Asymptotically Efficient and Efficiently Computable Bayesian Estimation

统计中使用的计算方法的准确性将被调查和改进。这些方法将用于更有效地分配救护车，改进数据中心的管理，以及其他应用。新的计算方法使贝叶斯统计领域得到了极大的扩展，为从金融到信息技术等领域提供了进步。尽管如此，广泛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，而且在实践中它们可能容易出错。在本研究项目中，将引入保证精度的计算方法，并将其用于包括上述应用在内的应用。准确地说，这个研究和教育项目的目标是给出贝叶斯估计器，它也可以有效地计算广泛类别的模型，这意味着可以在时间上获得准确的贝叶斯估计，它是样本大小和参数维的低次多项式。需要比统计误差更低的近似误差水平，这意味着近似估计量也是渐近有效的。为了激励和应用这些技术，将使用商业和非营利业务管理中出现的具有挑战性的统计问题。例如，救护车队操作和（分布式计算）数据中心操作将作为案例研究进行说明。

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.