A typical setup for many inverse problems is that one wishes to update
beliefs about a spatially dependent set of inputs x given rather
indirect observations y. Here, the inputs and observed outputs are
related by complex physical relationship y = N(x) + e.
Applications include medical and geological tomography, hydrology, and
the modeling of physical and biological systems. We consider
applications where the physical relationship N(x) can be well
approximated by detailed simulation code M(x).
When the forward simulation code M(x) is sufficiently fast, Bayesian
inference can, in principle, be carried out via MCMC. Difficulties arise
for two main reasons:
* Even though the code may accurately represent the physical process,
there are a large number of unknown, but required, inputs that must be
calibrated to match the observed data y.
* The computational burden of the fastest available forward simulators
is often large enough that approaches for speeding up the MCMC
calculations are required.
This talk discusses approaches for specifying effective low-dimensional
representations of the inputs x along with MCMC approaches for sampling
the posterior distribution. In particular we consider augmenting the
basic formulation with fast, possibly coarsened, formulations to improve
MCMC performance. This approach can be very easily implemented in a
parallel computing environment. We give examples in single photon
emission computed tomography (SPECT) and in hydrology.
This is joint work with Herbie Lee (UCSC) and Chris Holloman (Duke U).
A typical setup for many inverse problems is that one wishes to update
beliefs about a spatially dependent set of inputs x given rather
indirect observations y. Here, the inputs and observed outputs are
related by complex physical relationship y = N(x) + e.
Applications include medical and geological tomography, hydrology, and
the modeling of physical and biological systems. We consider
applications where the physical relationship N(x) can be well
approximated by detailed simulation code M(x).
When the forward simulation code M(x) is sufficiently fast, Bayesian
inference can, in principle, be carried out via MCMC. Difficulties arise
for two main reasons:
* Even though the code may accurately represent the physical process,
there are a large number of unknown, but required, inputs that must be
calibrated to match the observed data y.
* The computational burden of the fastest available forward simulators
is often large enough that approaches for speeding up the MCMC
calculations are required.
This talk discusses approaches for specifying effective low-dimensional
representations of the inputs x along with MCMC approaches for sampling
the posterior distribution. In particular we consider augmenting the
basic formulation with fast, possibly coarsened, formulations to improve
MCMC performance. This approach can be very easily implemented in a
parallel computing environment. We give examples in single photon
emission computed tomography (SPECT) and in hydrology.
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