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体视学极值推断AI 解读

In the production of clean steels, the occurrence of imperfections—so-called “inclusions”—is unavoidable. The strength of a clean steel block is largely dependent on the size of the largest imperfection that it contains, so inference on extreme inclusion size forms an important part of quality control. Sampling is generally done by measuring imperfections on planar slices, leading to an extreme value version of a standard stereological problem: how to make inference on large…

采用两类邻接关系条件自回归先验的牙周数据空间分析AI 解读

Attachment loss, the extent of a tooth's root (in millimeters) that is no longer attached to surrounding bone by periodontal ligament, is often used to measure the current state of a patient's periodontal disease and monitor disease progression. Attachment loss data can be analyzed using a conditionally autoregressive (CAR) prior distribution that smooths fitted values toward neighboring values. However, it may be desirable to have more than one class of neighbor relation in…

一种简单的风险调整指数加权移动平均AI 解读

In such contexts as medical monitoring there is a need for a simple procedure to estimate the level of a smoothly changing dynamic process while adjusting for risk factors associated with heterogeneous nonnormal observations. Standard methods exist for when the data are normal, and simple methods have been developed for nonnormal data without covariates. The dynamic generalized linear model (DGLM) may be considered a standard for nonnormal data with covariates, but perhaps…

利用半参数贝叶斯方法预测美国癌症死亡人数AI 解读

We present two models for the short-term prediction of the number of deaths arising from common cancers in the United States. The first is a local linear model, in which the slope of the segment joining the number of deaths for any two consecutive time periods is assumed to be random with a nonparametric distribution, which has a Dirichlet process prior. For slightly longer prediction periods, we present a local quadratic model. This extension of the local linear model…

利用多分辨率近似对分形过程进行推断AI 解读

We consider Bayesian inference via Markov chain Monte Carlo for a variety of fractal Gaussian processes on the real line. These models have unknown parameters in the covariance matrix, requiring inversion of a new covariance matrix at each Markov chain Monte Carlo iteration. The processes have no suitable independence properties so this becomes computationally prohibitive. We surmount these difficulties by developing a computational algorithm for likelihood evaluation based…

通过平滑样条自动估计多变量谱AI 解读

The classical method for estimating the spectral density of a multivariate time series is to first calculate the periodogram, and then smooth it to obtain a consistent estimator. Typically, to ensure the estimate is positive definite, all the elements of the periodogram are smoothed the same way. There are, however, many situations for which different components of the spectral matrix have different degrees of smoothness, and hence require different smoothing parameters in…

评价层级贝叶斯与经验贝叶斯模型的贝叶斯预测信息准则AI 解读

The problem of evaluating the goodness of the predictive distributions of hierarchical Bayesian and empirical Bayes models is investigated. A Bayesian predictive information criterion is proposed as an estimator of the posterior mean of the expected loglikelihood of the predictive distribution when the specified family of probability distributions does not contain the true distribution. The proposed criterion is developed by correcting the asymptotic bias of the posterior…

扩展常规先验以检验线性模型中的一般假设AI 解读

We consider that observations come from a general normal linear model and that it is desirable to test a simplifying null hypothesis about the parameters. We approach this problem from an objective Bayesian, model-selection perspective. Crucial ingredients for this approach are ‘proper objective priors’ to be used for deriving the Bayes factors. Jeffreys-Zellner-Siow priors have good properties for testing null hypotheses defined by specific values of the parameters in…

构建稠密可变形模板估计的统一统计框架AI 解读

Summary The problem of estimating probabilistic deformable template models in the field of computer vision or of probabilistic atlases in the field of computational anatomy has not yet received a coherent statistical formulation and remains a challenge. We provide a careful definition and analysis of a well-defined statistical model based on dense deformable templates for grey level images of deformable objects. We propose a rigorous Bayesian framework for which we prove…

非独立同分布观测下后验分布的收敛速度AI 解读

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the posterior measure relative to distances derived from a testing criterion. We then specialize our results to independent, nonidentically distributed observations, Markov processes, stationary Gaussian time series and the white noise model. We…

自适应重要性采样混合方案的收敛AI 解读

In the design of efficient simulation algorithms, one is often beset with a poor choice of proposal distributions. Although the performance of a given simulation kernel can clarify a posteriori how adequate this kernel is for the problem at hand, a permanent on-line modification of kernels causes concerns about the validity of the resulting algorithm. While the issue is most often intractable for MCMC algorithms, the equivalent version for importance sampling algorithms can…

树结构回归与积分的微分AI 解读

This paper provides answers to questions regarding the almost sure limiting behavior of rooted, binary tree-structured rules for regression. Examples show that questions raised by Gordon and Olshen in 1984 have negative answers. For these examples of regression functions and sequences of their associated binary tree-structured approximations, for all regression functions except those in a set of the first category, almost sure consistency fails dramatically on events of full…

简单线性模型的预测与估计：真的如此简单吗？AI 解读

Consider the simple normal linear regression model for estimation/prediction at a new design point. When the slope parameter is not obviously nonzero, hypothesis testing and information criteria can be used for identifying the right model. We compare the performances of such methods both theoretically and empirically from different perspectives for more insight. The testing approach at the conventional size of 0.05, in spite of being the “standard approach,” performs poorly…

涉及有限差分程序的计算机实验经验贝叶斯分析AI 解读

Computer experiments are increasingly used in scientific investigations as substitutes for physical experiments in cases where the latter are difficult or impossible to perform. A computer experiment consists of several runs of a computer model or “code” for the purpose of better understanding the input → output relationship. One practical difficulty in the use of these models is that a single run may require a prohibitive amount of computational resources in some…

在遗传连锁分析中纳入不同异质性水平的贝叶斯方法AI 解读

A widely used approach for dealing with locus heterogeneity in linkage analysis is based on mixture likelihood, in which a single mixing (heterogeneity) parameter represents the probability that each family is of linked type. However, in general, different types of families exhibit different heterogeneity levels. To incorporate this variability, we propose a new approach wherein each family has its own heterogeneity parameter representing the probability that it is of linked…

层次 Dirichlet 过程AI 解读

We consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups. We assume that the number of mixture components is unknown a priori and is to be inferred from the data. In this setting it is natural to consider sets of Dirichlet processes, one for each group, where the well-known clustering property of the Dirichlet process provides a nonparametric prior…

信息性抽样下的多层模型AI 解读

We consider a model-dependent approach for multi-level modelling that accounts for informative probability sampling of first- and lower-level population units. The proposed approach consists of first extracting the hierarchical model holding for the sample data given the selected sample, as a function of the corresponding population model and the first- and lower-level sample selection probabilities, and then fitting the resulting sample model using Bayesian methods. An…

计数时间序列参数驱动模型的辅助混合抽样及状态空间应用AI 解读

We consider parameter-driven models of time series of counts, where the observations are assumed to arise from a Poisson distribution with a mean changing over time according to a latent process. Estimation of these models is carried out within a Bayesian framework using data augmentation and Markov chain Monte Carlo methods. We suggest a new auxiliary mixture sampler, which possesses a Gibbsian transition kernel, where we draw from full conditional distributions belonging…

部分观测扩散模型的贝叶斯模型选择AI 解读

We present an approach to Bayesian model selection for finitely observed diffusion processes. We use data augmentation by treating the paths between observed points as missing data. For a fixed model formulation, the strong dependence between the missing paths and the volatility of the diffusion can be broken down by adopting the method of Roberts & Stramer (2001). We describe how this method may be extended to the case of model selection via reversible jump Markov chain…

Cox 回归模型的后验适定性与计算：缺失协变量应用AI 解读

In this paper, we carry out an in-depth theoretical investigation of Bayesian inference for the Cox regression model. We establish necessary and sufficient conditions for posterior propriety of the regression coefficient, β, in Cox's partial likelihood, which can be obtained as the limiting marginal posterior distribution of β through the specification of a gamma process prior for the cumulative baseline hazard and a uniform improper prior for β. We also examine necessary…

利用贝叶斯树形捕获再捕获模型构造后分层AI 解读

For the problem of dual system estimation, we propose a Bayesian treed capture-recapture model to account for heterogeneity of capture probabilities where individual auxiliary information is available. The model uses a binary tree to partition the covariate space into ‘homogeneous’ regions, within each of which the capture response can be described adequately by a simple model that assumes equal catchability. The attractive features of the proposed model include reduction of…

无限维指数族贝叶斯密度估计的收敛速度AI 解读

We study the rate of convergence of posterior distributions in density estimation problems for log-densities in periodic Sobolev classes characterized by a smoothness parameter p. The posterior expected density provides a nonparametric estimation procedure attaining the optimal minimax rate of convergence under Hellinger loss if the posterior distribution achieves the optimal rate over certain uniformity classes. A prior on the density class of interest is induced by a prior…

渐近极小极大贝叶斯预测密度AI 解读

Given a random sample from a distribution with density function that depends on an unknown parameter θ, we are interested in accurately estimating the true parametric density function at a future observation from the same distribution. The asymptotic risk of Bayes predictive density estimates with Kullback–Leibler loss function D(fθ||{f̂})=∫fθ log(fθ/f̂) is used to examine various ways of choosing prior distributions; the principal type of choice studied is minimax. We seek…

多单位序贯时钟拍卖的实证模型AI 解读

Abstract We construct a model of participation and bidding at multi‐unit, sequential, clock auctions when bidders have multi‐unit demand. We describe conditions sufficient to characterize a symmetric, perfect‐Bayesian equilibrium and then demonstrate that this equilibrium induces an efficient allocation. We propose an algorithm, based on the generalized Vickrey auction, to calculate the expected winning bid for each unit sold. This algorithm allows us to construct a…