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Sequential Monte Carlo Methods for Dynamic Systems

动态系统的序贯蒙特卡洛方法

We provide a general framework for using Monte Carlo methods in dynamic systems and discuss its wide applications. Under this framework, several currently available techniques are studied and generalized to accommodate more complex features. All of these methods are partial combinations of three ingredients: importance sampling and resampling, rejection sampling, and Markov chain iterations. We provide guidelines on how they should be used and under what circumstance each…

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Rejection Control and Sequential Importance Sampling

拒绝控制与序贯重要性抽样

We discuss ways of combining rejection sampling and importance sampling methods in Monte Carlo computations and demonstrate their usefulness in updating dynamic systems. Specifically, we propose the rejection controlled sequential importance sampling (RC-SIS) algorithm, which is designed to simultaneously reduce Monte Carlo variation and retain independent samples in sequential importance sampling. The proposed method is demonstrated by three examples taken from…

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Bayesian Analysis in Econometrics and Statistics: The Zellner View and Papers

计量经济学与统计学中的贝叶斯分析:Zellner 的观点与论文

Part 1 Introduction. Part 2 Overview of Bayesian analysis. Part 3 Bayesian priors, models and information processing. Part 4 Bayesian methods. Part 5 Bayesian forecasting.

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Stochastic Approximation Algorithms and Applications

随机逼近算法及其应用

Applications (1978) 7 Vorob'ev, Game Theory: Lectures for Economists and Systems Scientists (1977) 8 Shiryayev, Optimal Stopping Rules (1978) 9 IbragimovlRozanov, Gaussian Random Processes (1978) Wonham, Linear Multivariable Control: A Geometric Approach, Third Ed.

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A Weak Convergence Approach to the Theory of Large Deviations

大偏差理论的弱收敛方法

Formulation of Large Deviation Theory in Terms of the Laplace Principle. First Example: Sanov's Theorem. Second Example: Mogulskii's Theorem. Representation Formulas for Other Stochastic Processes. Compactness and Limit Properties for the Random Walk Model. Laplace Principle for the Random Walk Model with Continuous Statistics. Laplace Principle for the Random Walk Model with Discontinuous Statistics. Laplace Principle for the Empirical Measures of a Markov Chain. Extensions…

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Linear Mixed Models in Practice: A SAS-Oriented Approach

线性混合模型实践:面向 SAS 的方法

1 Introduction.- 2 An Example-Based Tour in Linear Mixed Models.- 2.1 Fixed Effects and Random Effects in Mixed Models.- 2.2 General Linear Mixed Models.- 2.3 Variance Components Estimation and Best Linear Unbiased Prediction.- 2.3.1 Variance Components Estimation.- 2.3.2 Best Linear Unbiased Prediction (BLUP).- 2.3.3 Examples and the SAS Procedure MIXED.- 2.4 Fixed Effects: Estimation and Hypotheses Testing.- 2.4.1 General Considerations.- 2.4.2 Examples and the SAS…

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Statistical Evidence: A Likelihood Paradigm

统计证据:似然范式

The First Principle Introduction The Law of Likelihood Three Questions Towards Verification Relativity of Evidence Strength of Evidence Counterexamples Testing Simple Hypotheses Composite Hypotheses Another Counterexample Irrelevance of the Sample Space The Likelihood Principle Evidence and Uncertainty Summary Exercises Neyman-Pearson Theory Introduction Neyman-Pearson Statistical Theory Evidential Interpretation of Results of Neyman-Pearson Decision Procedures…

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Large Cluster Results for Two Parametric Multinomial Extra Variation Models

两个参数化多项额外变异模型的大簇结果

Two parametric extra variation models are considered. Approximate closed-form expressions are given for the Fisher information matrices. The expressions are useful in computing maximum likelihood estimates and obtaining large cluster efficiencies. A simulation study shows that the approximations perform very well even in clusters of moderate size. The models are applied in illustrative examples. A goodness-of-fit test is developed that is applicable even when the cluster…

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Discretization of Continuous Markov Chains and Markov Chain Monte Carlo Convergence Assessment

连续状态马尔可夫链的离散化与 MCMC 收敛评估

We show that continuous state-space Markov chains can be rigorously discretized into finite Markov chains. The idea is to subsample the continuous chain at renewal times related to small sets that control the discretization. Once a finite Markov chain is derived from the Markov chain Monte Carlo output, general convergence properties on finite state spaces can be exploited for convergence assessment in several directions. Our choice is based on a divergence criterion derived…

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Correlation and High-Dimensional Consistency in Pattern Recognition

模式识别中的相关性与高维一致性

Classical discriminant analysis breaks down when the feature vectors are of extremely high dimension; for example, when the basic observation is a random function observed over a fine grid. Alternative methods have been developed assuming a simplified form for the covariance structure. We analyze the high-dimensional asymptotics of some of these methods, emphasizing the effects of correlations such as occur when the baseline is random. For instance, the Euclidean distance…

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A Model for Evaluating Sensitivity and Specificity for Correlated Diagnostic Tests in Efficacy Studies with an Imperfect Reference Test

参考检验不完美时相关诊断检验的灵敏度与特异度评估模型

The purpose of a diagnostic efficacy study is to evaluate and compare the sensitivities and specificities of several diagnostic tests. Usually the diagnostic tests are correlated conditional on disease status, and the reference test is subject to error. In the Chlamydia trachomatis study, five screening tests for detecting chlamydia in endocervical specimens were compared. The five tests are correlated, and the reference test (the cell culture test) has less than 100%…

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Bayesian Identification of Outliers in Computerized Adaptive Tests

计算机自适应测试中异常作答者的贝叶斯识别

We consider the problem of identifying examinees with aberrant response patterns in a computerized adaptive test (CAT). The vector Y of responses of an examinee from a CAT is a multivariate response vector. Multivariate observations may be outlying in many different directions, and we characterize specific directions as corresponding to outliers with different interpretations. We develop a class of outlier statistics to identify different types of outliers based on a control…

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