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利用先验反馈法进行序约束下的最大似然估计AI 解读

Algorithms for deriving isotonic regression estimators in order-restricted linear models and more generally restricted maximum likelihood estimators are usually quite dependent on the particular problem considered. We propose here an optimization method based on a sequence of formal Bayes estimates whose variances converge to zero. This method, akin to simulated annealing, can be applied “universally”; that is, as long as these Bayes estimators can be derived by exact…

存在加性异常值的自回归过程的稳健贝叶斯模型选择AI 解读

Autoregressive (AR) models of order k are often used for forecasting and control of time series, as well as for the estimation of functionals such as the spectrum. Here we propose a method that consists of calculating the posterior probabilities of the competing AR(k) models in a way that is robust to outliers, and then obtaining the predictive distributions of quantities of interest, such as future observations and the spectrum, as a weighted average of the predictive…

用于模型选择与预测的内在贝叶斯因子AI 解读

In the Bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions, it is typically not possible to utilize standard noninformative (or default) prior distributions. This has led Bayesians to use conventional proper prior distributions or crude approximations to Bayes factors. In this article we introduce a new criterion called the intrinsic Bayes factor, which is fully automatic in the sense of requiring only standard…

存在不可忽略缺失的纵向有序临床试验依从性数据：贝叶斯 Tobit 建模AI 解读

In the Lung Health Study (LHS), compliance with the use of inhaled medication was assessed at each follow-up visit both by self-report and by weighing the used medication canisters. One or both of these assessments were missing if the participant failed to attend the visit or to return all canisters. Approximately 30% of canister-weight data and 5% to 15% of self-report data were missing at different visits. We use Gibbs sampling with data augmentation and a multivariate…

群体药代动力学模型的贝叶斯分析AI 解读

Pharmacokinetics is the study of the time course of a drug and its metabolites following its introduction into the body. Population pharmacokinetic studies are becoming increasingly important as an aid to drug development. The data from such studies typically consist of dose histories, drug concentrations with associated sampling times, and often covariate measurements such as the age and weight of each subject. These studies aim to provide an understanding of the…

Medicare 脑卒中患者转入专业护理机构的比例：含未观测异质性的贝叶斯逻辑回归AI 解读

We determine factors, both hospital-specific and market area-specific, associated with hospitals' propensities for discharging Medicare stroke patients to skilled nursing facilities (SNF's) in California and Florida. Logistic regression is generalized to the case of a betabinomial, hierarchical model, in which covariate information is included in the hyperparameters of the second-stage beta distribution. It is found that the posterior mean of the proportion discharged to SNF…

摘要暂缺

含加性异常值的自回归过程稳健贝叶斯模型选择AI 解读

Autoregressive (AR) models of order k are often used for forecasting and control of time series, as well as for the estimation of functionals such as the spectrum. Here we propose a method that consists of calculating the posterior probabilities of the competing AR(k) models in a way that is robust to outliers, and then obtaining the predictive distributions of quantities of interest, such as future observations and the spectrum, as a weighted average of the predictive…

存在不可忽略缺失的纵向有序临床试验依从性数据：贝叶斯 Tobit 建模AI 解读

In the Lung Health Study (LHS), compliance with the use of inhaled medication was assessed at each follow-up visit both by self-report and by weighing the used medication canisters. One or both of these assessments were missing if the participant failed to attend the visit or to return all canisters. Approximately 30% of canister-weight data and 5% to 15% of self-report data were missing at different visits. We use Gibbs sampling with data augmentation and a multivariate…

Medicare 中风患者转入专业护理机构的比例：含未观测异质性的贝叶斯逻辑回归AI 解读

We determine factors, both hospital-specific and market area-specific, associated with hospitals' propensities for discharging Medicare stroke patients to skilled nursing facilities (SNF's) in California and Florida. Logistic regression is generalized to the case of a betabinomial, hierarchical model, in which covariate information is included in the hyperparameters of the second-stage beta distribution. It is found that the posterior mean of the proportion discharged to SNF…

利用先验反馈法进行顺序约束下的极大似然估计AI 解读

Algorithms for deriving isotonic regression estimators in order-restricted linear models and more generally restricted maximum likelihood estimators are usually quite dependent on the particular problem considered. We propose here an optimization method based on a sequence of formal Bayes estimates whose variances converge to zero. This method, akin to simulated annealing, can be applied “universally”; that is, as long as these Bayes estimators can be derived by exact…

时间序列贝叶斯推断的渐近理论AI 解读

This paper develops an asymptotic theory of Bayesian inference for time series. A limiting representation of the Bayesian data density is obtained and shown to be of the same general exponential form for a wide class of likelihoods and prior distributions. Continuous time and discrete time cases are studied. In discrete time, an embedding theorem is given which shows how to embed the exponential density in a continuous time process. From the embedding we obtain a large…

