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粒子 Markov 链 Monte Carlo 方法AI 解读

Summary Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show…

用平滑回归混合模型逼近条件密度AI 解读

This paper shows that large nonparametric classes of conditional multivariate densities can be approximated in the Kullback–Leibler distance by different specifications of finite mixtures of normal regressions in which normal means and variances and mixing probabilities can depend on variables in the conditioning set (covariates). These models are a special case of models known as “mixtures of experts” in statistics and computer science literature. Flexible specifications…

可选 Pólya 树与贝叶斯推断AI 解读

We introduce an extension of the Pólya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random measures that are absolutely continuous with piecewise smooth densities on partitions that can adapt to fit the data. The resulting “optional Pólya tree” distribution has large support in total variation topology and yields posterior distributions…

采用 Dirichlet 过程混合误差的加性三次样条回归AI 解读

The goal of this article is to develop a flexible Bayesian analysis of regression models for continuous and categorical outcomes. In the models we study, covariate (or regression) effects are modeled additively by cubic splines, and the error distribution (that of the latent outcomes in the case of categorical data) is modeled as a Dirichlet process mixture. We employ a relatively unexplored but attractive basis in which the spline coefficients are the unknown function…

大数据集可数混合模型的后验模拟AI 解读

Mixture models, or convex combinations of a countable number of probability distributions, offer an elegant framework for inference when the population of interest can be subdivided into latent clusters having random characteristics that are heterogeneous between, but homogeneous within, the clusters. Traditionally, the different kinds of mixture models have been motivated and analyzed from very different perspectives, and their common characteristics have not been fully…

惩罚样条估计的同时置信带AI 解读

In this article we construct simultaneous confidence bands for a smooth curve using penalized spline estimators. We consider three types of estimation methods: (a) as a standard (fixed effect) nonparametric model, (b) using the mixed-model framework with the spline coefficients as random effects, and (c) a full Bayesian approach. The volume-of-tube formula is applied for the first two methods and compared with Bayesian simultaneous confidence bands from a frequentist…

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…

不完整多项数据的贝叶斯推断：病原体多样性问题AI 解读

With recent advances in genetic analysis, it has become feasible to classify a pathogen into genetically distinct variants even though they apparently cause an infected subject similar symptoms. The availability of such data opens up the interesting problem of studying the spatiotemporal variation in the diversity of variants of a pathogen. Data on pathogen variants often suffer the problems of (i) low cell counts, (ii) incomplete classification due to laboratory problems…

大型多性状遗传试验的分层空间过程模型AI 解读

This article expands upon recent interest in Bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets of multiple traits of interest. Direct application of such multivariate models to large spatial datasets is often computationally infeasible because of cubic order matrix algorithms involved in estimation. The situation is…

用于音乐分析的动态非参数贝叶斯模型AI 解读

The dynamic hierarchical Dirichlet process (dHDP) is developed to model complex sequential data, with a focus on audio signals from music. The music is represented in terms of a sequence of discrete observations, and the sequence is modeled using a hidden Markov model (HMM) with time-evolving parameters. The dHDP imposes the belief that observations that are temporally proximate are more likely to be drawn from HMMs with similar parameters, while also allowing for…

分析有序偏好数据的贝叶斯向量多维尺度方法AI 解读

Multidimensional scaling (MDS) comprises a family of geometric models for the multidimensional representation of data and a corresponding set of methods for fitting such models to actual data. In this paper, we develop a new Bayesian vector MDS model to analyze ordered successive categories preference/dominance data commonly collected in many social science and business studies. A joint spatial representation of the row and column elements of the input data matrix is…

服务于冬季道路养护的概率天气预测AI 解读

Winter road maintenance is one of the main tasks for the Washington State Department of Transportation. Anti-icing, that is, the preemptive application of chemicals, is often used to keep the roadways free of ice. Given the preventive nature of anti-icing, accurate predictions of road ice are needed. Currently, anti-icing decisions are usually based on deterministic weather forecasts. However, the costs of the two kinds of errors are highly asymmetric because the cost of a…

贝叶斯多尺度多重插补及其数据保密含义AI 解读

Many scientific, sociological, and economic applications present data that are collected on multiple scales of resolution. One particular form of multiscale data arises when data are aggregated across different scales both longitudinally and by economic sector. Frequently, such datasets experience missing observations in a manner that they can be accurately imputed, while respecting the constraints imposed by the multiscale nature of the data, using the method we propose…

