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最大似然估计的曲率与推断AI 解读

Maximum likelihood estimates are sufficient statistics in exponential families, but not in general. The theory of statistical curvature was introduced to measure the effects of MLE insufficiency in one-parameter families. Here, we analyze curvature in the more realistic venue of multiparameter families—more exactly, curved exponential families, a broad class of smoothly defined nonexponential family models. We show that within the set of observations giving the same value…

基于经验过程的MCMC经验贝叶斯推断与贝叶斯敏感性分析AI 解读

Consider a Bayesian situation in which we observe $Y\sim p_{\theta}$, where $\theta\in\Theta$, and we have a family $\{\nu_{h},h\in\mathcal{H}\}$ of potential prior distributions on $\Theta$. Let $g$ be a real-valued function of $\theta$, and let $I_{g}(h)$ be the posterior expectation of $g(\theta)$ when the prior is $\nu_{h}$. We are interested in two problems: (i) selecting a particular value of $h$, and (ii) estimating the family of posterior expectations $\{I_{g}(h),h\in\mathcal{H}\}$…

高频金融数据的随机尾指数模型与贝叶斯分析AI 解读

This paper proposes a new dynamic model called Stochastic Tail Index (STI) model to analyze time-varying tail index for financial asset using high frequency return data. Bayesian tools are developed to estimate the model, make related inferences, and perform model selection. To construct efficient posterior sampler for the STI model by an approximation approach, a new algorithm called ALSO (Auxiliary Least Squares Optimization) is introduced, which can quickly make…

含难以计算的归一化函数时的贝叶斯推断AI 解读

Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference for these models is complicated because the normalizing functions of their probability distributions include the parameters of interest. In Bayesian analysis, they result in so-called doubly intractable posterior distributions which pose…

优化动态治疗方案的贝叶斯机器学习方法AI 解读

Medical therapy often consists of multiple stages, with a treatment chosen by the physician at each stage based on the patient's history of treatments and clinical outcomes. These decisions can be formalized as a dynamic treatment regime. This paper describes a new approach for optimizing dynamic treatment regimes that bridges the gap between Bayesian inference and existing approaches, like Q-learning. The proposed approach fits a series of Bayesian regression models, one…

免疫治疗的贝叶斯 I/II 期临床试验设计AI 解读

Immunotherapy is an innovative treatment approach that stimulates a patient's immune system to fight cancer. It demonstrates characteristics distinct from conventional chemotherapy and stands to revolutionize cancer treatment. We propose a Bayesian phase I/II dosefinding design that incorporates the unique features of immunotherapy by simultaneously considering three outcomes: immune response, toxicity and efficacy. The objective is to identify the biologically optimal dose,…

评估昼夜节律随时间规律性的潜变量泊松模型AI 解读

Many researchers in biology and medicine have focused on trying to understand biological rhythms and their potential impact on disease. A common biological rhythm is circadian, where the cycle repeats itself every 24 hours. However, a disturbance of the circadian pattern may be indicative of future disease. In this article, we develop new statistical methodology for assessing the degree of disturbance or irregularity in a circadian pattern for count sequences that are…

线性回归中贝叶斯因子的零假设分布AI 解读

We show that under the null, the 2 log(Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and the normal prior. Our results have three immediate impacts. First, we can compute analytically a p-value associated with a Bayes factor without the need of permutation. We provide…

再生核希尔伯特空间在函数型分类中的应用AI 解读

The Hájek–Feldman dichotomy establishes that two Gaussian measures are either mutually absolutely continuous with respect to each other (and hence there is a Radon–Nikodym density for each measure with respect to the other one) or mutually singular. Unlike the case of finite-dimensional Gaussian measures, there are nontrivial examples of both situations when dealing with Gaussian stochastic processes. This article provides: (a) Explicit expressions for the optimal (Bayes)…

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…

错误发现率平滑AI 解读

We present false discovery rate (FDR) smoothing, an empirical-Bayes method for exploiting spatial structure in large multiple-testing problems. FDR smoothing automatically finds spatially localized regions of significant test statistics. It then relaxes the threshold of statistical significance within these regions, and tightens it elsewhere, in a manner that controls the overall false discovery rate at a given level. This results in increased power and cleaner spatial…

惩罚化间接推断AI 解读

Parameter estimates of structural economic models are often difficult to interpret at the light of the underlying economic theory. Bayesian methods have become increasingly popular as a tool for conducting inference on structural models since priors offer a way to exert control over the estimation results. Similarly to Bayesian estimation, this paper proposes a penalized indirect inference estimator that allows researchers to obtain economically meaningful parameter…

