Asymptotically Efficient and Efficiently Computable Bayesian Estimation

渐近有效且高效可计算的贝叶斯估计

• 批准号: 1406599
• 负责人: Laurent Saloff-Coste
• 金额: $ 12万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1406599&HistoricalAwards=false
• 关键词: Asymptotically; Efficient; Efficiently; Computable; Bayesian

The accuracy of computational methods used in statistics will be investigated and improved. These methods will be used to perform more efficient allocation of ambulances, and improved management of datacenters, among other applications. New computational methods have allowed the field of Bayesian statistics to dramatically expand, providing advances in areas from finance to information technology. Despite this, the biggest challenge for the wider adoption of these approaches is still the limitations of the computational methods: there are very few guarantees on their accuracy, and in practice they can be error-prone. In this research project, computational methods with guarantees on accuracy will be introduced and used to benefit applications including the ones listed above. Precisely, the goal of this research and education project is to give Bayes estimators that are also efficiently computable for broad classes of models, meaning that an accurate Bayes estimate can be obtained in time that is a low-degree polynomial of the sample size and the parameter dimension. A lower level of approximation error than of statistical error is required, meaning that the approximated estimator is also asymptotically efficient. For motivation and application of the techniques, challenging statistical problems arising in management of commercial and nonprofit operations will be used. For instance, ambulance fleet operations and (distributed computing) datacenter operations will be illustrated as case studies.

将调查和改进统计中使用的计算方法的准确性。 这些方法将用于更有效地分配救护车，改善救护中心的管理等。 新的计算方法使贝叶斯统计领域得到了极大的扩展，在从金融到信息技术的各个领域都取得了进步。 尽管如此，更广泛地采用这些方法的最大挑战仍然是计算方法的局限性：它们的准确性几乎没有保证，并且在实践中它们可能容易出错。在本研究项目中，将介绍保证准确性的计算方法，并用于包括上述应用程序在内的应用程序。准确地说，这个研究和教育项目的目标是给出贝叶斯估计，这些估计也可以有效地计算广泛的模型类别，这意味着可以及时获得准确的贝叶斯估计，这是样本大小和参数维度的低次多项式。需要比统计误差更低水平的近似误差，这意味着近似估计量也是渐近有效的。 对于动机和技术的应用，具有挑战性的统计问题，在商业和非营利业务的管理将被使用。例如，救护车车队运营和（分布式计算）数据中心运营将作为案例研究进行说明。