Mathematical Sciences: Methodological and Computational Aspects of Statistical Modeling and Inference

这项工作将集中在三个领域的理论 统计学：（1）贝叶斯建模和时间序列分析， 包括时域和频域方法 长记忆和短记忆模型，（2）其他贝叶斯项目 包括非线性回归模型和测量误差 模型，以及（3）贝叶斯因果网络和信念函数， 包括这些新模型的数学特征， 以及制定模型构建的原则， 这是实际使用所需要的计算。 登普斯特在理论统计学方面的工作正在成为 为其他科学家试图将 不确定性的现实输入专家计算机系统。 在 除了扩展相关理论外，他还将解决 计算瓶颈现在阻碍了成功的广泛传播 这些模式的实施。

This work will focus on three areas of theoretical statistics: (1) Bayesian modelling and analysis of time series, including time domain and frequency domain approaches to both long memory and short memory models, (2) other Bayesian projects including nonlinear regression models and measurement error models, and (3) Bayes causal networks and belief functions, including mathematical characterization of these new models, as well as the development of principles for model construction and computation that are required for practical use. Dempster's work in theoretical statistics is becoming foundational for other scientists attempting to incorporate the realities of uncertainty into expert computer systems. In addition to extending relevant theory, he will tackle the computational bottleneck that now blocks successful widespread implementation of these models.