132 citations · 604 across the 33 of their papers we have counts for
35 papers
Classification of small-ball modes and maximum a posteriori estimators in metric spaces
Ilja Klebanov, Hefin Lambley, T. J. Sullivan
A mode, or `most likely point', for a probability measure can be defined in various ways via the asymptotic behaviour of the -mass of balls as their radius tends to zero. Su…
Images of Gaussian and other stochastic processes under closed, densely-defined, unbounded linear operators
Tadashi Matsumoto, T. J. Sullivan
Gaussian processes (GPs) are widely-used tools in spatial statistics and machine learning and the formulae for the mean function and covariance kernel of a GP that is the ima…
Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem
Mattes Mollenhauer, Nicole Mücke, T. J. Sullivan
We consider the problem of learning a linear operator between two Hilbert spaces from empirical observations, which we interpret as least squares regression in infinite dimensi…
Dimension-independent Markov chain Monte Carlo on the sphere
H. C. Lie, D. Rudolf, B. Sprungk +1
We consider Bayesian analysis on high-dimensional spheres with angular central Gaussian priors. These priors model antipodally symmetric directional data, are easily defined in Hil…
Γ-convergence of Onsager-Machlup functionals. Part II: Infinite product measures on Banach spaces
Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie +1
We derive Onsager-Machlup functionals for countable product measures on weighted subspaces of the sequence space . Each measure in the product is…
Γ-convergence of Onsager-Machlup functionals. Part I: With applications to maximum a posteriori estimation in Bayesian inverse problems
Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie +1
The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a MAP estimator. The MAP estimator essentially coincides with…