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利用混合样条模型进行限制似然比失拟检验AI 解读

Summary Penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non-linearity in the smooth function estimates. This motivates the study of lack-of-fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values. For this one-sided testing problem a further complication is that the variance component…

变系数模型中的平滑样条估计AI 解读

Summary Smoothing spline estimators are considered for inference in varying-coefficient models with one effect modifying covariate. Bayesian ‘confidence intervals’ are developed for the coefficient curves and efficient computational methods are derived for computing the curve estimators, fitted values, posterior variances and data-adaptive methods for selecting the levels of smoothing. The efficacy and utility of the methodology proposed are demonstrated through a small…

带协变量调整的生存分布比较非参数检验AI 解读

Summary The analysis of covariance is a technique that is used to improve the power of a k-sample test by adjusting for concomitant variables. If the end point is the time of survival, and some observations are right censored, the score statistic from the Cox proportional hazards model is the method that is most commonly used to test the equality of conditional hazard functions. In many situations, however, the proportional hazards model assumptions are not satisfied.…

部分观测连续时间模型的精确滤波AI 解读

Summary The forward–backward algorithm is an exact filtering algorithm which can efficiently calculate likelihoods, and which can be used to simulate from posterior distributions. Using a simple result which relates gamma random variables with different rates, we show how the forward–backward algorithm can be used to calculate the distribution of a sum of gamma random variables, and to simulate from their joint distribution given their sum. One application is to calculating…

时间序列分析中的非参数多步预测AI 解读

Summary We consider the problem of multistep-ahead prediction in time series analysis by using nonparametric smoothing techniques. Forecasting is always one of the main objectives in time series analysis. Research has shown that non-linear time series models have certain advantages in multistep-ahead forecasting. Traditionally, nonparametric k-step-ahead least squares prediction for non-linear autoregressive AR(d) models is done by estimating E(Xt+k |Xt, …, Xt−d+1) via…

Summary Deconvolution problems are naturally represented in the Fourier domain, whereas thresholding in wavelet bases is known to have broad adaptivity properties. We study a method which combines both fast Fourier and fast wavelet transforms and can recover a blurred function observed in white noise with O{n log (n)2} steps. In the periodic setting, the method applies to most deconvolution problems, including certain ‘boxcar’ kernels, which are important as a model of…

散射计风场反演问题的贝叶斯分析：若干新方法AI 解读

Summary The retrieval of wind vectors from satellite scatterometer observations is a non-linear inverse problem. A common approach to solving inverse problems is to adopt a Bayesian framework and to infer the posterior distribution of the parameters of interest given the observations by using a likelihood model relating the observations to the parameters, and a prior distribution over the parameters. We show how Gaussian process priors can be used efficiently with a variety…

遥感高维反演的马尔可夫链蒙特卡洛方法AI 解读

Summary We discuss the inversion of the gas profiles (ozone, NO3, NO2, aerosols and neutral density) in the upper atmosphere from the spectral occultation measurements. The data are produced by the ‘Global ozone monitoring of occultation of stars’ instrument on board the Envisat satellite that was launched in March 2002. The instrument measures the attenuation of light spectra at various horizontal paths from about 100 km down to 10–20 km. The new feature is that these data…

时频曲面估计的贝叶斯变量选择与正则化AI 解读

Summary We describe novel Bayesian models for time–frequency inverse modelling of non-stationary signals. These models are based on the idea of a Gabor regression, in which a time series is represented as a superposition of translated, modulated versions of a window function exhibiting good time–frequency concentration. As a necessary consequence, the resultant set of potential predictors is in general overcomplete—constituting a frame rather than a basis—and hence the…

随访时间不规则且依赖结局的纵向数据分析AI 解读

Summary A frequent problem in longitudinal studies is that subjects may miss scheduled visits or be assessed at self-selected points in time. As a result, observed outcome data may be highly unbalanced and the availability of the data may be directly related to the outcome measure and/or some auxiliary factors that are associated with the outcome. If the follow-up visit and outcome processes are correlated, then marginal regression analyses will produce biased estimates.…

相关非参数贝叶斯模型之间的联合推断方法AI 解读

Summary We consider the problem of combining inference in related nonparametric Bayes models. Analogous to parametric hierarchical models, the hierarchical extension formalizes borrowing strength across the related submodels. In the nonparametric context, modelling is complicated by the fact that the random quantities over which we define the hierarchy are infinite dimensional. We discuss a formal definition of such a hierarchical model. The approach includes a regression at…

复杂模型的概率敏感性分析：贝叶斯方法AI 解读

Summary In many areas of science and technology, mathematical models are built to simulate complex real world phenomena. Such models are typically implemented in large computer programs and are also very complex, such that the way that the model responds to changes in its inputs is not transparent. Sensitivity analysis is concerned with understanding how changes in the model inputs influence the outputs. This may be motivated simply by a wish to understand the implications…

