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用于生存分析的随机网络模型AI 解读

We present methodology giving highly accurate approximations for Bayesian predictive densities and distribution functions of first passage times between states of a semi-Markov process with a finite number of states. When the states describe a degenerative disorder with an absorbing end state, such predictive distributions are the survival distributions of a patient. We illustrate these methods with a variety of examples, including data from the San Francisco AIDS study. We…

分类变量随机有序分布的贝叶斯分析AI 解读

This article considers a finite set of discrete distributions all having the same finite support. The problem of interest is to assess the strength of evidence produced by sampled data for a hypothesis of a specified stochastic ordering among the underlying distributions and to estimate these distributions subject to the ordering. We present a Bayesian approach that is an alternative to using the posterior probability of the hypothesis and the Bayes factor in favor of the…

大西洋鳕鱼种群年龄构成的序约束贝叶斯估计AI 解读

The management of a commercial fishery often requires estimates of the age composition. These estimates are typically based on age and length data obtained from sampling the commercial landings from the fishery and the catches from a research vessel survey. We use data from annual research cruises of Georges Bank conducted by the Canadian Department of Fisheries and Oceans to show how inferences for Atlantic cod (Gadus morhua) can be improved. Traditionally, two-phase…

贝叶斯线性模型中删例重要性抽样权重的变异性AI 解读

I consider a standard specification of the Bayesian linear model and derive necessary and sufficient conditions for the variance of the case-deletion importance sampling weights to be finite. The conditions have an intuitive interpretation in terms of familiar frequentist measures of leverage and influence and are easy to verify. I present two real data examples in which the necessary conditions fail to hold for some observations and the corresponding importance sampling…

正态均值的乘积分割模型AI 解读

I consider probability models for the estimation of normal means that allow for some of the means to be equal. These probability models, called product partition models, specify prior probabilities for a random partition. The posterior probability of the partition given the observations has the same form. The resulting estimate of the means—the product estimate—is obtained by conditioning on the partition and summing over all possible partitions. The large number of…

线性回归模型的贝叶斯模型平均AI 解读

We consider the problem of accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. A Bayesian solution to this problem involves averaging over all possible models (i.e., combinations of predictors) when making inferences about quantities of interest. This approach is often not practical. In this…

正态均值的乘积分割模型AI 解读

I consider probability models for the estimation of normal means that allow for some of the means to be equal. These probability models, called product partition models, specify prior probabilities for a random partition. The posterior probability of the partition given the observations has the same form. The resulting estimate of the means—the product estimate—is obtained by conditioning on the partition and summing over all possible partitions. The large number of…

临床试验设计中的贝叶斯方法与伦理AI 解读

Partial table of contents: MAJOR ISSUES Ethically Optimizing Clinical Trials (K. Schaffner) Admissibility of Treatment (N. Sedransk) TEST CASE: VERAPAMIL/NITROPRUSSIDE The Mechanics of Conducting a Clinical Trial (E. Heitmiller & T. Blanck) Issues of Statistical Design (N. Sedransk) Operational History and Procedural Feasibility (J. Kadane) Verapamil versus Nitroprusside: Results of the Clinical Trial I (J. Kadane & N. Sedransk) Verapamil versus Nitroprusside: Results of the…

大西洋鳕鱼种群年龄组成的序约束贝叶斯估计AI 解读

The management of a commercial fishery often requires estimates of the age composition. These estimates are typically based on age and length data obtained from sampling the commercial landings from the fishery and the catches from a research vessel survey. We use data from annual research cruises of Georges Bank conducted by the Canadian Department of Fisheries and Oceans to show how inferences for Atlantic cod (Gadus morhua) can be improved. Traditionally, two-phase…

贝叶斯 VAR 模型估计与推断的数值方法AI 解读

In Bayesian analysis of vector autoregressive models, and especially in forecasting applications, the Minnesota prior of Litterman is frequently used. In many cases other prior distributions provided better forecasts and are preferable from a theoretical standpoint. Several of these priors require numerical methods in order to evaluate the posterior distribution. Different ways of implementing Monte Carlo integration are considered. It is found that Gibbs sampling performs…

