论文检索

均值乘积的估计：基于参考先验的贝叶斯分析AI 解读

Suppose that we observe X ∼ N(α, 1) and, independently, Y ∼ N(β, 1), and are concerned with inference (mainly estimation and confidence statements) about the product of means θ = αβ. This problem arises, most obviously, in situations of determining area based on measurements of length and width. It also arises in other practical contexts, however. For instance, in gypsy moth studies, the hatching rate of larvae per unit area can be estimated as the product of the mean of egg…

区间原假设的贝叶斯因子下界AI 解读

Expressions are derived for lower bounds on Bayes factors for interval null hypotheses. These are then studied for varying interval lengths and are related to two interesting results—one for point null hypotheses and another for one-sided hypotheses. These results are illustrated with two of the most frequently used hypothesis tests—the normal test and Student's t test.

预测分布的最优报告策略AI 解读

Consider a problem in which you and a group of other experts must report your individual predictive distributions for an observable random variable X to some decision maker. Suppose that the report of each expert is assigned a prior weight by the decision maker and that these weights are then updated based on the observed value of X. In this situation you will try to maximize your updated, or posterior, weight by appropriately choosing the distribution that you report,…

区间原假设贝叶斯因子的下界AI 解读

Expressions are derived for lower bounds on Bayes factors for interval null hypotheses. These are then studied for varying interval lengths and are related to two interesting results—one for point null hypotheses and another for one-sided hypotheses. These results are illustrated with two of the most frequently used hypothesis tests—the normal test and Student's t test.

缺失数据的统计分析AI 解读

Preface.PART I: OVERVIEW AND BASIC APPROACHES.Introduction.Missing Data in Experiments.Complete-Case and Available-Case Analysis, Including Weighting Methods.Single Imputation Methods.Estimation of Imputation Uncertainty.PART II: LIKELIHOOD-BASED APPROACHES TO THE ANALYSIS OF MISSING DATA.Theory of Inference Based on the Likelihood Function.Methods Based on Factoring the Likelihood, Ignoring the Missing-Data Mechanism.Maximum Likelihood for General Patterns of Missing Data:…

指数回归模型使用非正常先验的若干讨论AI 解读

We consider Bayesian inference on the exponential regression model. It is known that standard improper priors on the parameters of this model lead to marginal posterior distributions on one of the parameters involved which are also improper on the interval (0, 1). This has sometimes been interpreted as meaning that the observations are irrelevant. We re-analyse this problem using a finitely-additive approach and show that the above conclusion is not generally correct. This…

交换经济中不完全信息下的实施AI 解读

This paper studies the problem of implementation of allocation rules in economic environments when agents are incompletely informed about the environment. The concept of equilibrium used is that of Bayesian Nash equilibrium. The authors show that a condition called Bayesian monotonicity is necessary for implementation, as is an incentive compatibility condition. They also show that, when there are at least three agents, Bayesian monotonicity and a slightly stronger incentive…

利用横截面的第一与第二选择数据估计市场弹性AI 解读

This article develops a method for using first-choice/second-choice information to estimate the ratio of cross-elasticities to own-elasticities. I then use Bayesian techniques to couple this information with prior knowledge of the elasticities. This leads to elasticity estimates reflecting the decision maker's prior knowledge as well as existing data on customer first-choice/second-choice preferences.

一份来自前线的报告AI 解读

This study provides quantitative evidence of the professional impact of the Bayesian viewpoint as measured by the percentage of pages devoted to Bayesian topics in econometrics textbooks and leading econometrics and statistics journals.

贝叶斯分析中影响与敏感性评估的近似方法AI 解读

We use asymptotic approximations to posterior expectations in deriving diagnostics for case influence and prior sensitivity. We obtain an easily-interpreted expression for the change in posterior expectation following perturbation of the problem, which also produces a useful interpretation of the likelihood displacement discussed by Cook & Weisberg (1982). In addition, we propose two simple diagnostics of posterior nonnor mality. The leukaemia data analysed by Feigl & Zelen…

二元二项分布的贝叶斯推断AI 解读

A bivariate distribution is investigated in connection with an application in microbiology. It has binomial marginal and conditional distributions. The parameter structure is examined, and it is shown that a conjugate Bayesian prior distribution arises from prior independence specifications. Under these specifications the usual limiting conjugate prior can be obtained via invariance considerations.

二维列联表潜类别分析的贝叶斯方法AI 解读

Latent class analysis in two-way contingency tables usually suffers from unidentifiability problems. These an be overcome by using Bayesian techniques in which prior distributions are assumed on the latent parameters. Application of these techniques, however, involves some unusual computational difficulties. Bayesian techniques suitable for latent class analyses together with a remedy to the computational difficulties are discussed in this paper.