Dirichlet 过程随机效应模型的估计AI 解读

We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the multinomial and Dirichlet distributions, and is shown to be an improvement, in terms of operator norm and efficiency, over other commonly used MCMC algorithms. We also investigate methods for the estimation of the precision parameter of…

基于时间变换的随机波动率模型推断AI 解读

We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrization defined through transformations that operate on the time scale of the diffusion. A novel MCMC scheme which overcomes the inherent difficulties of time change transformations is also presented. The algorithm is fast to implement and applies to models with stochastic…

违约率估计与专家信息AI 解读

Default is a rare event, even in segments in the midrange of a bank’s portfolio. Inference about default rates is essential for risk management and for compliance with the requirements of Basel II. Most commercial loans are in the middle-risk categories and are to unrated companies. Expert information is crucial in inference about defaults. A Bayesian approach is proposed and illustrated using a prior distribution assessed from an industry expert. The binomial model, most…

离散时空系统的统计主体模型AI 解读

Agent-based models have been used to mimic natural processes in a variety of fields, from biology to social science. By specifying mechanistic models that describe how small-scale processes function and then scaling them up, agent-based approaches can result in very complicated large-scale behavior while often relying on only a small set of initial conditions and intuitive rules. Although many agent-based models are used strictly in a simulation context, statistical…

大规模离散选择模型的变分推断AI 解读

Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact inference is often intractable. Markov chain Monte Carlo techniques make approximate inference possible, but the computational cost is prohibitive on the large datasets now becoming routinely available. Variational methods provide a…

基于集合预报与贝叶斯模型平均的风速概率预测AI 解读

The current weather forecasting paradigm is deterministic, based on numerical models. Multiple estimates of the current state of the atmosphere are used to generate an ensemble of deterministic predictions. Ensemble forecasts, while providing information on forecast uncertainty, are often uncalibrated. Bayesian model averaging (BMA) is a statistical ensemble postprocessing method that creates calibrated predictive probability density functions (PDFs). Probabilistic wind…

不可忽略无应答与抽样选择下小域 BMI 数据的贝叶斯分析AI 解读

Here we analyze body mass index (BMI) data for children and adolescents from the Third National Health and Nutrition Examination Survey (NHANES III). Because of the lack of BMI values for a considerable number of the children and adolescents, and the differential probabilities of selection of these individuals, serious nonresponse and selection bias in inference can be present. To analyze the NHANES III BMI data, a nonignorable nonresponse model has been proposed to estimate…

医疗结局风险调整下的服务提供者评估：贝叶斯与频率学方法AI 解读

“Provider profiling” is the evaluation of the performance of hospitals, doctors, and other medical practitioners to enhance the quality of medical care. We propose a new method and compare conventional and Bayesian methodologies that are used or proposed for use for such “report cards.” Conventional statistical approaches to these provider assessments use likelihood-based frequentist methodologies, and the new Bayesian method is patterned after these. For each of three…

通过广义信息准则选择正则化参数AI 解读

We apply the nonconcave penalized likelihood approach to obtain variable selections as well as shrinkage estimators. This approach relies heavily on the choice of regularization parameter, which controls the model complexity. In this paper, we propose employing the generalized information criterion (GIC), encompassing the commonly used Akaike information criterion (AIC) and Bayesian information criterion (BIC), for selecting the regularization parameter. Our proposal makes a…

在高维分类器中纳入类别先验概率AI 解读

In standard parametric classifiers, or classifiers based on nonparametric methods but where there is an opportunity for estimating population densities, the prior probabilities of the respective populations play a key role. However, those probabilities are largely ignored in the construction of high-dimensional classifiers, partly because there are no likelihoods to be constructed or Bayes risks to be estimated. Nevertheless, including information about prior probabilities…

贝叶斯检验与估计及其在小波阈值化中的应用AI 解读

We consider the problem of estimating the unknown response function in the Gaussian white noise model. We first utilize the recently developed Bayesian maximum a posteriori testimation procedure of Abramovich et al. (2007) for recovering an unknown high-dimensional Gaussian mean vector. The existing results for its upper error bounds over various sparse lp-balls are extended to more general cases. We show that, for a properly chosen prior on the number of nonzero entries of…