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多变点问题的非参数最大似然方法AI 解读

In multiple change-point problems, different data segments often follow different distributions, for which the changes may occur in the mean, scale or the entire distribution from one segment to another. Without the need to know the number of change-points in advance, we propose a nonparametric maximum likelihood approach to detecting multiple change-points. Our method does not impose any parametric assumption on the underlying distributions of the data sequence, which is…

维数增长下弯曲指数族的后验推断AI 解读

In this paper, we study the large‐sample properties of the posterior‐based inference in the curved exponential family under increasing dimensions. The curved structure arises from the imposition of various restrictions on the model, such as moment restrictions, and plays a fundamental role in econometrics and others branches of data analysis. We establish conditions under which the posterior distribution is approximately normal, which in turn implies various good properties…

门槛回归中的 BootstrapAI 解读

This paper develops a general procedure to check the bootstrap validity in M -estimation. We apply the procedure in discontinuous threshold regression to show the inconsistency of the nonparametric bootstrap for inference on the threshold point. Especially, the conditional weak limit of the nonparametric bootstrap is shown not to exist. By comparing with two other boundaries in the literature, we show the fact that the threshold point is a boundary of the covariate that…

协变量依赖混合模型条件密度估计的后验一致性AI 解读

This paper considers Bayesian nonparametric estimation of conditional densities by countable mixtures of location-scale densities with covariate dependent mixing probabilities. The mixing probabilities are modeled in two ways. First, we consider finite covariate dependent mixture models, in which the mixing probabilities are proportional to a product of a constant and a kernel and a prior on the number of mixture components is specified. Second, we consider kernel…

用于贝叶斯推断的贝塔乘积相依Pitman–Yor过程AI 解读

Multiple time series data may exhibit clustering over time and the clustering effect may change across different series. This paper is motivated by the Bayesian non-parametric modelling of the dependence between clustering effects in multiple time series analysis. We follow a Dirichlet process mixture approach and define a new class of multivariate dependent Pitman–Yor processes (DPY). The proposed DPY are represented in terms of vectors of stick-breaking processes which…

出生队列生育率的贝叶斯预测AI 解读

There are signs that fertility in rich countries may have stopped declining, but this depends critically on whether women currently in reproductive ages are postponing or reducing lifetime fertility. Analysis of average completed family sizes requires forecasts of remaining fertility for women born 1970–1995. We propose a Bayesian model for fertility that incorporates a priori information about patterns over age and time. We use a new dataset, the Human Fertility Database…

用数据增广支持结局延迟的一至二期临床试验AI 解读

A practical impediment in adaptive clinical trials is that outcomes must be observed soon enough to apply decision rules to choose treatments for new patients. For example, if outcomes take up to six weeks to evaluate and the accrual rate is one patient per week, on average three new patients will be accrued while waiting to evaluate the outcomes of the previous three patients. The question is how to treat the new patients. This logistical problem persists throughout the…

带归一化权重的贝叶斯非参数回归：阿尔茨海默病海马萎缩研究AI 解读

Hippocampal volume is one of the best established biomarkers for Alzheimer’s disease. However, for appropriate use in clinical trials research, the evolution of hippocampal volume needs to be well understood. Recent theoretical models propose a sigmoidal pattern for its evolution. To support this theory, the use of Bayesian nonparametric regression mixture models seems particularly suitable due to the flexibility that models of this type can achieve and the unsatisfactory…

用于合并不同实验生存数据的一类风险率混合模型AI 解读

Mixture models for hazard rate functions are widely used tools for addressing the statistical analysis of survival data subject to a censoring mechanism. The present article introduced a new class of vectors of random hazard rate functions that are expressed as kernel mixtures of dependent completely random measures. This leads to define dependent nonparametric prior processes that are suitably tailored to draw inferences in the presence of heterogenous observations. Besides…

EMVS：基于 EM 算法的贝叶斯变量选择AI 解读

Despite rapid developments in stochastic search algorithms, the practicality of Bayesian variable selection methods has continued to pose challenges. High-dimensional data are now routinely analyzed, typically with many more covariates than observations. To broaden the applicability of Bayesian variable selection for such high-dimensional linear regression contexts, we propose EMVS, a deterministic alternative to stochastic search based on an EM algorithm which exploits a…

凸优化、形状约束、复合决策与经验贝叶斯规则AI 解读

Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new perspectives. The first, motivated by Brown and Greenshtein, introduces a nonparametric maximum likelihood estimator of the mixture density subject to a monotonicity constraint on the resulting Bayes rule. The second, motivated by Jiang and Zhang, proposes a new approach to computing the Kiefer–Wolfowitz nonparametric…

