Markov Random Fields with Higher-order Interactions

Discrete-state Markov random fields on regular arrays have played a significant role in spatial statistics and image analysis. For example, they are used to represent objects against background in computer vision and pixel-based classification of a region into different crop types in remote sensing. Convenience has generally favoured formulations that involve only pairwise interactions. Such models are in themselves unrealistic and, although they often perform surprisingly well in tasks such as the restoration of degraded images, they are unsatisfactory for many other purposes. In this paper, we consider particular forms of Markov random fields that involve higher-order interactions and therefore are better able to represent the large-scale properties of typical spatial scenes. Interpretations of the parameters are given and realizations from a variety of models are produced via Markov chain Monte Carlo. Potential applications are illustrated in two examples. The first concerns Bayesian image analysis and confirms that pairwise-interaction priors may perform very poorly for image functionals such as number of objects, even when restoration apparently works well. The second example describes a model for a geological dataset and obtains maximum-likelihood parameter estimates using Markov chain Monte Carlo. Despite the complexity of the formulation, realizations of the estimated model suggest that the representation is quite realistic.     

Functional and dynamic magnetic resonance imaging using vector adaptive weights smoothing

We consider the problem of statistical inference for functional and dynamic magnetic resonance imaging (MRI). A new approach is proposed which extends the adaptive weights smoothing procedure of Polzehl and Spokoiny that was originally designed for image denoising. We demonstrate how the adaptive weights smoothing method can be applied to time series of images, which typically occur in functional and dynamic MRI. It is shown how signal detection in functional MRI and the analysis of dynamic MRI can benefit from spatially adaptive smoothing. The performance of the procedure is illustrated by using real and simulated data.     

Spatial Matérn Fields Driven by Non‐Gaussian Noise

The article studies non‐Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is on non‐Gaussian random fields with Matérn covariance functions, and in particular, we show how the SPDE formulation of a Laplace moving‐average model can be used to obtain an efficient simulation method as well as an accurate parameter estimation technique for the model. This should be seen as a demonstration of how these techniques can be used, and generalizations to more general SPDEs are readily available.     

Nonlinear voxel-based modelling of the haemodynamic response in fMRI

A common assumption for data analysis in functional magnetic resonance imaging is that the response signal can be modelled as the convolution of a haemodynamic response (HDR) kernel with a stimulus reference function. Early approaches modelled spatially constant HDR kernels, but more recently spatially varying models have been proposed. However, convolution limits the flexibility of these models and their ability to capture spatial variation. Here, a range of (nonlinear) parametric curves are fitted by least squares minimisation directly to individual voxel HDRs (i.e., without using convolution). A ‘constrained gamma curve’ is proposed as an efficient form for fitting the HDR at each individual voxel. This curve allows for spatial variation in the delay of the HDR, but places a global constraint on the temporal spread. The approach of directly fitting individual parameters of HDR shape is demonstrated to lead to an improved fit of response estimates.     

On Exact Simulation of Markov Random Fields Using Coupling from the Past

A general framework for exact simulation of Markov random fields using the Propp–Wilson coupling from the past approach is proposed. Our emphasis is on situations lacking the monotonicity properties that have been exploited in previous studies. A critical aspect is the convergence time of the algorithm; this we study both theoretically and experimentically. Our main theoretical result in this direction says, roughly, that if interactions are sufficiently weak, then the expected running time of a carefully designed implementation is O ( N log N ), where N is the number of interacting components of the system. Computer experiments are carried out for random q -colourings and for the Widom–Rowlinson lattice gas model.     

On the Second‐Order Random Walk Model for Irregular Locations

Abstract. The second‐order random walk (RW2) model is commonly used for smoothing data and for modelling response functions. It is computationally efficient due to the Markov properties of the joint (intrinsic) Gaussian density. For evenly spaced locations the RW2 model is well established, whereas for irregularly spaced locations there is no well established construction in the literature. By considering the RW2 model as the solution of a stochastic differential equation (SDE), a discretely observed integrated Wiener process, it is possible to derive the density preserving the Markov properties by augmenting the state‐space with the velocities. Here, we derive a computationally more efficient RW2 model for irregular locations using a Galerkin approximation to the solution of the SDE without the need of augmenting the state‐space. Numerical comparison with the exact solution demonstrates that the error in the Galerkin approximation is small and negligible in applications.     

SLA研究的理论模式与研究领域

第二语言习得(SLA)研究作为一门独立的学科已经有了三十多年的历史,其间理论假设层出不穷,莫衷一是。本文梳理了五种有代表性的、对外语教学有指导意义的主要SLA理论,希望能对广大的外语教学工作者有教学参考价值。     

同轴方形载流线圈间的磁力(英文)

为获得二同轴方形载流线圈间相互作用磁力，计算出了线圈间的互感系数。将虚功原理作为一种简捷方法加以运用，对该力极值位置进行了分析和图示。讨论平面内二同心方形线圈载流时一线圈不受磁张力的优良力学状态。     

The Efficacy of Different Methods for Informing the Public About the Range Dependency of Magnetic Fields from High Voltage Power Lines

The AC electric and magnetic fields associated with high voltage power lines have become a concern as a possible health risk. In most cases the strength of these fields decreases as the inverse square of the distance from the line. In earlier work, we found that laypeople do not understand how rapidly field strength decreases with distance. Most believe that any high voltage power line they can see is exposing them to strong fields. This paper confirms the earlier finding and explores a number of strategies which might be used in risk communications to correct this misperception. We found it relatively easy to provide subjects with a better understanding of the range-dependency of magnetic field strength. Moreover, the quality of this acquisition was apparently independent of the manner in which they were instructed. Such successful instruction is markedly different from the well-established difficulty of teaching people about many qualitative domains, such as physics or ideas in probability. Clearly, while some erroneous beliefs are highly resistant to change, others can be altered quite readily. We suspect that an important distinction between knowledge about the range-dependency of power-frequency magnetic fields and less tractable topics involves the presence or absence of prior folk-theories or "mental models" of the domain.     

Approximate Bayesian Inference for Survival Models

Abstract. Bayesian analysis of time‐to‐event data, usually called survival analysis, has received increasing attention in the last years. In Cox‐type models it allows to use information from the full likelihood instead of from a partial likelihood, so that the baseline hazard function and the model parameters can be jointly estimated. In general, Bayesian methods permit a full and exact posterior inference for any parameter or predictive quantity of interest. On the other side, Bayesian inference often relies on Markov chain Monte Carlo (MCMC) techniques which, from the user point of view, may appear slow at delivering answers. In this article, we show how a new inferential tool named integrated nested Laplace approximations can be adapted and applied to many survival models making Bayesian analysis both fast and accurate without having to rely on MCMC‐based inference.