连续单参数指数族经验贝叶斯检验的最优收敛率AI 解读

The empirical Bayes linear loss two-action problem in the continuous one-parameter exponential family is studied. Previous results on this problem construct empirical Bayes tests via kernel density estimates. They also obtain upper bounds for the unconditional regret at some prior distribution. In this paper, we discuss the general question of how difficult the above empirical Bayes problem is, and why empirical Bayes rules based on kernel density estimates are useful.…

复合紧参数高斯位移实验中渐近最优且可容许的决策规则AI 解读

Asymptotically optimal and admissible compound decision rules are obtained in a Hilbert-parameterized Gaussian shift experiment. The component parameter set is restricted to compact. For the squared error loss, every compound Bayes estimator is admissible and every compound estimator Bayes versus full support hyperprior mixture of iid priors on the compound parameter is asymptotically optimal. For the latter class of rules induced by full support hyperpriors, asymptotic…

后验期望的局部敏感性AI 解读

We investigate the degree to which posterior expectations are sensitive to prior distributions, using a local method based on functional differentiation. Invariance considerations suggest a family of norms which can be used to measure perturbations to the prior. The sensitivity measure is seen to depend heavily on the choice of norm; asymptotic results suggest which norm will yield the most useful results in practice. We find that to maintain asymptotically sensible…

局部均匀先验分布AI 解读

Suppose that $X_{\sigma} | \mathbf{\theta} \sim N(\mathbf{\theta}, \sigma^2)$ and that $\sigma \to 0$. For which prior distributions on $\mathbf{\theta}$ is the posterior distribution of $\mathbf{\theta}$ given $X_{\sigma}$ asymptotically $N(X_{\sigma}, \sigma^2)$ when in fact $X_{\sigma} \sim N(\theta_0, \sigma^2)$? It is well known that the stated convergence occurs when $\mathbf{\theta}$ has a prior density that is positive and continuous at $\theta_0$. It turns out that…

马尔可夫链模拟方法的收敛性AI 解读

The Markov chain simulation method has been successfully used in many problems, including some that arise in Bayesian statistics. We give a self-contained proof of the convergence of this method in general state spaces under conditions that are easy to verify.

This paper proposes a consistent nonparametric empirical Bayes estimator of the prior density for directional data. The methodology is to use Fourier analysis on $S^2$ to adapt Euclidean techniques to this non-Euclidean environment. General consistency results are obtained. In addition, a discussion of efficient numerical computation of Fourier transforms on $S^2$ is given, and their applications to the methods suggested in this paper are sketched.

分层有限总体中的准线性贝叶斯估计AI 解读

SUMMARY In this paper a Bayesian least squares approximation is proposed for descriptive inference in a finite population when a categorical auxiliary variable is known. A hierarchical model II analysis of variance is assumed. The solution consists of a projection on the vector of group totals and on the between and within sums of squares. The approximation can be seen as a normal approximation of the joint distribution of the statistic and of the parameter of interest,…

多项数据的推断：从一袋弹珠中学习AI 解读

SUMMARY A new method is proposed for making inferences from multinomial data in cases where there is no prior information. A paradigm is the problem of predicting the colour of the next marble to be drawn from a bag whose contents are (initially) completely unknown. In such problems we may be unable to formulate a sample space because we do not know what outcomes are possible. This suggests an invariance principle: inferences based on observations should not depend on the…

校准的贝叶斯方法AI 解读

The authors develop a Bayesian approach to calibration which enables the incorporation of uncertainty regarding the parameters of the theoretical model under investigation. Their procedure involves the specification of prior distributions over parameter values, which in turn induce distributions over the statistical properties of artificial data simulated from the model. These distributions are compared with their empirical counterparts in order to assess the model's fit.…

偏序偏好的表示AI 解读

This essay considers decision-theoretic foundations for robust Bayesian statistics. We modify the approach of Ramsey, de Finetti, Savage and Anscombe and Aumann in giving axioms for a theory of robust preferences. We establish that preferences which satisfy axioms for robust preferences can be represented by a set of expected utilities. In the presence of two axioms relating to state-independent utility, robust preferences are represented by a set of probability/utility…

贝叶斯推断的局部敏感性诊断AI 解读

We investigate diagnostics for quantifying the effect of small changes to the prior distribution over a k-dimensional parameter space. We show that several previously suggested diagnostics, such as the norm of the Fréchet derivative, diverge at rate $n^{k/2}$ if the base prior is an interior point in the class of priors, under the density ratio topology. Diagnostics based on $\phi$-divergences exhibit similar asymptotic behavior. We show that better asymptotic behavior can…

后验分布的收敛AI 解读

Z.A general (asymptotic) theory of estimation was developed by Ibragimov and Has’minskii under certain conditions on the normalized likelihood ratios. In an earlier work, the present authors studied the limiting behaviour of the posterior distributions under the general setup of Ibragimov and Has’minskii. In particular, they obtained a necessary condition for the convergence of a suitably centered (and normalized) posterior to a constant limit in terms of the limiting…