Sequential Inference in Dynamical Models
About the project
Statistical Methods for dynamic and spatio-temporal data are
essential in the environmental sciences, public health, inusurance
claims analysis and other fileds where the data have high
dependence in time and space.
For such complex dependence, hierarchical models have gained
increasing both withinthe statistical community. The main advantage
in using hierarchical models is the use of many simple conditional
distributions to model a complex model for high-dimensional problems.
In particular, the division of a process model and an observation
model makes it possible to separate the modelling of the process at
question and integration of different data sources in a coherent way.
In general, we can see hierarchical models in three levels:
Data Model: [data|process, paremeters]
Process Model: [process|parameters]
Parameter Model: [parameters]
Many natural processes evolve in time. Within time-series applications,
state-space models (a particular case of hierarchical models) have a long
history (Harvey, 1990). Modelling the state process through dynamic
(deterministic or stochastic) models are often beneficial in order to infer
causal relationships (Cressie & Wikle, 2011). For linear Gaussian models,
inference can be performed through the Kalman filter. For many realistic
problems, non-linearities frequently occur, making inference problematic.
This is both with respect to computation and more fundamental issues related
to identifiability and model evaluation. Such problems grow exponentially
with the dimension of the state vector.
In this project we will concentrate on the computational issues related
to high-dimensional dynamic hierarchical models (DHM). Many approaches
have been considered for such problems, e.g. extended Kalman filtering,
ensemble Kalman filtering, Markov chain Monte Carlo (MCMC), sequential
Monte Carlo (SMC), integrated nested Laplace approximations (INLA), see
Cressie & Wikle (2011, Chapter 8) for a recent review. Our emphasis will
be sequential methods where inference can be updated as data are included/
arrives, i.e. calculation of the posterior recursively.
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