Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A computational framework for infinite-dimensional Bayesian inverse
  problems: Part II. Stochastic Newton MCMC with application to ice sheet flow
  inverse problems   We address the numerical solution of infinite-dimensional inverse problems in
the framework of Bayesian inference. In the Part I companion to this paper
(arXiv.org:1308.1313), we considered the linearized infinite-dimensional
inverse problem. Here in Part II, we relax the linearization assumption and
consider the fully nonlinear infinite-dimensional inverse problem using a
Markov chain Monte Carlo (MCMC) sampling method. To address the challenges of
sampling high-dimensional pdfs arising from Bayesian inverse problems governed
by PDEs, we build on the stochastic Newton MCMC method. This method exploits
problem structure by taking as a proposal density a local Gaussian
approximation of the posterior pdf, whose construction is made tractable by
invoking a low-rank approximation of its data misfit component of the Hessian.
Here we introduce an approximation of the stochastic Newton proposal in which
we compute the low-rank-based Hessian at just the MAP point, and then reuse
this Hessian at each MCMC step. We compare the performance of the proposed
method to the original stochastic Newton MCMC method and to an independence
sampler. The comparison of the three methods is conducted on a synthetic ice
sheet inverse problem. For this problem, the stochastic Newton MCMC method with
a MAP-based Hessian converges at least as rapidly as the original stochastic
Newton MCMC method, but is far cheaper since it avoids recomputing the Hessian
at each step. On the other hand, it is more expensive per sample than the
independence sampler; however, its convergence is significantly more rapid, and
thus overall it is much cheaper. Finally, we present extensive analysis and
interpretation of the posterior distribution, and classify directions in
parameter space based on the extent to which they are informed by the prior or
the observations.

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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc