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Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We…

潜在断棒过程AI 解读

We develop a model for stochastic processes with random marginal distributions. Our model relies on a stick-breaking construction for the marginal distribution of the process, and introduces dependence across locations by using a latent Gaussian copula model as the mechanism for selecting the atoms. The resulting latent stick-breaking process (LaSBP) induces a random partition of the index space, with points closer in space having a higher probability of being in the same…

函数型数据的混合式 Dirichlet 混合模型AI 解读

Summary In functional data analysis, curves or surfaces are observed, up to measurement error, at a finite set of locations, for, say, a sample of n individuals. Often, the curves are homogeneous, except perhaps for individual-specific regions that provide heterogeneous behaviour (e.g. ‘damaged’ areas of irregular shape on an otherwise smooth surface). Motivated by applications with functional data of this nature, we propose a Bayesian mixture model, with the aim of…

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空间边界不对齐数据的完全模型化方法AI 解读

We consider inference using multivariate data that are spatially misaligned; that is, involving variables (typically counts or rates) that are aggregated over differing sets of regional boundaries. Geographic information systems enable the simultaneous display of such datasets, but their current capabilities are essentially only descriptive, not inferential. We describe a hierarchical modeling approach that provides a natural solution to this problem through its ability to…

空间错位数据的完全模型化分析方法AI 解读

We consider inference using multivariate data that are spatially misaligned; that is, involving variables (typically counts or rates) that are aggregated over differing sets of regional boundaries. Geographic information systems enable the simultaneous display of such datasets, but their current capabilities are essentially only descriptive, not inferential. We describe a hierarchical modeling approach that provides a natural solution to this problem through its ability to…

广义线性模型的可识别性、非正常先验与 Gibbs 抽样AI 解读

Markov chain Monte Carlo algorithms are widely used in the fitting of generalized linear models (GLMs). Such model fitting is somewhat of an art form, requiring suitable trickery and tuning to obtain results in which one can have confidence. A wide range of practical issues arise. The focus here is on parameter identifiability and posterior propriety. In particular, we clarify that nonidentifiability arises for usual GLMs and discuss its implications for simulation-based…

住宅成交数据的时空建模AI 解读

This article focuses on the location, time, and spatio-temporal components associated with suitably aggregated data to improve prediction of individual asset values. Such effects are introduced in the context of hierarchical models, which we find more natural than attempting to model covariance structure. Indeed, our cross-sectional database, a sample of 7,936 transactions for 49 subdivisions over a 10-year period in Baton Rouge, Louisiana, precludes covariance modeling. A…

生物尺寸关系的断裂：含测量误差的截断半参数回归AI 解读

Biological size relationships (i.e., regression of one size variable on another) are typically monotone but often break down at extreme values of the variables. Here we study the way in which a plant's biomass is apportioned to reproductive and other life activities. Working with a theory proposed by Weiner (1988) based an analogy between a biological plant and an industrial plant leads to a truncated regression model formulation. We consider a dataset involving 542…

生物体大小关系的失效：含测量误差的截断半参数回归AI 解读

Biological size relationships (i.e., regression of one size variable on another) are typically monotone but often break down at extreme values of the variables. Here we study the way in which a plant's biomass is apportioned to reproductive and other life activities. Working with a theory proposed by Weiner (1988) based an analogy between a biological plant and an industrial plant leads to a truncated regression model formulation. We consider a dataset involving 542…

破纪录数据问题的参数似然推断AI 解读

In this paper we consider the analysis of record breaking data sets, where only observations that exceed, or only those that fall below, the current extreme value are recorded. Example application areas include industrial stress testing, meteorological analysis, sporting and athletic events, and oil and mining surveys. A closely related area is that of threshold modelling, where the observations are those that cross a certain threshold value. The inherent missing data…

破纪录数据问题的参数似然推断AI 解读

In this paper we consider the analysis of record breaking data sets, where only observations that exceed, or only those that fall below, the current extreme value are recorded. Example application areas include industrial stress testing, meteorological analysis, sporting and athletic events, and oil and mining surveys. A closely related area is that of threshold modelling, where the observations are those that cross a certain threshold value. The inherent missing data…

利用纵向CD4 T细胞数量研究HIV感染进展的层级贝叶斯模型AI 解读

Taking the absolute number of CD4 T-cells as a marker of disease progression for persons infected with the human immunodeficiency virus (HIV), we model longitudinal series of such counts for a sample of 327 subjects in the San Francisco Men's Health Study (Waves 1–8, excluding zidovudine cases). We conduct a fully Bayesian analysis of these data. We employ individual level nonlinear models incorporating such critical features as incomplete and unbalanced data, population…

利用 Gibbs 采样分析参数约束与截断数据问题AI 解读

Constrained parameter problems arise in a wide variety of applications, including bioassay, actuarial graduation, ordinal categorical data, response surfaces, reliability development testing, and variance component models. Truncated data problems arise naturally in survival and failure time studies, ordinal data models, and categorical data studies aimed at uncovering underlying continuous distributions. In many applications both parameter constraints and data truncation are…

构造准确参数经验贝叶斯置信区间的样本再利用方法AI 解读

SUMMARY Parametric empirical Bayes (EB) methods of point estimation for a vector of unknown parameters date to the landmark paper of James and Stein (1961). The usual approach is to use the mean of the estimated posterior distribution of each parameter, where the estimation of the prior parameters (‘hyperparameters’) is accomplished through the marginal distribution of the data. While point estimates computed this way usually perform well, interval estimates based on the…

含有序多分类响应的非参数贝叶斯生物测定AI 解读

Previous attempts at implementing fully Bayesian nonparametric bioassay have enjoyed limited success due to computational difficulties. We show here how this problem may be generally handled using a sampling based approach to develop desired marginal posterior distributions and their features. A useful extension is presented which treats the case of ordered polytomous response. Illustrative examples are provided.

用 Gibbs 抽样展示正态数据模型的贝叶斯推断AI 解读

The use of the Gibbs sampler as a method for calculating Bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models, including variance components, unordered and ordered means, hierarchical growth curves, and missing data in a crossover trial. In all cases the approach is straightforward to specify distributionally and to implement computationally, with output readily adapted for required inference summaries.

经验贝叶斯置信区间的构造方法AI 解读

Parametric empirical Bayes (EB) methods of point estimation date to the landmark paper by James and Stein (1961). Interval estimation through parametric empirical Bayes techniques has a somewhat shorter history, which was summarized by Laird and Louis (1987). In the exchangeable case, one obtains a “naive” EB confidence interval by simply taking appropriate percentiles of the estimated posterior distribution of the parameter, where the estimation of the prior parameters…

经验贝叶斯置信区间的构造方法AI 解读

Parametric empirical Bayes (EB) methods of point estimation date to the landmark paper by James and Stein (1961). Interval estimation through parametric empirical Bayes techniques has a somewhat shorter history, which was summarized by Laird and Louis (1987). In the exchangeable case, one obtains a “naive” EB confidence interval by simply taking appropriate percentiles of the estimated posterior distribution of the parameter, where the estimation of the prior parameters…

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