不适定逆问题的贝叶斯方法与最大熵AI 解读

In this paper, we study linear inverse problems where some generalized moments of an unknown positive measure are observed. We introduce a new construction, called the maximum entropy on the mean method (MEM), which relies on a suitable sequence of finite-dimensional discretized inverse problems. Its advantage is threefold: It allows us to interpret all usual deterministic methods as Bayesian methods; it gives a very convenient way of taking into account prior information;…

存在不依从的随机实验中因果效应的贝叶斯推断AI 解读

For most of this century, randomization has been a cornerstone of scientific experimentation, especially when dealing with humans as experimental units. In practice, however, noncompliance is relatively common with human subjects, complicating traditional theories of inference that require adherence to the random treatment assignment. In this paper we present Bayesian inferential methods for causal estimands in the presence of noncompliance, when the binary treatment…

混合谱时间序列的半参数贝叶斯推断AI 解读

Summary A Bayesian analysis is presented of a time series which is the sum of a stationary component with a smooth spectral density and a deterministic component consisting of a linear combination of a trend and periodic terms. The periodic terms may have known or unknown frequencies. The advantage of our approach is that different features of the data—such as the regression parameters, the spectral density, unknown frequencies and missing observations—are combined in a…

季节单位根与季节均值变动的贝叶斯分析AI 解读

In this paper we propose a Bayesian analysis of seasonal unit roots in quarterly observed time series. Seasonal unit root processes are useful to describe economic series with changing seasonal fluctuations. A natural alternative model for similar purposes contains deterministic seasonal mean shifts instead of seasonal stochastic trends. This leads to analysing seasonal unit roots in the presence of mean shifts using Bayesian techniques. Our method is illustrated using…

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具有随机波动的贝叶斯向量自回归AI 解读

This paper proposes a Bayesian approach to a vector autoregression with stochastic volatility, where the multiplicative evolution of the precision matrix is driven by a multivariate beta variate. Exact updating formulas are given to the nonlinear filtering of the precision matrix. Estimation of the autoregressive parameters requires numerical methods: an importance-sampling-based approach is explained here.

利用逻辑斯蒂回归与汇总统计量的经验贝叶斯小区域估计AI 解读

Many available methods for estimating small area parameters are model-based, where auxiliary variables are used to predict the variable of interest. For nonlinear models, prediction is not straightforward. MacGibbon and Tomberlin (1989) and Farrell, MacGibbon, and Tomberlin (1994) have proposed methods which require micro-data for each individual in a small area. Here, the authors use a second-order Taylor series expansion to obtain model-based predictions which only require…

使用收缩估计量从面板数据估计能源需求的短期与长期弹性AI 解读

This article discusses the problem of obtaining short-run and long-run elasticities of energy demand for each of 49 states in the United States using data for 21 years. Estimation using the time series data by each state gave several wrong signs for the coefficients. Estimation using pooled data was not valid because the hypothesis of homogeneity of the coefficients was rejected. Shrinkage estimators gave more reasonable results. The article presents in a unified framework…

生命历程分析中的序贯预测模型评估AI 解读

We extend the prequential approach introduced by A. P. Dawid to continuous time marked pint processes. A prequential forecasting system is expressed by means of the stochastic intensities of the point process. The exact independence and 1-exponentiality of the derived compensators are used to assess the predictive performance of the model and the inferential procedure. Some key words : Bayesian inference; Goodness of fit; Marked pint process; Markov chain Monte Carlo;…

概率统计史研究第四十四篇：t 分布的先驱AI 解读

The t-distribution first occurred in a paper by Lüroth (1876) on the classical theory of errors in connection with a Bayesian result.

模型选择中的广义信息准则AI 解读

The problem of evaluating the goodness of statistical models is investigated from an information-theoretic point of view. Information criteria are proposed for evaluating models constructed by various estimation procedures when the specified family of probability distributions does not contain the distribution generating the data. The proposed criteria are applied to the evaluation of models estimated by maximum likelihood, robust, penalised likelihood, Bayes procedures,…

离散持续期与竞争风险模型中风险率及时变效应的平滑估计AI 解读

State-space or dynamic approaches to discrete or grouped duration data with competing risks or multiple terminating events allow simultaneous modeling and smooth estimation of hazard functions and time-varying effects in a flexible way. Full Bayesian or posterior mean estimation, using numerical integration techniques or Monte Carlo methods, can become computationally rather demanding or even infeasible for higher dimensions and larger datasets. Therefore, based on previous…