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使用全局—局部收缩先验的默认贝叶斯分析AI 解读

We provide a framework for assessing the default nature of a prior distribution using the property of regular variation, which we study for global-local shrinkage priors. In particular, we show that the horseshoe priors, originally designed to handle sparsity, are regularly varying and thus are appropriate for default Bayesian analysis. To illustrate our methodology, we discuss four problems of noninformative priors that have been shown to be highly informative for nonlinear…

混合表示、包络表示与层级对偶AI 解读

Summary We develop a connection between mixture and envelope representations of objective functions that arise frequently in statistics. We refer to this connection by using the term ‘hierarchical duality’. Our results suggest an interesting and previously underexploited relationship between marginalization and profiling, or equivalently between the Fenchel–Moreau theorem for convex functions and the Bernstein–Widder theorem for Laplace transforms. We give several different…

贝叶斯桥估计AI 解读

Summary We propose the Bayesian bridge estimator for regularized regression and classification. Two key mixture representations for the Bayesian bridge model are developed: a scale mixture of normal distributions with respect to an α-stable random variable; a mixture of Bartlett–Fejer kernels (or triangle densities) with respect to a two-component mixture of gamma random variables. Both lead to Markov chain Monte Carlo methods for posterior simulation, and these methods turn…

利用 Pólya–Gamma 潜变量进行逻辑模型贝叶斯推断AI 解读

We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Pólya–Gamma distributions, which are constructed in detail. A variety of examples are presented to show the versatility of the method, including logistic regression, negative binomial regression, nonlinear mixed-effect models, and spatial models for count data. In each case, our data-augmentation strategy leads to simple,…

结合 Google 流感趋势数据与状态空间 SEIR 模型追踪疫情AI 解读

In this article, we use Google Flu Trends data together with a sequential surveillance model based on state-space methodology to track the evolution of an epidemic process over time. We embed a classical mathematical epidemiology model [a susceptible-exposed-infected-recovered (SEIR) model] within the state-space framework, thereby extending the SEIR dynamics to allow changes through time. The implementation of this model is based on a particle filtering algorithm, which…

局部收缩规则、Lévy 过程与正则化回归AI 解读

Summary We use Lévy processes to generate joint prior distributions, and therefore penalty functions, for a location parameter β=(β1,…,βp) as p grows large. This generalizes the class of local–global shrinkage rules based on scale mixtures of normals, illuminates new connections between disparate methods and leads to new results for computing posterior means and modes under a wide class of priors. We extend this framework to large-scale regularized regression problems where…

利用动态分割模型进行宏观金融预测AI 解读

Dynamic partition models are used to predict movements in the term structure of interest rates. This allows one to understand historic cycles in the performance of how interest rates behave, and to offer policy makers guidance regarding future expectations on their evolution. Our approach allows for a random number of possible change points in the term structure of interest rates. We use particle learning to learn about the unobserved state variables in a new class of…

用于学习与试验设计的动态树AI 解读

Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in online application settings. We create a sequential tree model whose state changes in time with the accumulation of new data, and provide particle learning algorithms that allow for the efficient online posterior filtering of tree states. A major advantage of tree regression is that it allows for the use of very simple models within each…

带序贯参数学习的实用滤波方法AI 解读

Summary The paper develops a simulation-based approach to sequential parameter learning and filtering in general state space models. Our approach is based on approximating the target posterior by a mixture of fixed lag smoothing distributions. Parameter inference exploits a sufficient statistic structure and the methodology can be easily implemented by modifying state space smoothing algorithms. We avoid reweighting particles and hence sample degeneracy problems that plague…

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贝叶斯投资组合选择：标普500指数1970—1996年的实证分析AI 解读

In this article we present a technique for implementing large-scale optimal portfolio selection. We use high-frequency daily data to capture valuable statistical information in asset returns. We describe several statistical issues involved in quantitative approaches to portfolio selection. Our methodology applies to large-scale portfolio-selection problems in which the number of possible holdings is large relative to the estimation period provided by historical data. We…

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随机波动模型的贝叶斯分析AI 解读

New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain converge in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance…

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Gibbs 采样器的几何收敛AI 解读

SUMMARY The rate of convergence of the Gibbs sampler is discussed. The Gibbs sampler is a Monte Carlo simulation method with extensive application to computational issues in the Bayesian paradigm. Conditions for the geometric rate of convergence of the algorithm for discrete and continuous parameter spaces are derived, and an illustrative exponential family example is given.

基于扩散过程离散观测的贝叶斯因子AI 解读

We present an approach to model selection for a time series of data on a fine time scale. The underlying process generating the data is modelled as a continuous time stochastic process. The underlying continuous processes are assumed to be diffusions with time varying drift and diffusion coefficient. Several approaches to modelling the diffusion coefficient are described. To perform model selection, we propose an approximation to the Bayes factor that uses only the discrete…

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位置模型后验均值的一种表示AI 解读

An exact representation of the posterior mean is developed for a location model and the class of priors that are normal scale mixtures. The result makes use of the conditional distribution of the maximum likelihood estimator and Masreliez's theorem. Directions for future development are indicated.