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波动率非对称建模：树结构多元 GARCH 模型的贝叶斯分析AI 解读

A new class of multivariate threshold GARCH models is proposed for the analysis and modelling of volatility asymmetries in financial time series. The approach is based on the idea of a binary tree where every terminal node parametrizes a (local) multivariate GARCH model for a specific partition of the data. A Bayesian stochastic method is developed and presented for the analysis of the proposed model consisting of parameter estimation, model selection and volatility…

正态均值问题中贝叶斯检验与估计结合方法的最优性AI 解读

We consider a problem of recovering a high-dimensional vector μ observed in white noise, where the unknown vector μ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family of l0-type penalties. The penalties are associated with various choices of the prior distributions πn(⋅) on the number of nonzero entries of μ and, hence, are easy to interpret. The resulting Bayesian estimators lead to a general thresholding rule…

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贝叶斯非参数混合模型中强化机制的控制AI 解读

Summary The paper deals with the problem of determining the number of components in a mixture model. We take a Bayesian non-parametric approach and adopt a hierarchical model with a suitable non-parametric prior for the latent structure. A commonly used model for such a problem is the mixture of Dirichlet process model. Here, we replace the Dirichlet process with a more general non-parametric prior obtained from a generalized gamma process. The basic feature of this model is…

稀疏时点观测的动态空间格点数据连续时间建模AI 解读

Summary We consider statistical and computational aspects of simulation-based Bayesian inference for a spatial–temporal model based on a multivariate point process which is only observed at sparsely distributed times. The point processes are indexed by the sites of a spatial lattice, and they exhibit spatial interaction. For specificity we consider a particular dynamical spatial lattice data set which has previously been analysed by a discrete time model involving unknown…

多重变点问题的在线推断AI 解读

Summary We propose an on-line algorithm for exact filtering of multiple changepoint problems. This algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models. The computational cost of this exact algorithm is quadratic in the number of observations. We further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of…

贝叶斯Probit回归MCMC算法的收敛速度与渐近标准误AI 解读

Summary Consider a probit regression problem in which Y1, …, Yn are independent Bernoulli random variables such that Pr(Yi=1)=Φ(xiTβ) where xi is a p-dimensional vector of known covariates that are associated with Yi, β is a p-dimensional vector of unknown regression coefficients and Φ(·) denotes the standard normal distribution function. We study Markov chain Monte Carlo algorithms for exploring the intractable posterior density that results when the probit regression…

用于评估海洋混合层深度趋势的主观似然AI 解读

This article describes a Bayesian statistical analysis of long-term changes in the depth of the ocean's mixed layer. The data are thermal profiles recorded by ships. For these data, there is no good sampling model and thus no obvious likelihood function. Our approach is to elicit posterior distributions for training data directly from the expert. We then infer the likelihood function and use it on large datasets.

结果依赖型随访的纵向研究AI 解读

We propose Bayesian parametric and semiparametric partially linear regression methods to analyze the outcome-dependent follow-up data when the random time of a follow-up measurement of an individual depends on the history of both observed longitudinal outcomes and previous measurement times. We begin with the investigation of the simplifying assumptions of Lipsitz, Fitzmaurice, Ibrahim, Gelber, and Lipshultz, and present a new model for analyzing such data by allowing…

有限混合回归模型中的变量选择AI 解读

In the applications of finite mixture of regression (FMR) models, often many covariates are used, and their contributions to the response variable vary from one component to another of the mixture model. This creates a complex variable selection problem. Existing methods, such as the Akaike information criterion and the Bayes information criterion, are computationally expensive as the number of covariates and components in the mixture model increases. In this article we…

通过最小二乘近似统一 LASSO 估计AI 解读

We propose a method of least squares approximation (LSA) for unified yet simple LASSO estimation. Our general theoretical framework includes ordinary least squares, generalized linear models, quantile regression, and many others as special cases. Specifically, LSA can transfer many different types of LASSO objective functions into their asymptotically equivalent least squares problems. Thereafter, the standard asymptotic theory can be established and the LARS algorithm can…

基于小波的贝叶斯曲线分类AI 解读

We propose classification models for binary and multicategory data where the predictor is a random function. We use Bayesian modeling with wavelet basis functions that have nice approximation properties over a large class of functional spaces and can accommodate a wide variety of functional forms observed in real life applications. We develop an unified hierarchical model to encompass both the adaptive wavelet-based function estimation model and the logistic classification…