函数数据的富集折棒过程AI 解读

In many applications involving functional data, prior information is available about the proportion of curves having different attributes. It is not straightforward to include such information in existing procedures for functional data analysis. Generalizing the functional Dirichlet process (FDP), we propose a class of stick-breaking priors for distributions of functions. These priors incorporate functional atoms drawn from constrained stochastic processes. The…

采用收缩与扩散先验的贝叶斯变量选择AI 解读

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the well-known spike and slab Gaussian priors with a distinct feature, that is, the prior variances depend on the sample size through which appropriate shrinkage can be achieved. We show the strong selection consistency of the proposed method in…

非线性结构时间序列模型的贝叶斯推断AI 解读

We consider efficient methods for likelihood inference applied to structural models. In particular, we introduce a particle filter method which concentrates upon disturbances in the Markov state of the approximating solution to the structural model. A particular feature of such models is that the conditional distribution of interest for the disturbances is often multimodal. We provide a fast and effective method for approximating such distributions. We estimate a…

长期投资者的战略资产配置：参数不确定性与先验信息AI 解读

SUMMARY We study the effect of parameter uncertainty on the long‐run risk for three asset classes: stocks, bills and bonds. Using a Bayesian vector autoregression with an uninformative prior we find that parameter uncertainty raises the annualized long‐run volatilities of all three asset classes proportionally with the same factor relative to volatilities that are conditional on maximum likelihood parameter estimates. As a result, the horizon effect in optimal asset…

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病例对照研究中似然与贝叶斯分析的回顾—前瞻对称性AI 解读

Prentice & Pyke (1979) established that the maximum likelihood estimate of an odds ratio in a case-control study is the same as would be found by fitting a logistic regression; in other words, for this specific target the incorrect prospective model is inferentially equivalent to the correct retrospective model.Similar results have been obtained for other models, and conditions have also been identified under which the corresponding Bayesian property holds, namely that the…

迭代插补的平稳分布AI 解读

Iterative imputation, in which variables are imputed one at a time conditional on all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modelling problem with relatively simple univariate regressions. In this paper, we begin to characterize the stationary distributions of iterative imputations and their statistical properties, accounting for the conditional models being iteratively estimated from data…

利用多带宽 Gaussian 过程估计各向异性函数AI 解读

In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on defining a Bayesian procedure that leads to the minimax optimal rate of posterior contraction (up to a log factor) adapting to the unknown dimension and anisotropic smoothness of the true surface. We propose such an approach based on a…

Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. This paper studies the cepstral random field model, providing recursive formulas that connect the spatial cepstral coefficients to an equivalent moving-average random field, which facilitates easy computation of the autocovariance matrix. We also provide a comprehensive treatment of the asymptotic theory for…

动态回归模型中的时变稀疏性AI 解读

A novel Bayesian method for inference in dynamic regression models is proposed where both the values of the regression coefficients and the importance of the variables are allowed to change over time. We focus on forecasting and so the parsimony of the model is important for good performance. A prior is developed which allows the shrinkage of the regression coefficients to suitably change over time and an efficient Markov chain Monte Carlo method for posterior inference is…

具有内生马尔可夫状态转换参数的状态空间模型估计AI 解读

This study proposes and estimates state‐space models with endogenous Markov regime‐switching parameters. It complements regime‐switching dynamic linear models by allowing the discrete regime to be jointly determined with observed or unobserved continuous state variables. The estimation framework involves a Bayesian Markov chain Monte Carlo scheme to simulate the latent state variable that controls the regime shifts. A simulation exercise shows that neglecting endogeneity…

半参数线性模型中的贝叶斯变量选择AI 解读

There is a rich literature on Bayesian variable selection for parametric models. Our focus is on generalizing methods and asymptotic theory established for mixtures of g-priors to semiparametric linear regression models having unknown residual densities. Using a Dirichlet process location mixture for the residual density, we propose a semiparametric g-prior which incorporates an unknown matrix of cluster allocation indicators. For this class of priors, posterior computation…

倾向得分估计的不确定性：贝叶斯变量选择与模型平均因果效应AI 解读

Causal inference with observational data frequently relies on the notion of the propensity score (PS) to adjust treatment comparisons for observed confounding factors. As decisions in the era of "big data" are increasingly reliant on large and complex collections of digital data, researchers are frequently confronted with decisions regarding which of a high-dimensional covariate set to include in the PS model in order to satisfy the assumptions necessary for estimating…