Bayesian Modeling and Computations
贝叶斯建模和计算
基本信息
- 批准号:RGPIN-2014-05328
- 负责人:
- 金额:$ 1.31万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2018
- 资助国家:加拿大
- 起止时间:2018-01-01 至 2019-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The broad objective of my research proposal is the development and implementation of complex statistical models with a focus on computation in Bayesian settings. I attempt to work in subject areas corresponding to real problems.**In the subject area of social networks, I am investigating the assessment of ``accuracy'' corresponding to interpersonal perceptions. Triadic data are the richest type of interpersonal perception data where all individuals in a study have ratings on every pair of individuals. The assessment of accuracy is a fundamental problem and is one of the oldest issues in social and personal psychology. Are people's perceptions of others valid? The approach that I am considering extends a traditional random effects model where analysis has remained illusive from a classical point of view. Various modeling assumptions and the introduction of prior distributions leads to complex and high dimensional Bayesian models.**A second project involves the modeling and analysis of a special type of categorical data. In surveys, categorical data are often misclassified. For example, a subject whose ``true'' classification is the first category may be incorrectly classified in the second category. In such cases, severely biased estimators can occur when the effect of misclassification is ignored. In this project, I will attempt to account for misclassification for data extending from a single multinomial cohort to the case of subject-specific covariates. In addition, the presence of gold standard data will be considered. The complexity of the models brings nonidentifiability issues to the forefront and the need to elicit subjective prior distributions.**Statistics in sport is a general application area in which I am involved. One problem that I plan to pursue concerns optimal team selection in Twenty20 cricket. An innovation in this work is that traditional cricket statistics are not used in determining player worth. Instead, run differential with and without a given player in the lineup is the true measure of value. I propose an empirical Bayes procedure to infer batting and bowling characteristics of players. Via simulation, these characteristics can be used to assess the quality of given lineups. Lineups may then be optimized over a huge combinatorial space via fine tuning of the simulated annealing algorithm. This work may benefit teams in terms of roster selection.**A methodological project which I am considering concerns the development of importance sampling algorithms. Importance sampling is a fundamental sampling strategy that is important in the approximation of integrals arising in Bayesian statistics. Importance sampling has two specific advantages over popular Markov chain methods: (i) generated variates are independent which simplifies error assessment and (ii) there is no need to diagnose convergence to stationarity. Nevertheless, it is sometimes said that importance sampling does not work well in high dimensions. I do not believe this sentiment to be entirely true. Rather, importance sampling has not been implemented using sufficiently rich families for higher dimensional problems. Typically, the multivariate normal and Student distributions have been used for importance sampling. It is my goal to develop multivariate importance sampling algorithms using alternative multivariate distributions such as skew-symmetric families. I also plan on developing an adaptive component to importance sampling whereby the importance sampler is improved over successive iterations. Obtaining proofs of the convergence of the adaptive algorithm forms part of the project.
我的研究提案的广泛目标是开发和实施复杂的统计模型,重点是在贝叶斯环境下进行计算。我试图在与现实问题相对应的主题领域工作。**在社交网络的主题领域,我正在调查与人际感知相对应的“准确性”评估。三元数据是最丰富的人际感知数据类型,研究中的所有个人都对每一对个人进行了评级。对准确性的评估是一个基本问题,也是社会心理学和个人心理学中最古老的问题之一。人们对他人的看法是正确的吗?我正在考虑的方法扩展了传统的随机效应模型,从经典的角度来看,分析仍然是虚幻的。各种建模假设和先验分布的引入导致了复杂和高维的贝叶斯模型。**第二个项目涉及对一种特殊类型的分类数据的建模和分析。在调查中,分类数据经常被错误分类。例如,“真”分类为第一类的主题可能被错误地归类为第二类。在这种情况下,当忽略错误分类的影响时,可能会出现严重的偏向估计器。在这个项目中,我将试图解释从单个多项式队列到特定于主题的协变量的数据的错误分类。此外,还将考虑是否存在金本位数据。模型的复杂性将不可识别性问题带到了最重要的位置,需要得出主观的先验分布。**体育统计是我参与的一个普遍应用领域。我计划解决的一个问题是关于Twenty20板球比赛的最佳团队选择。这项工作的一个创新之处在于,不使用传统的板球统计数据来确定球员的价值。相反,阵容中有没有特定球员的跑动差异才是真正的价值衡量标准。我提出了一种经验贝叶斯方法来推断球员的击球和保龄球特征。通过仿真,这些特性可以用来评估给定阵容的质量。然后,通过对模拟退火法的微调,可以在一个巨大的组合空间上优化阵容。这项工作可能会使团队在名册选择方面受益。**我正在考虑的一个方法学项目涉及重要性抽样算法的开发。重要性抽样是一种基本的抽样策略,在贝叶斯统计中产生的积分的逼近中是重要的。与流行的马尔可夫链方法相比,重要性抽样有两个独特的优点:(I)生成的变量是独立的,这简化了误差评估;(Ii)不需要诊断收敛到平稳性。然而,人们有时会说,重要性抽样在高维中并不奏效。我不相信这种情绪是完全正确的。相反,重要性抽样还没有使用足够丰富的族来实现,以解决更高维度的问题。通常,多变量正态分布和学生分布用于重要性抽样。我的目标是开发使用其他多变量分布的多变量重要性抽样算法,例如斜对称族。我还计划开发一个针对重要性采样的自适应组件,从而在连续的迭代中改进重要性采样器。获得自适应算法的收敛证明是该项目的一部分。
项目成果
期刊论文数量(0)
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专利数量(0)
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Swartz, Tim其他文献
Swartz, Tim的其他文献
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{{ truncateString('Swartz, Tim', 18)}}的其他基金
Statistical Methods and Computation for Sports Analytics
体育分析的统计方法和计算
- 批准号:
RGPIN-2019-03971 - 财政年份:2022
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Statistical Methods and Computation for Sports Analytics
体育分析的统计方法和计算
- 批准号:
RGPIN-2019-03971 - 财政年份:2021
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Statistical Methods and Computation for Sports Analytics
体育分析的统计方法和计算
- 批准号:
RGPIN-2019-03971 - 财政年份:2020
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Statistical Methods and Computation for Sports Analytics
体育分析的统计方法和计算
- 批准号:
RGPIN-2019-03971 - 财政年份:2019
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Bayesian Modeling and Computations
贝叶斯建模和计算
- 批准号:
RGPIN-2014-05328 - 财政年份:2017
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Bayesian Modeling and Computations
贝叶斯建模和计算
- 批准号:
RGPIN-2014-05328 - 财政年份:2016
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Bayesian Modeling and Computations
贝叶斯建模和计算
- 批准号:
RGPIN-2014-05328 - 财政年份:2015
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Bayesian Modeling and Computations
贝叶斯建模和计算
- 批准号:
RGPIN-2014-05328 - 财政年份:2014
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Bayesian methodology and applications
贝叶斯方法和应用
- 批准号:
9268-2009 - 财政年份:2013
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Bayesian methodology and applications
贝叶斯方法和应用
- 批准号:
9268-2009 - 财政年份:2012
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
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