摘要翻译:
在非参数统计模型中,我们使用重标高斯过程作为函数参数的先验模型。我们展示了后验分布的收缩率如何依赖于标度因子。特别地,我们展示了重新标度的高斯过程先验,产生了在最优收敛速度下围绕真实参数收缩的后验。为了得到我们的结果,我们建立了光滑平稳高斯过程的小偏差概率的界。
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英文标题:
《Bayesian inference with rescaled Gaussian process priors》
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作者:
Aad van der Vaart, Harry van Zanten
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit rescaled Gaussian process priors yielding posteriors that contract around the true parameter at optimal convergence rates. To derive our results we establish bounds on small deviation probabilities for smooth stationary Gaussian processes.
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PDF链接:
https://arxiv.org/pdf/710.3679