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一阶内蕴自回归与 de Wijs 过程AI 解读

We discuss intrinsic autoregressions for a first-order neighbourhood on a two-dimensional rectangular lattice and give an exact formula for the variogram that extends known results to the asymmetric case. We obtain a corresponding asymptotic expansion that is more accurate and more general than previous ones and use this to derive the de Wijs variogram under appropriate averaging, a result that can be interpreted as a two-dimensional spatial analogue of Brownian motion…

农业田间试验的贝叶斯分析AI 解读

Summary The paper describes Bayesian analysis for agricultural field experiments, a topic that has received very little previous attention, despite a vast frequentist literature. Adoption of the Bayesian paradigm simplifies the interpretation of the results, especially in ranking and selection. Also, complex formulations can be analysed with comparative ease, by using Markov chain Monte Carlo methods. A key ingredient in the approach is the need for spatial representations…

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论条件自回归与内蕴自回归AI 解读

Gaussian conditional autoregressions have been widely used in spatial statistics and Bayesian image analysis, where they are intended to describe interactions between random variables at fixed sites in Euclidean space. The main appeal of these distributions is in the Markovian interpretation of their full conditionals. Intrinsic autoregressions are limiting forms that retain the Markov property. Despite being improper, they can have advantages over the standard…

摘要暂缺

空间统计与贝叶斯计算AI 解读

SUMMARY Markov chain Monte Carlo (MCMC) algorithms, such as the Gibbs sampler, have provided a Bayesian inference machine in image analysis and in other areas of spatial statistics for several years, founded on the pioneering ideas of Ulf Grenander. More recently, the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a Markov random field has opened the way to the use of…

序贯 Monte Carlo p 值AI 解读

SUMMARY The assessment of statistical significance by Monte Carlo simulation may be costly in computer time. This paper looks at a number of ways of calculating exact Monte Carlo p-values by sequential sampling. Such p-values are shown to have properties similar to those obtained by sampling with a fixed sample size. Both standard and generalized Monte Carlo procedures are discussed and, in particular, a sequential method is proposed for dealing with situations in which…

受噪声污染图像的统计分析AI 解读

SUMMARY A continuous two-dimensional region is partitioned into a fine rectangular array of sites or “pixels”, each pixel having a particular “colour” belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that…

抗异常值方法与统计分析AI 解读

Some exploratory aspects of simple resistant techniques are described and demonstrated on three published sets of data. The examples involve resistant regression, resistant analysis of a two-way table and resistant analysis of a Latin square experiment, respectively. Emphasis is placed on the application of resistant techniques used in conjunction with, and not as a substitute for, classical statistical analysis.

抗异常值技术与统计分析AI 解读

Some exploratory aspects of simple resistant techniques are described and demonstrated on three published sets of data. The examples involve resistant regression, resistant analysis of a two-way table and resistant analysis of a Latin square experiment, respectively. Emphasis is placed on the application of resistant techniques used in conjunction with, and not as a substitute for, classical statistical analysis.

高斯格点模型的变量测量误差估计AI 解读

Summary It can happen that the variates of primary interest in a simple Gaussian lattice scheme are not directly observable. An errors-in-variables formulation may then be appropriate. This note describes the corresponding maximum-likelihood estimation of unknown parameter values. An example is given.

空间相互作用与格点系统的统计分析AI 解读

Summary The formulation of conditional probability models for finite systems of spatially interacting random variables is examined. A simple alternative proof of the Hammersley–Clifford theorem is presented and the theorem is then used to construct specific spatial schemes on and off the lattice. Particular emphasis is placed upon practical applications of the models in plant ecology when the variates are binary or Gaussian. Some aspects of infinite lattice Gaussian…