基于辅助统计量的模拟估计：ABC与模拟最小距离的联系AI 解读

The frequentist method of simulated minimum distance (SMD) is widely used in economics to estimate complex models with an intractable likelihood. In other disciplines, a Bayesian approach known as Approximate Bayesian Computation (ABC) is far more popular. This paper connects these two seemingly related approaches to likelihood-free estimation by means of a Reverse Sampler that uses both optimization and importance weighting to target the posterior distribution. Its hybrid…

Itô半鞅短时变动分布的精确贝叶斯矩推断AI 解读

We modify the Gallant and Tauchen (1996) efficient method of moments (EMM) method to perform exact Bayesian inference, where exact means no reliance on asymptotic approximations. We use this modification to evaluate the empirical plausibility of recent predictions from high frequency financial theory regarding the small-time movements of an Itô semimartingale. The theory indicates that the probability distribution of the small moves should be locally stable around the…

具有恒定覆盖率的自适应多组置信区间AI 解读

Commonly used interval procedures for multigroup data attain their nominal coverage rates across a population of groups on average, but their actual coverage rate for a given group will be above or below the nominal rate, depending on the group mean. While correct coverage for a given group can be achieved with a standard |$t$|-interval, this approach is not adaptive to the available information about the distribution of group-specific means. In this article we construct…

具有边与顶点对称性的高斯图模型精度及协方差矩阵贝叶斯估计AI 解读

Graphical Gaussian models with edge and vertex symmetries were introduced by Højsgaard & Lauritzen (2008), who gave an algorithm for computing the maximum likelihood estimate of the precision matrix for such models. In this paper, we take a Bayesian approach to its estimation. We consider only models with symmetry constraints and which thus form a natural exponential family with the precision matrix as the canonical parameter. We identify the Diaconis–Ylvisaker conjugate…

回归调整近似贝叶斯计算的收敛性AI 解读

We present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont et al. (2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior that, asymptotically, correctly quantifies uncertainty. Furthermore, for such a choice of bandwidth we can implement an importance sampling algorithm to sample from the posterior whose acceptance probability tends to unity as the data…

近似贝叶斯计算估计量的渐近效率AI 解读

Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian inference in such cases. We present results on the asymptotic variance of estimators obtained using approximate Bayesian computation in a large data limit. Our key assumption is that the data are summarized by a fixed-dimensional summary…

第一价格拍卖中模糊性的经验相关性AI 解读

We study the identification and estimation of first-price auctions with independent private values if bidders face ambiguity about the valuation distribution and have maxmin expected utility. Using variation in the number of bidders we nonparametrically identify the true valuation distribution and the lower envelope of the set of prior beliefs. We also allow for CRRA and unobserved auction heterogeneity, and propose a Bayesian estimation method based on Bernstein…

含随机波动的时变参数VAR的贝叶斯模型比较AI 解读

Summary We develop importance sampling methods for computing two popular Bayesian model comparison criteria, namely, the marginal likelihood and the deviance information criterion (DIC) for time‐varying parameter vector autoregressions (TVP‐VARs), where both the regression coefficients and volatilities are drifting over time. The proposed estimators are based on the integrated likelihood, which are substantially more reliable than alternatives. Using US data, we find…

广义线性模型的加权平均最小二乘估计AI 解读

The weighted-average least squares (WALS) approach, introduced by Magnus et al. (2010) in the context of Gaussian linear models, has been shown to enjoy important advantages over other strictly Bayesian and strictly frequentist model-averaging estimators when accounting for problems of uncertainty in the choice of the regressors. In this paper we extend the WALS approach to deal with uncertainty about the specification of the linear predictor in the wider class of…

任意删失生存数据的贝叶斯半参数建模统一框架：兼顾空间信息AI 解读

A comprehensive, unified approach to modeling arbitrarily censored spatial survival data is presented for the three most commonly used semiparametric models: proportional hazards, proportional odds, and accelerated failure time. Unlike many other approaches, all manner of censored survival times are simultaneously accommodated including uncensored, interval censored, current-status, left and right censored, and mixtures of these. Left-truncated data are also accommodated…

动态网络流量数据的可扩展贝叶斯建模、监测与分析AI 解读

Traffic flow count data in networks arise in many applications, such as automobile or aviation transportation, certain directed social network contexts, and Internet studies. Using an example of Internet browser traffic flow through site-segments of an international news website, we present Bayesian analyses of two linked classes of models which, in tandem, allow fast, scalable, and interpretable Bayesian inference. We first develop flexible state-space models for streaming…

静态因子模型中的不变推断与高效计算AI 解读

Factor models are used in a wide range of areas. Two issues with Bayesian versions of these models are a lack of invariance to ordering of and scaling of the variables and computational inefficiency. This article develops invariant and efficient Bayesian methods for estimating static factor models. This approach leads to inference that does not depend upon the ordering or scaling of the variables, and we provide arguments to explain this invariance. Beginning from identified…