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正态混合分布参数估计的拟贝叶斯方法AI 解读

This article proposes a very tractable approach to estimating parameters for mixtures of normal distributions. The analyst proceeds as if, in addition to the data, he or she had observed some pseudo data points drawn from each distribution whose values reflect his or her priors. The approach eliminates the singularities associated with maximum likelihood estimation and offer guidance for choosing among alternative local maximum likelihood estimates. Monte Carlo analysis…

删失数据线性回归的精确近似条件推断与贝叶斯推断AI 解读

A method to approximate marginal posterior distribution functions of regression coefficients and scale parameters is presented. It is based on a general asymptotic formula of DiCiccio, Field & Fraser (1990) for approximating marginal tail probabilities. In developing the method, it is shown that the accuracy of the approximation of DiCiccio et al. can be substantially increased in certain cases by using a suitable change of variables, and a general approach to deriving such…

含随机效应的广义线性模型估计AI 解读

A conceptually very simple but general algorithm for the estimation of the fixed effects, random effects, and components of dispersion in generalized linear models with random effects is proposed. Conditions are described under which the algorithm yields approximate maximum likelihood or quasi-maximum likelihood estimates of the fixed effects and dispersion components, and approximate empirical Bayes estimates of the random effects. The algorithm is applied to two data sets…

光滑函数边际尾概率的近似及其贝叶斯与条件推断应用AI 解读

This paper presents an asymptotic approximation of marginal tail probabilities for a real-valued function of a random vector, where the function has continuous gradient that does not vanish at the mode of the joint density of the random vector. This approximation has error O(n−3/2) and improves upon a related standard normal approximation which has error O(n−½). Derivation involves the application of a tail probability formula given by DiCiccio, Field & Fraser (1990) to an…

回归参数稳定性的贝叶斯显著性检验AI 解读

This paper presents a Bayesian significance test for stationarity of a regression equation using the highest posterior density credible set. In addition, a solution to the Behrens-Fisher problem is provided. From a Monte Carlo simulation study, it has been shown that the Bayesian significance test has stronger power than the Cusum and the Cusum of squares tests. The Bayesian significance test may be useful in detecting individual parameter nonstationarity.

含有序多分类响应的非参数贝叶斯生物测定AI 解读

Previous attempts at implementing fully Bayesian nonparametric bioassay have enjoyed limited success due to computational difficulties. We show here how this problem may be generally handled using a sampling based approach to develop desired marginal posterior distributions and their features. A useful extension is presented which treats the case of ordered polytomous response. Illustrative examples are provided.

迈向可实施的贝叶斯非参数密度估计AI 解读

SUMMARY Nonparametric density estimators smooth the empirical distribution function and are sensitive to the choice of smoothing parameters. This paper develops an hierarchical Bayes formulation for the smoothing problem. The prior distribution for the density function is the logistic normal process, which is a logistic transform of a Gaussian process. The covariance of the Gaussian process is a smoothing kernel and has parameters that control the degree of smoothness. The…

In the exponential regression model, inference concerning the regression parameter is notoriously difficult, even when using the Bayesian noninformative prior approach. The reference prior approach (Bernardo, 1979; Berger & Bernardo, 1989) is considered, and argued to yield very satisfactory inferences. Estimation and credible sets are considered in a specific example.

存在删失时的贝叶斯残差分析AI 解读

Use of the posterior distribution of the realized error terms for residual analysis in a linear model was advocated by Zellner (1975) and Zellner & Moulton (1985). The same idea was used by Chaloner & Brant (1988) to define outliers and calculate posterior probabilities of observations being outliers. This paper extends the same concept to other models, including regression models for lifetime data, by using an approach similar to that of Cox & Snell (1968). Residual plots…

多次捕获—再捕获模型的贝叶斯分析AI 解读

In multiple capture-recapture surveys, the probability of capture can vary between sampling occasions. The model accounting for this variation is known as Mt. Bayes, empirical Bayes, and Bayes empirical Bayes solutions are given to the problems of interval estimation, decision making, and point estimation of the population size N. When the number of sampling occasions is small to moderate and the number of recaptured units observed on each sampling occasion is moderate,…

位置模型后验均值的一种表示AI 解读

An exact representation of the posterior mean is developed for a location model and the class of priors that are normal scale mixtures. The result makes use of the conditional distribution of the maximum likelihood estimator and Masreliez's theorem. Directions for future development are indicated.

贝叶斯风险的信息不等式AI 解读

This paper presents lower bounds, derived from the information inequality, for the Bayes risk under scaled quadratic loss. Some numerical results are also presented which give some idea concerning the precision of these bounds. An appendix contains a proof of the information inequality without conditions on the estimator. This result is a direct extension of an earlier result of Fabian and Hannan.

