Compound random measures and their use in Bayesian non‐parametrics
Compound random measures and their use in Bayesian non‐parametrics
复制标题
复合随机测量及其在贝叶斯非参数中的应用
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
F. Leisen
中科院分区：
文献类型：
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作者：
Jim E. Griffin;F. Leisen
提出了一类新的相依随机度量，我们称之为复合随机度量，并考虑在贝叶斯非参数混合模型中使用这些随机度量的归一化形式作为先验。它们的易处理性允许导出复合随机度量和归一化复合随机度量的性质。特别地，我们展示了如何用伽马、σ稳定和广义伽马过程边缘来构造复合随机度量。我们还推导了拉普拉斯指数的几种形式，并通过Lévy Copula和相关函数刻画了相关性。在非参数混合模型中使用归一化复合随机测度作为混合测度时，描述了后验推断的增广Pólya骨灰盒方案采样器和切片采样器，并讨论了一个数据实例。
A new class of dependent random measures which we call compound random measures is proposed and the use of normalized versions of these random measures as priors in Bayesian non‐parametric mixture models is considered. Their tractability allows the properties of both compound random measures and normalized compound random measures to be derived. In particular, we show how compound random measures can be constructed with gamma, σ‐stable and generalized gamma process marginals. We also derive several forms of the Laplace exponent and characterize dependence through both the Lévy copula and the correlation function. An augmented Pólya urn scheme sampler and a slice sampler are described for posterior inference when a normalized compound random measure is used as the mixing measure in a non‐parametric mixture model and a data example is discussed.
DOI：
10.1093/jnci/85.16.1319
发表时间：
1993-08
期刊：
Journal of the National Cancer Institute
影响因子：
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作者：
S. Lichtman;M. Ratain;D. A. Echo;G. Rosner;M. Egorin;D. Budman;N. Vogelzang;L. Norton;R. Schilsky
通讯作者：
S. Lichtman;M. Ratain;D. A. Echo;G. Rosner;M. Egorin;D. Budman;N. Vogelzang;L. Norton;R. Schilsky