17,142 research outputs found
Proposals which speed-up function-space MCMC
Inverse problems lend themselves naturally to a Bayesian formulation, in
which the quantity of interest is a posterior distribution of state and/or
parameters given some uncertain observations. For the common case in which the
forward operator is smoothing, then the inverse problem is ill-posed.
Well-posedness is imposed via regularisation in the form of a prior, which is
often Gaussian. Under quite general conditions, it can be shown that the
posterior is absolutely continuous with respect to the prior and it may be
well-defined on function space in terms of its density with respect to the
prior. In this case, by constructing a proposal for which the prior is
invariant, one can define Metropolis-Hastings schemes for MCMC which are
well-defined on function space, and hence do not degenerate as the dimension of
the underlying quantity of interest increases to infinity, e.g. under mesh
refinement when approximating PDE in finite dimensions. However, in practice,
despite the attractive theoretical properties of the currently available
schemes, they may still suffer from long correlation times, particularly if the
data is very informative about some of the unknown parameters. In fact, in this
case it may be the directions of the posterior which coincide with the (already
known) prior which decorrelate the slowest. The information incorporated into
the posterior through the data is often contained within some
finite-dimensional subspace, in an appropriate basis, perhaps even one defined
by eigenfunctions of the prior. We aim to exploit this fact and improve the
mixing time of function-space MCMC by careful rescaling of the proposal. To
this end, we introduce two new basic methods of increasing complexity,
involving (i) characteristic function truncation of high frequencies and (ii)
hessian information to interpolate between low and high frequencies
Deterministic Mean-field Ensemble Kalman Filtering
The proof of convergence of the standard ensemble Kalman filter (EnKF) from
Legland etal. (2011) is extended to non-Gaussian state space models. A
density-based deterministic approximation of the mean-field limit EnKF
(DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given
a certain minimal order of convergence between the two, this extends
to the deterministic filter approximation, which is therefore asymptotically
superior to standard EnKF when the dimension . The fidelity of
approximation of the true distribution is also established using an extension
of total variation metric to random measures. This is limited by a Gaussian
bias term arising from non-linearity/non-Gaussianity of the model, which exists
for both DMFEnKF and standard EnKF. Numerical results support and extend the
theory
Multilevel Particle Filters for L\'evy-driven stochastic differential equations
We develop algorithms for computing expectations of the laws of models
associated to stochastic differential equations (SDEs) driven by pure L\'evy
processes. We consider filtering such processes and well as pricing of path
dependent options. We propose a multilevel particle filter (MLPF) to address
the computational issues involved in solving these continuum problems. We show
via numerical simulations and theoretical results that under suitable
assumptions of the discretization of the underlying driving L\'evy proccess,
our proposed method achieves optimal convergence rates. The cost to obtain MSE
scales like for our method, as compared with
the standard particle filter
A hybrid asymptotic-modal analysis of the EM scattering by an open-ended S-shaped rectangular waveguide cavity
The electromagnetic fields (EM) backscatter from a 3-dimensional perfectly conducting S-shaped open-ended cavity with a planar interior termination is analyzed when it is illuminated by an external plane wave. The analysis is based on a self-consistent multiple scattering method which accounts for the multiple wave interactions between the open end and the interior termination. The scattering matrices which described the reflection and transmission coefficients of the waveguide modes reflected and transmitted at each junction between the different waveguide sections, as well at the scattering from the edges at the open end are found via asymptotic high frequency methods such as the geometrical and physical theories of diffraction used in conjunction with the equivalent current method. The numerical results for an S-shaped inlet cavity are compared with the backscatter from a straight inlet cavity; the backscattered patterns are different because the curvature of an S-shaped inlet cavity redistributes the energy reflected from the interior termination in a way that is different from a straight inlet cavity
Analysis of the 3DVAR Filter for the Partially Observed Lorenz '63 Model
The problem of effectively combining data with a mathematical model
constitutes a major challenge in applied mathematics. It is particular
challenging for high-dimensional dynamical systems where data is received
sequentially in time and the objective is to estimate the system state in an
on-line fashion; this situation arises, for example, in weather forecasting.
The sequential particle filter is then impractical and ad hoc filters, which
employ some form of Gaussian approximation, are widely used. Prototypical of
these ad hoc filters is the 3DVAR method. The goal of this paper is to analyze
the 3DVAR method, using the Lorenz '63 model to exemplify the key ideas. The
situation where the data is partial and noisy is studied, and both discrete
time and continuous time data streams are considered. The theory demonstrates
how the widely used technique of variance inflation acts to stabilize the
filter, and hence leads to asymptotic accuracy
Data Assimilation: A Mathematical Introduction
These notes provide a systematic mathematical treatment of the subject of
data assimilation
Not all the bots are created equal:the Ordering Turing Test for the labelling of bots in MMORPGs
This article contributes to the research on bots in Social Media. It takes as its starting point an emerging perspective which proposes that we should abandon the investigation of the Turing Test and the functional aspects of bots in favor of studying the authentic and cooperative relationship between humans and bots. Contrary to this view, this article argues that Turing Tests are one of the ways in which authentic relationships between humans and bots take place. To understand this, this article introduces the concept of Ordering Turing Tests: these are sort of Turing Tests proposed by social actors for purposes of achieving social order when bots produce deviant behavior. An Ordering Turing Test is method for labeling deviance, whereby social actors can use this test to tell apart rule-abiding humans and rule-breaking bots. Using examples from Massively Multiplayer Online Role-Playing Games, this article illustrates how Ordering Turing Tests are proposed and justified by players and service providers. Data for the research comes from scientific literature on Machine Learning proposed for the identification of bots and from game forums and other player produced paratexts from the case study of the game Runescape
- …