scholarly journals Stochastic Modelling of the Spatial Spread of Influenza in Germany

2016 ◽  
Vol 35 (1) ◽  
Author(s):  
Christiane Dargatz ◽  
Vera Georgescu ◽  
Leonhard Held
Keyword(s):  
Markov Random Fields ◽  
Temporal Structure ◽  
Stochastic Modelling ◽  
Cancer Registries ◽  
Spatial Spread ◽  
Explanatory Variables ◽  
Gaussian Markov Random Fields ◽  
Spatial Graphs ◽  
Geographical Epidemiology ◽  
Spatio Temporal

In geographical epidemiology, disease counts are typically available in discrete spatial units and at discrete time-points. For example, surveillance data on infectious diseases usually consists of weekly counts of new infections in pre-defined geographical areas. Similarly, but on a different timescale, cancer registries typically report yearly incidence or mortality counts in administrative regions.A major methodological challenge lies in building realistic models for spacetime interactions on discrete irregular spatial graphs. In this paper we will discuss an observation-driven approach, where past observed counts in neighboring areas enter directly as explanatory variables, in contrast to the parameterdriven approach through latent Gaussian Markov random fields (Rue and Held, 2005) with spatio-temporal structure. The main focus will lie on the demonstration of the spread of influenza in Germany, obtained through the design and simulation of a spatial extension of the classical SIR model (Hufnagel et al., 2004).

scholarly journals Multi-fidelity modelling via recursive co-kriging and Gaussian–Markov random fields

2015 ◽  
Vol 471 (2179) ◽  
pp. 20150018 ◽  
Author(s):  
P. Perdikaris ◽  
D. Venturi ◽  
J. O. Royset ◽  
G. E. Karniadakis
Keyword(s):  
Random Fields ◽  
Markov Random Fields ◽  
Stochastic Modelling ◽  
Response Surfaces ◽  
Circular Cylinders ◽  
Computationally Efficient ◽  
Initial State ◽  
Gaussian Markov Random Fields ◽  
Markov Random ◽  
Multi Level

We propose a new framework for design under uncertainty based on stochastic computer simulations and multi-level recursive co-kriging. The proposed methodology simultaneously takes into account multi-fidelity in models, such as direct numerical simulations versus empirical formulae, as well as multi-fidelity in the probability space (e.g. sparse grids versus tensor product multi-element probabilistic collocation). We are able to construct response surfaces of complex dynamical systems by blending multiple information sources via auto-regressive stochastic modelling. A computationally efficient machine learning framework is developed based on multi-level recursive co-kriging with sparse precision matrices of Gaussian–Markov random fields. The effectiveness of the new algorithms is demonstrated in numerical examples involving a prototype problem in risk-averse design, regression of random functions, as well as uncertainty quantification in fluid mechanics involving the evolution of a Burgers equation from a random initial state, and random laminar wakes behind circular cylinders.

Sampling from Gaussian Markov random fields conditioned on linear constraints

2008 ◽  
Vol 48 ◽  
pp. 1041 ◽  
Author(s):  
Daniel Peter Simpson ◽  
Ian W. Turner ◽  
A. N. Pettitt
Keyword(s):  
Random Fields ◽  
Markov Random Fields ◽  
Linear Constraints ◽  
Gaussian Markov Random Fields ◽  
Markov Random
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