用 Gibbs 抽样展示正态数据模型的贝叶斯推断AI 解读

The use of the Gibbs sampler as a method for calculating Bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models, including variance components, unordered and ordered means, hierarchical growth curves, and missing data in a crossover trial. In all cases the approach is straightforward to specify distributionally and to implement computationally, with output readily adapted for required inference summaries.

具有欧几里得结构模型中的贝叶斯推断AI 解读

When a parameter space is endowed with a Euclidean structure, there is a Euclidean measure, called the structural (or geometric) prior, which is an obvious candidate to represent ignorance concerning an unknown parameter. The rationale for using this prior is strengthened when the unknown parameter is the canonical parameter of an exponential family. Then the structural prior is the uniform prior for the canonical parameter. It is shown also that Euclidean structures can be…

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具有欧几里得结构的模型中的贝叶斯推断AI 解读

When a parameter space is endowed with a Euclidean structure, there is a Euclidean measure, called the structural (or geometric) prior, which is an obvious candidate to represent ignorance concerning an unknown parameter. The rationale for using this prior is strengthened when the unknown parameter is the canonical parameter of an exponential family. Then the structural prior is the uniform prior for the canonical parameter. It is shown also that Euclidean structures can be…

The results of forecasting experiments based on an error correction mechanism (ECM) model and various types of vector autoregressive (VAR) and Bayesian vector autoregressive (BVAR) models are presented. A Bayesian error correction mechanism (BECM) model is also tested. This model represents a hybrid of the BVAR and ECM models. The results from experiments using fifty industries and monthly Ohio labor market data demonstrate that the ECM model produces forecasts with much…

公共与私人信息：信息汇聚的实验研究AI 解读

This paper reports on an experimental study of the way in which individuals make inferences from publicly available information. We compare the predictions of a theoretical model of a common knowledge inference process with actual behavior. In the theoretical model, "perfect Bayesians," starting with private information, take actions; an aggregate statistic is made publicly available; the individuals do optimal Bayesian updating and take new actions; and the process…

战略互补博弈中的可理性化、学习与均衡AI 解读

The authors study a rich class of noncooperative games that includes models of oligopoly competition, macroeconomic coordination failures, arms races, bank runs, technology adoption and diffusion, R&D competition, pretrial bargaining, coordination in teams, and many others. For all these games, the sets of pure strategy Nash equilibria, correlated equilibria, and rationalizable strategies have identical bounds. Also, for a class of models of dynamic adaptive choice behavior…

利用定性调查数据探索通胀预期形成机制AI 解读

The objective of this article is to propose a method of exploring the mechanism of expectation formation based on qualitative survey data. The survey data are regarded as a sample from a multinomial distribution whose parameters are time-variant functions of inflation expectations. The parameters are estimated using a Bayesian recursive approach, which is a generalization of the Kalman filtering technique. For illustrative purposes, the method is applied to Japanese data.…

CUSUM 程序的决策论最优性AI 解读

Suppose $X_1, X_2, \ldots$ are independent random variables such that for some unknown $\nu$, each of $X_1, \ldots, X_{\nu - 1}$ is distributed according to $F_0$, while $X_\nu, X_{\nu + 1}, \ldots$ are all distributed according to $F_1$. We prove a result of Moustakides that claims that the CUSUM procedures are optimal in the sense of Lorden. We do that by proving that the procedures are Bayes for some stochastic mechanism of generating $\nu$.

多项分布贝叶斯因子的下界及其在卡方拟合检验中的应用AI 解读

Lower bounds on Bayes factors in favor of the null hypothesis in multinomial tests of point null hypotheses are developed. These are then applied to derive lower bounds on Bayes factors in both exact and asymptotic chi-squared testing situations. The general conclusion is that the lower bounds tend to be substantially larger than $P$-values, raising serious questions concerning the routine use of moderately small $P$-values (e.g., 0.05) to represent significant evidence…

基于贝塔过程的生命历程数据非参数贝叶斯估计AI 解读

Several authors have constructed nonparametric Bayes estimators for a cumulative distribution function based on (possibly right-censored) data. The prior distributions have, for example, been Dirichlet processes or, more generally, processes neutral to the right. The present article studies the related problem of finding Bayes estimators for cumulative hazard rates and related quantities, w.r.t. prior distributions that correspond to cumulative hazard rate processes with…

Let $l(\theta) = n^{-1} \log p(x, \theta)$ be the log likelihood of an $n$-dimensional $X$ under a $p$-dimensional $\theta$. Let $\hat{\theta}_j$ be the mle under $H_j: \theta^1 = \theta^1_0, \ldots, \theta^j = \theta^j_0$ and $\hat{\theta}_0$ be the unrestricted mle. Define $T_j$ as $\lbrack 2n\{l(\hat{\theta}_{j - 1}) - l(\hat{\theta}_j)\}\rbrack^{1/2} \operatorname{sgn}(\hat{\theta}^j_{j - 1} - \theta^j_0).$ Let $T = (T_1, \ldots, T_p)$. Then under regularity conditions,…