved variables

Model uncertainty quantification is an essential component of effective ...

Bayesian Multi-scale Modeling of Factor Matrix without using Partition Tree

The multi-scale factor models are particularly appealing for analyzing m...

Inference in Stochastic Epidemic Models via Multinomial Approximations

We introduce a new method for inference in stochastic epidemic models wh...

Data-driven time-scale separation of ODE right-hand sides using dynamic mode decomposition and time delay embedding

Multi-physics simulation often involve multiple different scales. The AR...

Please sign up or login with your details

Forgot password? Click here to reset