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通过混合模型刻画空间相关数据：贝叶斯方法AI 解读

Summary The paper develops mixture models for spatially indexed data. We confine attention to the case of finite, typically irregular, patterns of points or regions with prescribed spatial relationships, and to problems where it is only the weights in the mixture that vary from one location to another. Our specific focus is on Poisson-distributed data, and applications in disease mapping. We work in a Bayesian framework, with the Poisson parameters drawn from gamma priors,…

局部重组率估计的近似似然方法AI 解读

Summary There is currently great interest in understanding the way in which recombination rates vary, over short scales, across the human genome. Aside from inherent interest, an understanding of this local variation is essential for the sensible design and analysis of many studies aimed at elucidating the genetic basis of common diseases or of human population histories. Standard pedigree-based approaches do not have the fine scale resolution that is needed to address this…

模型复杂度与拟合的贝叶斯度量AI 解读

Summary We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure pD for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest. In general pD approximately corresponds to the trace of the product of Fisher's information and the…

含缺失值马尔可夫模型中变分似然下界的推断适用性AI 解读

Summary Variational methods have been proposed for obtaining deterministic lower bounds for log-likelihoods within missing data problems, but with little formal justification or investigation of the worth of the lower bound surfaces as tools for inference. We provide, within a general Markovian context, sufficient conditions under which estimators from the variational approximations are asymptotically equivalent to maximum likelihood estimators, and we show empirically, for…

核密度估计与局部似然密度估计的相对效率AI 解读

Summary Local likelihood methods enjoy advantageous properties, such as good performance in the presence of edge effects, that are rarely found in other approaches to nonparametric density estimation. However, as we argue in this paper, standard kernel methods can have distinct advantages when edge effects are not present. We show that, whereas the integrated variances of the two methods are virtually identical, the integrated squared bias of a conventional kernel estimator…

结合回归变量选择的贝叶斯模型平均AI 解读

Summary When a number of distinct models contend for use in prediction, the choice of a single model can offer rather unstable predictions. In regression, stochastic search variable selection with Bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors. Here we look at Bayes model averaging incorporating variable selection for prediction. This offers similar mean-square errors of prediction but with a vastly…

癌症预防研究中的生存数据模型AI 解读

Summary We propose a new parametric survival model for cancer prevention studies. The formulation of the model is in the spirit of stochastic modelling of the occurrences of tumours through two stages: initiation of an undetected tumour and promotion of the tumour to a detectable cancer. Several novel properties of the model proposed are derived. In addition, we examine the relationship of our model with the existing lagged regression model of Zucker and Lakatos. Also, we…

基于符号协方差矩阵的回归系数估计AI 解读

Summary A new estimator of the regression parameters is introduced in a multivariate multiple-regression model in which both the vector of explanatory variables and the vector of response variables are assumed to be random. The affine equivariant estimate matrix is constructed using the sign covariance matrix (SCM) where the sign concept is based on Oja's criterion function. The influence function and asymptotic theory are developed to consider robustness and limiting…

链图模型及其因果解释AI 解读

Summary Chain graphs are a natural generalization of directed acyclic graphs and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are many simple and apparently plausible, but ultimately fallacious, interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to flawed methods for applying background knowledge to…

降维空间的自适应估计AI 解读

Summary Searching for an effective dimension reduction space is an important problem in regression, especially for high dimensional data. We propose an adaptive approach based on semiparametric models, which we call the (conditional) minimum average variance estimation (MAVE) method, within quite a general setting. The MAVE method has the following advantages. Most existing methods must undersmooth the nonparametric link function estimator to achieve a faster rate of…

半参数混合模型的影响诊断与异常值检验AI 解读

Summary Semiparametric mixed models are useful in biometric and econometric applications, especially for longitudinal data. Maximum penalized likelihood estimators (MPLEs) have been shown to work well by Zhang and co-workers for both linear coefficients and nonparametric functions. This paper considers the role of influence diagnostics in the MPLE by extending the case deletion and subject deletion analysis of linear models to accommodate the inclusion of a nonparametric…

错误发现率程序的运行特征与扩展AI 解读

Summary We investigate the operating characteristics of the Benjamini–Hochberg false discovery rate procedure for multiple testing. This is a distribution-free method that controls the expected fraction of falsely rejected null hypotheses among those rejected. The paper provides a framework for understanding more about this procedure. We first study the asymptotic properties of the ‘deciding point' D that determines the critical p-value. From this, we obtain explicit…

