Collaborative Research: New Developments in Direct Probabilistic Inference on Interest Parameters

合作研究：兴趣参数直接概率推理的新进展

基本信息

批准号：
1811936
负责人：
Todd Kuffner
金额：
$ 10万
依托单位：
Washington University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-01 至 2021-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1811936&HistoricalAwards=false
关键词：
Collaborative Research New Developments Direct

项目摘要

The Bayesian approach to statistical learning relies on probabilistic models for all observables and unknowns. The need to model all aspects of the problem can restrict the scope of applications and, more generally, can be a burden to the data analyst who is often only interested in certain features of the unknowns. This project will develop a mathematically rigorous and computationally efficient framework in which Bayesian learning can be carried out directly in terms of only the features of interest. This reduces the modeling and computational burden on the data analyst and provides new insights about Bayesian learning more generallyA Bayesian approach is a powerful and rigorous framework for statistical learning. The downside is that it requires a full model for the observables as well as all unknown quantities, the specification of which can be a burden on the data analyst. In addition to the familiar challenges of prior specification, there are also risks of misspecification biases. A more subtle complication is due to selection effects that result from considering several candidate models. The data analyst's burden is further exaggerated in situations where only a feature of the unknowns is of interest, i.e., when there is an interest parameter and a (potentially high-dimensional) nuisance parameter and inference is required only for the former. That is, the Bayesian approach still requires that the data analyst make non-trivial efforts to specify prior distributions and carry out posterior computations relevant only to the nuisance parameter, which can be viewed as a waste. Yet having access to a posterior distribution for inference on the interest parameter is still a desirable feature, and the proposed research aims to develop a new framework for posterior inference directly on interest parameters. These direct posteriors (DiPs) effectively target the interest parameter, giving data analysts an opportunity to avoid the seemingly wasteful modeling and computation efforts involving nuisance parameters. This project will construct DiPs for finite- and infinite-dimensional interest parameters with rigorous theoretical guarantees, and will also develop efficient computational tools to facilitate DiP-based inference.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

贝叶斯学习的统计学习方法依赖于所有可观察物和未知数的概率模型。对问题的所有方面进行建模的需求可能会限制应用程序的范围，更普遍地说，数据分析师通常只对未知数的某些功能感兴趣。该项目将开发出数学上严格且在计算上有效的框架，在该框架中可以直接根据感兴趣的功能直接进行贝叶斯学习。这减少了数据分析师的建模和计算负担，并提供了有关贝叶斯学习的新见解。不利的一面是，它需要一个完整的模型以及所有未知数量的模型，其规范可能是数据分析师的负担。除了先前规范的熟悉挑战外，还存在错误指定偏见的风险。更微妙的并发症是由于选择了多个候选模型所产生的选择效应。在只有未知数的特征是感兴趣的情况下，即当有兴趣参数并且（可能具有高维的）滋扰参数和仅对于前者需要推理时，数据分析师的负担进一步夸大了。也就是说，贝叶斯方法仍然要求数据分析师做出非平凡的努力来指定先前的分布并进行后验计算，仅与滋扰参数相关，可以将其视为浪费。然而，访问后验分布以推断兴趣参数仍然是一个理想的特征，拟议的研究旨在为直接推断兴趣参数开发新的框架。这些直接的后代（DIPS）有效地针对兴趣参数，从而为数据分析师提供了一个机会，可以避免看似浪费的建模和计算工作，涉及滋扰参数。该项目将为具有严格的理论保证的有限和无限维度兴趣参数构建下降，还将开发有效的计算工具来促进基于DIP的推理。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的智力和更广泛影响的评估来通过评估来获得支持的值得审查的审查。