多变量极值的条件方法（附讨论）AI 解读

Summary Multivariate extreme value theory and methods concern the characterization, estimation and extrapolation of the joint tail of the distribution of a d-dimensional random variable. Existing approaches are based on limiting arguments in which all components of the variable become large at the same rate. This limit approach is inappropriate when the extreme values of all the variables are unlikely to occur together or when interest is in regions of the support of the…

大型空间数据集的似然近似AI 解读

Summary Likelihood methods are often difficult to use with large, irregularly sited spatial data sets, owing to the computational burden. Even for Gaussian models, exact calculations of the likelihood for n observations require O(n3) operations. Since any joint density can be written as a product of conditional densities based on some ordering of the observations, one way to lessen the computations is to condition on only some of the ‘past’ observations when computing the…

在 Metropolis–Hastings 更新中使用局部优化AI 解读

Summary We propose new Metropolis–Hastings algorithms for sampling from multimodal dis- tributions on ℜn. Tjelmeland and Hegstad have obtained direct mode jumping proposals by optimization within Metropolis–Hastings updates and different proposals for ‘forward’ and ‘backward’ steps. We generalize their scheme by allowing the probability distribution for forward and backward kernels to depend on the current state. We use the new setting to combine mode jumping proposals and…

基于风险函数的非参数生存函数估计AI 解读

Summary A representation is developed that expresses the bivariate survivor function as a function of the hazard function for truncated failure time variables. This leads to a class of nonparametric survivor function estimators that avoid negative mass. The transformation from hazard function to survivor function is weakly continuous and compact differentiable, so that such properties as strong consistency, weak convergence to a Gaussian process and bootstrap applicability…

筛选显著效应的简单程序AI 解读

Summary Given a large number of test statistics, a small proportion of which represent departures from the relevant null hypothesis, a simple rule is given for choosing those statistics that are indicative of departure. It is based on fitting by moments a mixture model to the set of test statistics and then deriving an estimated likelihood ratio. Simulation suggests that the procedure has good properties when the departure from an overall null hypothesis is not too small.

非线性加性自回归模型的滞后识别AI 解读

Summary We propose a lag selection method for non-linear additive autoregressive models that is based on spline estimation and the Bayes information criterion. The additive structure of the autoregression function is used to overcome the ‘curse of dimensionality’, whereas the spline estimators effectively take into account such a structure in estimation. A stepwise procedure is suggested to implement the method proposed. A comprehensive Monte Carlo study demonstrates good…

半参数非线性时间序列的模型选择AI 解读

Summary Semiparametric time series regression is often used without checking its suitability, resulting in an unnecessarily complicated model. In practice, one may encounter computational difficulties caused by the curse of dimensionality. The paper suggests that to provide more precise predictions we need to choose the most significant regressors for both the parametric and the nonparametric time series components. We develop a novel cross-validation-based model selection…

交叉分类计数的小区域估计AI 解读

Summary We develop a class of log-linear structural models that is suited to estimation of small area cross-classified counts based on survey data. This allows us to account for various associ- ation structures within the data and includes as a special case the restricted log-linear model underlying structure preserving estimation. The effect of survey design can be incorporated into estimation through the specification of an unbiased direct estimator and its associated…

非高斯 Ornstein–Uhlenbeck 随机波动过程的贝叶斯推断AI 解读

Summary We develop Markov chain Monte Carlo methodology for Bayesian inference for non-Gaussian Ornstein–Uhlenbeck stochastic volatility processes. The approach introduced involves expressing the unobserved stochastic volatility process in terms of a suitable marked Poisson process. We introduce two specific classes of Metropolis–Hastings algorithms which correspond to different ways of jointly parameterizing the marked point process and the model parameters. The performance…

间接推断中的估计函数AI 解读

Summary There are models for which the evaluation of the likelihood is infeasible in practice. For these models the Metropolis–Hastings acceptance probability cannot be easily computed. This is the case, for instance, when only departure times from a G/G/1 queue are observed and inference on the arrival and service distributions are required. Indirect inference is a method to estimate a parameter θ in models whose likelihood function does not have an analytical closed form,…

单变量存在不可忽略无应答时对数线性模型的区间估计AI 解读

Summary Log-linear models for multiway contingency tables where one variable is subject to non-ignorable non-response will often yield boundary solutions, with the probability of non-respondents being classified in some cells of the table estimated as 0. The paper considers the effect of this non-standard behaviour on two methods of interval estimation based on the distribution of the maximum likelihood estimator. The first method relies on the estimator being approximately…

序贯研究中的逐步似然比统计量AI 解读

Summary It is well known that in a sequential study the probability that the likelihood ratio for a simple alternative hypothesis H1versus a simple null hypothesis H0 will ever be greater than a positive constant c will not exceed 1/c under H0. However, for a composite alternative hypothesis, this bound of 1/c will no longer hold when a generalized likelihood ratio statistic is used. We consider a stepwise likelihood ratio statistic which, for each new observation, is…