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金融市场学习过程的计量经济学AI 解读

The asymptotic behavior of the sample paths of two popular statistics that test market efficiency are investigated when markets learn to have rational expectations. Two cases are investigated, where, should markets start out at a rational expectations equilibrium, both statistics would asymptotically generate standard Brownian motions. In a first case, where agents are Bayesian and payoffs exogenous, the statistics have identical sample paths, but they are not standard…

线性高斯状态空间模型的贝叶斯模型判别与贝叶斯因子AI 解读

SUMMARY It is shown how to discriminate between different linear Gaussian state space models for a given time series by means of a Bayesian approach which chooses the model that minimizes the expected loss. A practical implementation of this procedure requires a fully Bayesian analysis for both the state vector and the unknown hyperparameters and is carried out by Markov chain Monte Carlo methods. An application to some non-standard situations such as testing hypotheses on…

预测式模型选择AI 解读

SUMMARY We consider the problem of selecting one model from a large class of plausible models. A predictive Bayesian viewpoint is advocated to avoid the specification of prior probabilities for the candidate models and the detailed interpretation of the parameters in each model. Using criteria derived from a certain predictive density and a prior specification that emphasizes the observables, we implement the proposed methodology for three common problems arising in normal…

用于模型比较的分数贝叶斯因子AI 解读

SUMMARY Bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves. However, there are difficulties with this approach when prior information about the parameters of the various models is weak. Partial Bayes factors offer a resolution of the problem by setting aside part of the data as a training sample. The training sample is used to obtain an initial informative posterior distribution of the parameters in each model.…

模型不确定性的评估与传播AI 解读

SUMMARY In most examples of inference and prediction, the expression of uncertainty about unknown quantities y on the basis of known quantities x is based on a model M that formalizes assumptions about how x and y are related. M will typically have two parts: structural assumptions S, such as the form of the link function and the choice of error distribution in a generalized linear model, and parameters θ whose meaning is specific to a given choice of S. It is common in…

捕获—再捕获数据中迁移与存活概率的贝叶斯估计AI 解读

The Arnason–Schwarz model is usually used for estimating survival and movement probabilities of animal populations from capture-recapture data. The missing data structure of this capture-recapture model is exhibited and summarised via a directed graph representation. Taking advantage of this structure we implement a Gibbs sampling algorithm from which Bayesian estimates and credible intervals for survival and movement probabilities are derived. Convergence of the algorithm…

二元响应回归模型的贝叶斯残差分析AI 解读

In a binary response regression model, classical residuals are difficult to define and interpret due to the discrete nature of the response variable. In contrast, Bayesian residuals have continuous-valued posterior distributions which can be graphed to learn about outlying observations. Two definitions of Bayesian residuals are proposed for binary regression data. Plots of the posterior distributions of the basic ‘observed –fitted’ residuals can be helpful in outlier…

论条件自回归与内蕴自回归AI 解读

Gaussian conditional autoregressions have been widely used in spatial statistics and Bayesian image analysis, where they are intended to describe interactions between random variables at fixed sites in Euclidean space. The main appeal of these distributions is in the Markovian interpretation of their full conditionals. Intrinsic autoregressions are limiting forms that retain the Markov property. Despite being improper, they can have advantages over the standard…

可逆跳跃马尔可夫链蒙特卡洛计算与贝叶斯模型判定AI 解读

Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure. They have therefore not been available for application to Bayesian model determination, where the dimensionality of the parameter vector is typically not fixed. This paper proposes a new framework for the construction of reversible Markov chain samplers…

一类二项响应混合模型后验分布存在性的说明AI 解读

Necessary and sufficient conditions are given for the existence of the posterior distribution of the variance components in a class of mixed models for binomial responses. The implications of our results are illustrated through an example.

将两期交叉设计的贝叶斯分析扩展到缺失数据AI 解读

A procedure is developed for performing a Bayesian analysis of a simple two-period crossover design when some observations are missing in one, or both, treatment periods. The approach requires the numerical evaluation of a single integral to be performed for each posterior marginal distribution of interest. The relative efficiency of this approach to one in which patients with missing data are excluded is investigated.

信息性一般删失下分类数据的贝叶斯方法AI 解读

This paper develops a Bayesian approach to the problem of incomplete categorical data informatively censored where the reported sets are not restricted to follow any specific pattern. It generalises that introduced by Paulino & Pereira (1992) in not requiring a censoring pattern by partitions of the set of sampling categories. Some extensions are also discussed.