错误发现率的直接处理方法AI 解读

Summary Multiple-hypothesis testing involves guarding against much more complicated errors than single-hypothesis testing. Whereas we typically control the type I error rate for a single-hypothesis test, a compound error rate is controlled for multiple-hypothesis tests. For example, controlling the false discovery rate FDR traditionally involves intricate sequential p-value rejection methods based on the observed data. Whereas a sequential p-value method fixes the error rate…

含函数型预测变量的广义线性模型AI 解读

Summary We present a technique for extending generalized linear models to the situation where some of the predictor variables are observations from a curve or function. The technique is particularly useful when only fragments of each curve have been observed. We demonstrate, on both simulated and real data sets, how this approach can be used to perform linear, logistic and censored regression with functional predictors. In addition, we show how functional principal…

基于似然比的高功效拟合优度检验AI 解读

Summary A new approach of parameterization is proposed to construct a general goodness-of-fit test. It can not only generate traditional tests (including the Kolmogorov–Smirnov, Cramér–von Mises and Anderson–Darling tests) but also produce new types of omnibus tests, which are generally much more powerful than the old ones.

回归模型选择：残差似然方法AI 解读

Summary We obtain the residual information criterion RIC, a selection criterion based on the residual log-likelihood, for regression models including classical regression models, Box–Cox transformation models, weighted regression models and regression models with autoregressive moving average errors. We show that RIC is a consistent criterion, and that simulation studies for each of the four models indicate that RIC provides better model order choices than the Akaike…

2×2 表元分析中的发表偏差：平均蒙特卡洛 EM 算法AI 解读

Summary A major difficulty in meta-analysis is publication bias. Studies with positive outcomes are more likely to be published than studies reporting negative or inconclusive results. Correcting for this bias is not possible without making untestable assumptions. In this paper, a sensitivity analysis is discussed for the meta-analysis of 2×2 tables using exact conditional distributions. A Markov chain Monte Carlo EM algorithm is used to calculate maximum likelihood…

小波阈值估计的后验概率区间AI 解读

Summary We use cumulants to derive Bayesian credible intervals for wavelet regression estimates. The first four cumulants of the posterior distribution of the estimates are expressed in terms of the observed data and integer powers of the mother wavelet functions. These powers are closely approximated by linear combinations of wavelet scaling functions at an appropriate finer scale. Hence, a suitable modification of the discrete wavelet transform allows the posterior…

一种新的排序集抽样方差估计量AI 解读

Summary We develop an unbiased estimator of the variance of a population based on a ranked set sample. We show that this new estimator is better than estimating the variance based on a simple random sample and more efficient than the estimator based on a ranked set sample proposed by Stokes. Also, a test to determine the effectiveness of the judgment ordering process is proposed.

回归中条件第 k 阶矩的降维AI 解读

Summary The idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model. Central subspaces are designed to capture all the information for the regression and to provide a population structure for dimension reduction. Here, we introduce the central kth-moment subspace to capture information from the mean, variance and so on up to the kth conditional moment of…

复杂区域上的样条平滑AI 解读

Summary It is occasionally necessary to smooth data over domains in ℝ2 with complex irregular boundaries or interior holes. Traditional methods of smoothing which rely on the Euclidean metric or which measure smoothness over the entire real plane may then be inappropriate. This paper introduces a bivariate spline smoothing function defined as the minimizer of a penalized sum-of-squares functional. The roughness penalty is based on a partial differential operator and is…

已实现波动率的计量分析及其在随机波动率模型估计中的应用AI 解读

Summary The availability of intraday data on the prices of speculative assets means that we can use quadratic variation-like measures of activity in financial markets, called realized volatility, to study the stochastic properties of returns. Here, under the assumption of a rather general stochastic volatility model, we derive the moments and the asymptotic distribution of the realized volatility error—the difference between realized volatility and the discretized integrated…

密度估计中的高阶数据锐化AI 解读

Summary It is shown that data sharpening can be used to produce density estimators that enjoy arbitrarily high orders of bias reduction. Practical advantages of this approach, relative to competing methods, are demonstrated. They include the sheer simplicity of the estimators, which makes code for computing them particularly easy to write, very good mean-squared error performance, reduced ‘wiggliness' of estimates and greater robustness against undersmoothing.

样条非参数回归中的模型选择AI 解读

Summary A Bayesian approach is presented for model selection in nonparametric regression with Gaussian errors and in binary nonparametric regression. A smoothness prior is assumed for each component of the model and the posterior probabilities of the candidate models are approximated using the Bayesian information criterion. We study the model selection method by simulation and show that it has excellent frequentist properties and gives improved estimates of the regression…