The Bayesian solution to a statistical inverse problem can be summarised by a mode of the
posterior distribution, ie a maximum a posteriori (MAP) estimator. The MAP estimator …

This article shows that a large class of posterior measures that are absolutely continuous
with respect to a Gaussian prior have strong maximum a posteriori estimators in the sense of …

It is often desirable to summarize a probability measure on a space in terms of a mode, or
MAP estimator, ie, a point of maximum probability. Such points can be rigorously defined …

We prove that maximum a posteriori estimators are well-defined for diagonal Gaussian
priors $\mu $ on $\ell^ p $ under common assumptions on the potential $\Phi $. Further, we …

We develop a path integral framework for determining most probable paths for a class of
systems of stochastic differential equations with piecewise-smooth drift and additive noise …

The article presents a systematic study of the problem of conditioning a Gaussian random
variable\(\xi\) on nonlinear observations of the form\(F\circ {\varvec {\phi}}(\xi)\) …

In this work we connect two notions: that of the nonparametric mode of a probability
measure, defined by asymptotic small ball probabilities, and that of the Onsager–Machlup …

Classical parameter-space Bayesian inference for Bayesian neural networks (BNNs) suffers
from several unresolved prior issues, such as knowledge encoding intractability and …

We derive Onsager–Machlup functionals for countable product measures on weighted ℓp
subspaces of the sequence space RN. Each measure in the product is a shifted and scaled …

Eg the OM functional of a Gaussian measure on a Hilbert space is finite only on the
Cameron–Martin space, where it is half the square of the CM norm. The treatment of modes …