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

Using non-nutritive sucking to support feeding development for premature infants: A commentary on approaches and current practice

Non-nutritive sucking is often used with premature infants by either using a pacifier or an expressed breast nipple to support the introduction and development of early oral feeding. The pattern of non-nutritive sucking is distinct in that it involves two sucks per second in contrast to nutritive sucking which is one suck per second. Although some literature has identified that non-nutritive sucking has some benefit for the premature infant’s feeding development, it is not entirely clear why such an approach is helpful as neurologically, activation of non-nutritive and nutritive skills are different. A summary is presented of the main approaches that use non-nutritive sucking with reference to the literature. This paper also considers other factors and beneficial approaches to managing the introduction of infant feeding. These are: the infant’s toleration of enteral feeds pre oral trials, overall development and gestational age when introducing oral experiences, developing swallowing skills before sucking, physiological stability, health status, as well as the development and interpretation of infant oral readiness signs and early communication

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 $\kappa$ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF when the dimension $d<2\kappa$. 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

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

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

Determining White Noise Forcing From Eulerian Observations in the Navier Stokes Equation

The Bayesian approach to inverse problems is of paramount importance in quantifying uncertainty about the input to and the state of a system of interest given noisy observations. Herein we consider the forward problem of the forced 2D Navier Stokes equation. The inverse problem is inference of the forcing, and possibly the initial condition, given noisy observations of the velocity field. We place a prior on the forcing which is in the form of a spatially correlated temporally white Gaussian process, and formulate the inverse problem for the posterior distribution. Given appropriate spatial regularity conditions, we show that the solution is a continuous function of the forcing. Hence, for appropriately chosen spatial regularity in the prior, the posterior distribution on the forcing is absolutely continuous with respect to the prior and is hence well-defined. Furthermore, the posterior distribution is a continuous function of the data. We complement this theoretical result with numerical simulation of the posterior distribution