贝叶斯推断(BAYESIAN INFERENCE)是一种应用于不确定性条件下的决策的统计方法。贝叶斯推断的显著特征是,为了得到一个统计结论能够利用先验信息和样本信息。

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这是第一本介绍随机过程贝叶斯推理程序的书。贝叶斯方法有明显的优势(包括对先验信息的最佳利用)。最初,这本书以贝叶斯推理的简要回顾开始,并使用了许多与随机过程分析相关的例子,包括四种主要类型,即离散时间和离散状态空间以及连续时间和连续状态空间。然后介绍了理解随机过程所必需的要素,接着是专门用于此类过程的贝叶斯分析的章节。重要的是,这一章专门讨论随机过程中的基本概念。本文详细描述了离散时间马尔可夫链、马尔可夫跳跃过程、常规过程(如布朗运动和奥恩斯坦-乌伦贝克过程)、传统时间序列以及点过程和空间过程的贝叶斯推理(估计、检验假设和预测)。书中着重强调了许多来自生物学和其他科学学科的例子。为了分析随机过程,它将使用R和WinBUGS。

http://dl.booktolearn.com/ebooks2/science/statistics/9781138196131_Bayesian_Inference_for_Stochastic_Processes_52c4.pdf

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A Bayesian inference method for problems with small samples and sparse data is presented in this paper. A general type of prior ($\propto 1/\sigma^{q}$) is proposed to formulate the Bayesian posterior for inference problems under small sample size. It is shown that this type of prior can represents a broad range of priors such as classical noninformative priors and asymptotically locally invariant priors. It is further shown in this study that such priors can be derived as the limiting states of Normal-Inverse-Gamma conjugate priors, allowing for analytical evaluations of Bayesian posteriors and predictors. The performance of different noninformative priors under small sample size is compared using the global likelihood. The method of Laplace approximation is employed to evaluate the global likelihood. A numerical linear regression problem and a realistic fatigue reliability problem are used to demonstrate the method and identify the optimal noninformative prior. Results indicate the predictor using Jeffreys' prior outperforms others. The advantage of the noninformative Bayesian estimator over the regular least square estimator under small sample size is shown.

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