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.
