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递归贝叶斯预测分布AI 解读

P. Richard Hahna, Ryan Martinb* & Stephen G. Walkerca Booth School of Business, The University of Chicago, Chicago, ILb Department of Statistics, North Carolina State University, NCc Department of Mathematics, University of Texas at Austin, TXCONTACT Ryan Martin rgmarti3@ncsu.edu Department of Statistics, North Carolina State University, NC 27607Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA.ABSTRACTA Bayesian framework…

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…

股指日收益条件分布建模：一种替代性的贝叶斯半参数模型AI 解读

This article introduces a new family of Bayesian semiparametric models for the conditional distribution of daily stock index returns. The proposed models capture key stylized facts of such returns, namely, heavy tails, asymmetry, volatility clustering, and the “leverage effect.” A Bayesian nonparametric prior is used to generate random density functions that are unimodal and asymmetric. Volatility is modeled parametrically. The new model is applied to the daily returns of…

单调性、凸性及其他形状约束下的非参数函数估计AI 解读

This paper uses free-knot and fixed-knot regression splines in a Bayesian context to develop methods for the nonparametric estimation of functions subject to shape constraints in models with log-concave likelihood functions. The shape constraints we consider include monotonicity, convexity and functions with a single minimum. A computationally efficient MCMC sampling algorithm is developed that converges faster than previous methods for non-Gaussian models. Simulation…

贝叶斯非参数推断的分位数金字塔AI 解读

Pólya trees fix partitions and use random probabilities in order to construct random probability measures. With quantile pyramids we instead fix probabilities and use random partitions. For nonparametric Bayesian inference we use a prior which supports piecewise linear quantile functions, based on the need to work with a finite set of partitions, yet we show that the limiting version of the prior exists. We also discuss and investigate an alternative model based on the…

非参数单调函数估计的贝叶斯方法AI 解读

Summary The paper proposes two Bayesian approaches to non-parametric monotone function estimation. The first approach uses a hierarchical Bayes framework and a characterization of smooth monotone functions given by Ramsay that allows unconstrained estimation. The second approach uses a Bayesian regression spline model of Smith and Kohn with a mixture distribution of constrained normal distributions as the prior for the regression coefficients to ensure the monotonicity of…

平稳模型的贝叶斯一致性AI 解读

In this paper, we provide a Doob-style consistency theorem for stationary models. Many applications involving Bayesian inference deal with non independent and identically distributed data, in particular, with stationary data. However, for such models, there is still a theoretical gap to be filled regarding the asymptotic properties of Bayesian procedures. The primary goal to be achieved is establishing consistency of the sequence of posterior distributions. Here we provide…

无限维模型中后验分布的收敛速度AI 解读

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of convergence for models including the mixture of Dirichlet process model and the random Bernstein polynomial model.

数据追踪与贝叶斯一致性的理解AI 解读

We deal with strong consistency for Bayesian density estimation. An awkward consequence of inconsistency is described. It is pointed out that consistency at some density f0 depends on the prior mass assigned to the ‘pathological’ set of those densities that are close to f0, in a weak sense, and far apart from f0, in a Hellinger sense. An analysis of these sets leads to the identification of the notion of ‘data tracking’. Specific examples in which this phenomenon cannot…

由递增加性过程驱动的归一化随机测度AI 解读

This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we present results for the distribution of means under both prior and posterior conditions and, via the use of strategic latent variables, undertake a full Bayesian analysis. Our class of priors includes the well-known and widely used mixture…

随机分布及相关函数的贝叶斯非参数推断AI 解读

Summary In recent years, Bayesian nonparametric inference, both theoretical and computational, has witnessed considerable advances. However, these advances have not received a full critical and comparative analysis of their scope, impact and limitations in statistical modelling; many aspects of the theory and methods remain a mystery to practitioners and many open questions remain. In this paper, we discuss and illustrate the rich modelling and analytic possibilities that…

采用贝叶斯非参数混合的层级广义线性模型与脆弱性模型AI 解读

Summary This paper proposes Bayesian nonparametric mixing for some well-known and popular models. The distribution of the observations is assumed to contain an unknown mixed effects term which includes a fixed effects term, a function of the observed covariates, and an additive or multiplicative random effects term. Typically these random effects are assumed to be independent of the observed covariates and independent and identically distributed from a distribution from some…