时间序列模型的模拟平滑器AI 解读

Recently suggested procedures for simulating from the posterior density of states given a Gaussian state space time series are refined and extended. We introduce and study the simulation smoother, which draws from the multivariate posterior distribution of the disturbances of the model, so avoiding the degeneracies inherent in state samplers. The technique is important in Gibbs sampling with non-Gaussian time series models, and for performing Bayesian analysis of Gaussian…

尺度模型的渐近贝叶斯风险下界及二阶极小极大估计AI 解读

The problem of Bayes estimation of the scale parameter is considered. Lower bounds for the asymptotic Bayes risk are given as the restricted parameter space increases to the positive half-line. The results are next applied to establish the second-order minimax estimator of the scale parameter. Surprisingly, the least favorable distribution coincides with that for the corresponding location parameter problem.

双参数指数族后验分布的可积展开AI 解读

Asymptotic expansions of posterior distributions are derived for a two-dimensional exponential family, which includes normal, gamma, inverse gamma and inverse Gaussian distributions. Reparameterization allows us to use a data-dependent transformation, convert the likelihood function to the two-dimensional standard normal density and apply a version of Stein's identity to assess the posterior distributions. Applications are given to characterize optimal noninformative priors…

通过逐次替代抽样进行不完整数据的贝叶斯非参数估计AI 解读

In the problem of estimating an unknown distribution function $F$ in the presence of censoring, one can use a nonparametric estimator such as the Kaplan-Meier estimator, or one can consider parametric modeling. There are many situations where physical reasons indicate that a certain parametric model holds approximately. In these cases a nonparametric estimator may be very inefficient relative to a parametric estimator. On the other hand, if the parametric model is only a…

探索后验分布的马尔可夫链方法AI 解读

Several Markov chain methods are available for sampling from a posterior distribution. Two important examples are the Gibbs sampler and the Metropolis algorithm. In addition, several strategies are available for constructing hybrid algorithms. This paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues. On the theoretical side, results from the theory of general state space Markov chains can be used to obtain…

利用奥卡姆窗口进行图模型选择并处理模型不确定性AI 解读

We consider the problem of model selection and accounting for model uncertainty in high-dimensional contingency tables, motivated by expert system applications. The approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic P values leading to the selection of a single model; inference is then conditional on the selected model. The sampling properties of such a strategy are complex, and the failure to take account of model uncertainty…

组序贯临床试验：贝叶斯决策论设计的经典统计评价AI 解读

Bayesian decision-theoretic designs for a clinical trial comparing two treatments for a disease with binary outcomes are developed and evaluated. The probability of successful outcome with treatment i is denoted by pi , i = 1, 2, and prior knowledge regarding each pi is assumed to follow a beta distribution. The pi are assumed to be independent. To facilitate comparison with frequentist clinical trial designs, we take a hypothesis-testing approach. The null hypothesis is δ <…

合并受控与非受控研究结果的随机效应元分析模型AI 解读

A random effects model is used to analyze meta-analyses containing both controlled and uncontrolled studies. A noniterative estimator of the treatment effect is derived using least squares, with the between-study variance substituted by an empirical Bayes estimator. The estimator is shown to be strongly consistent when the between-study variance is known, and the variance estimator is also shown to be strongly consistent. The estimator is shown to have desirable heuristic…

合并有对照与无对照研究结果的元分析随机效应模型AI 解读

A random effects model is used to analyze meta-analyses containing both controlled and uncontrolled studies. A noniterative estimator of the treatment effect is derived using least squares, with the between-study variance substituted by an empirical Bayes estimator. The estimator is shown to be strongly consistent when the between-study variance is known, and the variance estimator is also shown to be strongly consistent. The estimator is shown to have desirable heuristic…

一般不完全数据模型中的可忽略性AI 解读

Rubin (1976) defined ignorability conditions for frequentist and Bayes/likelihood analyses of data subject to missing observations. More recently, Heitjan & Rubin (1991) and Heitjan (1993) generalised the Rubin model to encompass other forms of incompleteness, establishing ignorability conditions for Bayes/likelihood inferences only. This paper extends the Heitjan-Rubin model by explicitly defining the observed degree of coarseness as a data element. This permits the…

双指数先验下正态均值后验矩的一个注记AI 解读

SUMMARY General results on the behaviour of the posterior mean and variance of the mean of a normal distribution with known variance using a double-exponential prior are derived and complement the conjectures and particular examples given by Pericchi and Smith (1992) and Pericchi and Walley (1991).