用于发现基因调控网络的回归混合模型变量选择AI 解读

The profusion of genomic data through genome sequencing and gene expression microarray technology has facilitated statistical research in determining gene interactions regulating a biological process. Current methods generally consist of a two-stage procedure: clustering gene expression measurements and searching for regulatory “switches,” typically short, conserved sequence patterns (motifs) in the DNA sequence adjacent to the genes. This process often leads to misleading…

营养流行病学中的结构化测量误差AI 解读

Preterm birth, defined as delivery before 37 completed weeks' gestation, is a leading cause of infant morbidity and mortality. Identifying factors related to preterm delivery is an important goal of public health professionals who wish to identify etiologic pathways to target for prevention. Validation studies are often conducted in nutritional epidemiology in order to study measurement error in instruments that are generally less invasive or less expensive than "gold…

基于种群的可逆跳跃马尔可夫链蒙特卡洛AI 解读

In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target measures. In such cases, MCMC methods may not adequately traverse the support of the target; the simulation results will be unreliable. We develop population methods to deal with such problems, and give a result proving the uniform ergodicity of…

发现新物种概率的贝叶斯非参数估计AI 解读

We consider the problem of evaluating the probability of discovering a certain number of new species in a new sample of population units, conditional on the number of species recorded in a basic sample. We use a Bayesian nonparametric approach. The different species proportions are assumed to be random and the observations from the population exchangeable. We provide a Bayesian estimator, under quadratic loss, for the probability of discovering new species which can be…

用于非贝叶斯推断的积分似然函数AI 解读

Consider a model with parameter θ = (ψ, λ), where ψ is the parameter of interest, and let L(ψ, λ) denote the likelihood function. One approach to likelihood inference for ψ is to use an integrated likelihood function, in which λ is eliminated from L(ψ, λ) by integrating with respect to a density function π(λ|ψ). The goal of this paper is to consider the problem of selecting π(λ|ψ) so that the resulting integrated likelihood function is useful for non-Bayesian likelihood…

临床试验的最优自适应随机设计AI 解读

Optimal decision-analytic designs are deterministic. Such designs are appropriately criticized in the context of clinical trials because they are subject to assignment bias. On the other hand, balanced randomized designs may assign an excessive number of patients to a treatment arm that is performing relatively poorly. We propose a compromise between these two extremes, one that achieves some of the good characteristics of both. We introduce a constrained optimal adaptive…

Bayesian variable selection has gained much empirical success recently in a variety of applications when the number K of explanatory variables $(x_1,\ldots,x_K)$ is possibly much larger than the sample size $n$. For generalized linear models, if most of the $x_j$’s have very small effects on the response $y$, we show that it is possible to use Bayesian variable selection to reduce overfitting caused by the curse of dimensionality $K\gg n$. In this approach a suitable prior…

检验大小、功效与错误发现率AI 解读

Modern scientific technology has provided a new class of large-scale simultaneous inference problems, with thousands of hypothesis tests to consider at the same time. Microarrays epitomize this type of technology, but similar situations arise in proteomics, spectroscopy, imaging, and social science surveys. This paper uses false discovery rate methods to carry out both size and power calculations on large-scale problems. A simple empirical Bayes approach allows the false…

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…

基于 VAR 近似的协整检验修正信息准则AI 解读

We consider the cointegration tests of Johansen (1988, Journal of Economic Dynamics and Control 12, 231–254; 1991, Econometrica 59, 1551–1580) when a vector autoregressive (VAR) process of order k is used to approximate a more general linear process with a possibly infinite VAR representation. Traditional methods to select the lag order, such as Akaike's information criterion (AIC) or the Bayesian information criterion, often lead to too parsimonious a model with the…

混合条件异方差模型的贝叶斯推断AI 解读

We estimate by Bayesian inference the mixed conditional heteroskedasticity model of Haas et al. (2004a Journal of Financial Econometrics 2, 211--50). We construct a Gibbs sampler algorithm to compute posterior and predictive densities. The number of mixture components is selected by the marginal likelihood criterion. We apply the model to the SP500 daily returns. Copyright Royal Economic Society 2007