6632
eng
1600
1629
4
6
article
0
--
2018-01-04
--
Random forward models and log-likelihoods in Bayesian inverse problems
We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive model is approximated using a cheaper stochastic surrogate, as in Gaussian process emulation (kriging), or in the field of probabilistic numerical methods. We show that the Hellinger distance between the exact and approximate Bayesian posteriors is bounded by moments of the difference between the true and approximate log-likelihoods. Example applications of these stability results are given for randomised misfit models in large data applications and the probabilistic solution of ordinary differential equations.
SIAM/ASA Journal on Uncertainty Quantification
1438-0064
urn:nbn:de:0297-zib-66324
1712.05717
10.1137/18M1166523
2018
yes
Han Cheng Lie
Tim Sullivan
T. J. Sullivan
Aretha Teckentrup
ZIB-Report
18-03
eng
uncontrolled
Bayesian inverse problem
eng
uncontrolled
random likelihood
eng
uncontrolled
surrogate model
eng
uncontrolled
posterior consistency
eng
uncontrolled
probabilistic numerics
eng
uncontrolled
uncertainty quantification
eng
uncontrolled
randomised misfit
STATISTICS
NUMERICAL ANALYSIS
COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)
Numerical Mathematics
Sullivan, Tim
SFB1114 A06
https://opus4.kobv.de/opus4-zib/files/6632/random-bip.pdf
6241
2018
2018
eng
1
6
6
8
23
article
0
2018-02-21
--
--
Quasi-invariance of countable products of Cauchy measures under non-unitary dilations
Electronic Communications in Probability
1611.10289
10.1214/18-ECP113
Yes
Han Cheng Lie
Regine Kossick
T. J. Sullivan
Numerical Mathematics
Sullivan, Tim
no-project
6934
2018
eng
conferenceobject
0
--
--
--
Implicit probabilistic integrators for ODEs
Advances in Neural Information Processing Systems 31 (NIPS 2018)
1805.07970
http://papers.nips.cc/paper/7955-implicit-probabilistic-integrators-for-odes
2018
yes
Onur Teymur
Tim Sullivan
Han Cheng Lie
T. J. Sullivan
Ben Calderhead
Numerical Mathematics
Sullivan, Tim
no-project
7105
2018
eng
129601
12
34
article
0
--
--
--
Erratum: Equivalence of weak and strong modes of measures on topological vector spaces (2018 Inverse Problems 34 115013)
Inverse Problems
10.1088/1361-6420/aae55b
yes
2018
Han Cheng Lie
Tim Sullivan
T. J. Sullivan
Numerical Mathematics
Sullivan, Tim
no-project
Lie, Han
6660
2018
eng
115013
11
34
article
0
--
--
--
Equivalence of weak and strong modes of measures on topological vector spaces
Modes of a probability measure on an infinite-dimensional Banach space X are often defined by maximising the small-radius limit of the ratio of measures of norm balls. Helin and Burger weakened the definition of such modes by considering only balls with centres in proper subspaces of X, and posed the question of when this restricted notion coincides with the unrestricted one. We generalise these definitions to modes of arbitrary measures on topological vector spaces, defined by arbitrary bounded, convex, neighbourhoods of the origin. We show that a coincident limiting ratios condition is a necessary and sufficient condition for the equivalence of these two types of modes, and show that the coincident limiting ratios condition is satisfied in a wide range of topological vector spaces.
Inverse Problems
1708.02516
10.1088/1361-6420/aadef2
yes
Han Cheng Lie
Tim Sullivan
T. J. Sullivan
Numerical Mathematics
Sullivan, Tim
no-project
Lie, Han
7146
2018
eng
article
0
--
--
--
Convergence rates of Gaussian ODE filters
1807.09737
under review
no
Hans Kersting
Tim Sullivan
T. J. Sullivan
Philipp Hennig
Numerical Mathematics
Sullivan, Tim
no-project
6975
eng
reportzib
0
--
2018-08-01
--
A Shape Trajectories Approach to Longitudinal Statistical Analysis
For Kendallâ€™s shape space we determine analytically Jacobi fields and parallel transport, and compute geodesic regression. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and reduce the computational expense by several orders of magnitude. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data.
As application example we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative. Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data only.
1438-0064
urn:nbn:de:0297-zib-69759
Esfandiar Nava-Yazdani
Hans-Christian Hege
Hans-Christian Hege
Christoph von Tycowicz
T. J. Sullivan
ZIB-Report
18-42
eng
uncontrolled
shape space, shape trajectories, geodesic regression, longitudinal analysis, osteoarthritis
PROBABILITY AND STATISTICS
DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)
STATISTICS
Visual Data Analysis
Visual Data Analysis in Science and Engineering
Therapy Planning
Hege, Hans-Christian
Tycowicz, Christoph von
Sullivan, Tim
Navayazdani, Esfandiar
ECMath-CH15
https://opus4.kobv.de/opus4-zib/files/6975/shape_trj.pdf