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Summary: Spatial-temporal modelling for tomography with Markov chain Monte Carlo techniques
Sha Meng, Robert Aykroyd, and Robert West
University of Leeds
Experiment:
Objective: Given voltage measurements, estimate the resistivity distribution
For the complete electrode model, the voltage are computed using Gauss's equation,
derived from Maxwell's equations
where = 1/ is the conductivity ( is the resistivity), u is the electric potential, and
the Neumann boundary conditions:
Measurements:
· In turn, a current is applied across each
electrode and a reference electrode
· Voltages are then measured between each
electrode and the reference electrode
· For 8 electrodes, this gives 7x7=49 readings
MCMC techniques:
· An iterative approach that enables solution even if the priors are complex
· Simulates from a Markov chain with required posterior as its equilibrium
distribution
· Collect posterior sample and base estimates on sample quantities
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