摘要翻译:
本文通过实例讨论了动态广义线性模型的贝叶斯预测问题。采用近似贝叶斯分析,基于共轭形式和贝叶斯线性估计,描述了理论框架,并给出了响应分布的详细例子,包括二项式、泊松、负二项式、几何、正态、对数正态、gamma、指数、Weibull、Pareto、beta和逆高斯。我们给出了所有分布(正态分布除外)的数值说明。将上述所有分布组合在一起,我们给出了一个统一的非高斯时间序列分析的贝叶斯方法,其应用范围从金融和医学到生物学和行为科学。在整个模型中,我们讨论了贝叶斯预测,并对每个模型导出了多步预测均值。最后,我们用似然函数描述了模型评估,以及贝叶斯模型监控。
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英文标题:
《Dynamic generalized linear models for non-Gaussian time series
forecasting》
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作者:
K. Triantafyllopoulos
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最新提交年份:
2008
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分类信息:
一级分类:Statistics 统计学
二级分类:Methodology 方法论
分类描述:Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计,调查,模型选择,多重检验,多元方法,信号和图像处理,时间序列,平滑,空间统计,生存分析,非参数和半参数方法
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一级分类:Statistics 统计学
二级分类:Applications 应用程序
分类描述:Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学,教育学,流行病学,工程学,环境科学,医学,物理科学,质量控制,社会科学
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英文摘要:
The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear estimation, we describe the theoretical framework and then we provide detailed examples of response distributions, including binomial, Poisson, negative binomial, geometric, normal, log-normal, gamma, exponential, Weibull, Pareto, beta, and inverse Gaussian. We give numerical illustrations for all distributions (except for the normal). Putting together all the above distributions, we give a unified Bayesian approach to non-Gaussian time series analysis, with applications from finance and medicine to biology and the behavioural sciences. Throughout the models we discuss Bayesian forecasting and, for each model, we derive the multi-step forecast mean. Finally, we describe model assessment using the likelihood function, and Bayesian model monitoring.
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PDF链接:
https://arxiv.org/pdf/802.0219