• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文会议>Bayesian Inference and Maximum Entropy Methods in Science and Engineering >Information Theoretic Approach to Bayesian Inference
【24h】

Information Theoretic Approach to Bayesian Inference

机译：贝叶斯推理的信息理论方法

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

A problem of central importance in formulating theoretical explanations of some observed process is the construction of a quantitative comparison of observations and examples within the context of a specific theory. From a Bayesian perspective, the ultimate goal is to compute the posterior probability for a theory given the observations. A direct approach to Bayesian inference can be prohibited when the likelihood itself is not known (i.e. or computationally intractable to compute, as in the case of non-linear processes with stochastic initial conditions). An information theoretic approach to this problem is developed in which a sequence of exponential family Gibbs densities are used as approximations to the likelihood. The sequence of Gibbs densities are constructed by successively matching expectation value constraints, giving a positive Gibbs Information Gain, or rate of convergence to the limiting density in the Kullback-Leibler distance sense. Evaluating the sequence of Gibbs densities for the observed data gives a sequence of Bayesian posterior densities which are successively more concentrated. It is shown that the successive confidence intervals form a decreasing sequence of subsets which include, and converge to, the true Bayesian confidence intervals. This provides a justifiable approach for extending Bayesian inference to problems where the likelihood is unknown, as "error bars" are simply larger. Furthermore, the Bayes Information Gain, defined as the rate at which the confidence intervals contract to the limiting interval, is shown to be maximized by a "greedy" approach to inference when constructing the Gibbs likelihoods.
机译：在制定某些观测过程的理论解释时，最重要的问题是在特定理论的背景下对观测结果和实例进行定量比较。从贝叶斯角度来看，最终目标是根据给定的观察结果计算理论的后验概率。当似然本身未知时（例如，在具有随机初始条件的非线性过程的情况下，在计算上难以计算），可以禁止直接采用贝叶斯推理方法。开发了一种针对该问题的信息理论方法，其中使用一系列指数族吉布斯密度作为似然的近似值。通过连续匹配期望值约束来构造吉布斯密度序列，从而给出正的吉布斯信息增益或在Kullback-Leibler距离意义上达到极限密度的收敛速度。对所观察到的数据评估吉布斯密度的序列，得出了一系列贝叶斯后验密度，其顺序越来越集中。结果表明，连续的置信区间形成子集的递减序列，该子集包括并收敛到真实的贝叶斯置信区间。这为将贝叶斯推断扩展到可能性未知的问题提供了一种合理的方法，因为“误差棒”只是更大。此外，贝叶斯信息增益（定义为置信区间收缩到极限区间的速率）在构造吉布斯似然时通过“贪婪”推理来显示为最大化。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号