非线性函数的边际密度近似AI 解读

This paper presents an asymptotic approximation for the marginal density of a nonlinear function g(θ) that is applicable when the joint density of θ is dominated by a single mode and the Jacobian of g is of full rank near that mode. The approximation is based on Laplace's method and its asymptotic properties are similar to those of the saddlepoint approximation. The approximation is applied to the computation of a marginal posterior density, a marginal sampling density and a…

论参数密度估计AI 解读

The paper makes a critical assessment of Aitchison's criterion of density estimation. It seems not to satisfy certain intuitive requirements. A new criterion based on decisions theoretic considerations is introduced. It is shown through examples that the judgement about the choice of density estimates is seriously dependent on the criterion chosen. Some other density estimates are introduced which look similar to Bayesian predictive density estimates without using a prior…

指数回归模型分析中使用非正常先验的几点讨论AI 解读

We consider Bayesian inference on the exponential regression model. It is known that standard improper priors on the parameters of this model lead to marginal posterior distributions on one of the parameters involved which are also improper on the interval (0, 1). This has sometimes been interpreted as meaning that the observations are irrelevant. We re-analyse this problem using a finitely-additive approach and show that the above conclusion is not generally correct. This…

有限总体的贝叶斯自助法AI 解读

A Bayesian bootstrap for a finite population is introduced; its small-sample distributional properties are discussed and compared with those of the frequentist bootstrap for a finite population. It is also shown that the two are first-order asymptotically equivalent.

两行动问题经验贝叶斯规则的收敛速率：离散情形AI 解读

The purpose of this paper is to investigate the convergence rates of a sequence of empirical Bayes decision rules for the two-action decision problems where the distributions of the observations belong to a discrete exponential family. It is found that the sequence of the empirical Bayes decision rules under study is asymptotically optimal, and the order of associated convergence rates is $O(\exp(-cn))$, for some positive constant $c$, where $n$ is the number of accumulated…

Identifiability problems have previously precluded a general approach to testing the hypothesis of a "pure" distribution against the alternative of a mixture of distributions. Three types of identifiability are defined, and it is shown that $B$-identifiability allows a Bayesian solution to the testing problem. First, an equivalence relation is defined over parametrizations of probability functions. Then the projection onto the quotient space is shown to give a $B$-identifiabl…

正态均值混合分布的估计及其在复合决策问题中的应用AI 解读

A procedure for estimating the mixing distribution for a normal mean is presented. The estimator is shown to be consistent regardless of the mixing distribution, and it is suggested that the estimation techniques may be applied in a similar manner to estimate mixing distributions for a wide class of location parameter families. Implied marginal density and derivative estimates for the normal case are shown to be consistent, converging at near-optimal rates. In addition,…

不同损失函数下的风险控制：折中决策问题AI 解读

Controlling Bayes and/or minimax risks under possibly different loss functions is formulated as a problem faced by two or more statisticians who must compromise and agree on the use of a single decision procedure. The theory characterizing solutions to Bayes compromise problems and minimax-Bayes compromise problems is presented. In a Bayes compromise problem, Bayes risks under different prior distributions and/or loss functions are minimized simultaneously. In a…

平滑样条的贝叶斯置信区间AI 解读

The frequency properties of Wahba's Bayesian confidence intervals for smoothing splines are investigated by a large-sample approximation and by a simulation study. When the coverage probabilities for these pointwise confidence intervals are averaged across the observation points, the average coverage probability (ACP) should be close to the nominal level. From a frequency point of view, this agreement occurs because the average posterior variance for the spline is similar to…

线性回归中的贝叶斯变量选择AI 解读

This article is concerned with the selection of subsets of predictor variables in a linear regression model for the prediction of a dependent variable. It is based on a Bayesian approach, intended to be as objective as possible. A probability distribution is first assigned to the dependent variable through the specification of a family of prior distributions for the unknown parameters in the regression model. The method is not fully Bayesian, however, because the ultimate…

回归结构稳定性的多重决策理论分析AI 解读

Using the theory of multiple decisions, this paper conducts an analysis of structural stability in location and variance for the linear-regression model. It shows that both cusum and cusum-of-squares techniques are in certain senses optimal. However, the same tests are optimal for changes in location and variance. It is also shown that there is an inherent contradiction between the use of recursive residuals and cusum techniques. The concept of a localized Bayes rule is…

十九个 OECD 国家实际 GDP 的长期与周期行为：1957—1983年AI 解读

Log per capita real gross domestic product is modeled as a third-order autoregression with a pair of complex roots whose amplitude is smaller than the amplitude of the real root. The behavior of this terms series is interpreted in terms of these two amplitudes, the periodicity of the complex roots, and the standard deviation of the disturbance. Restrictions are evaluated and inference is conducted using the likelihood principle, applying Monte Carlo integration with…