Bayesian statistical computation, methodology, and applications

贝叶斯统计计算、方法和应用

• 批准号: 170066-2011
• 负责人: Neal, Radford
• 金额: $ 1.53万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=569540
• 关键词: Bayesian; statistical; computation; methodology; applications

Numerous applications of statistics in fields ranging from marketing, to analysis of the human genome, to cosmology deal with large amounts of data and with complex phenomena. Analysing such data is statistically and computationally challenging - naive approaches may not obtain the benefit that is possible from such data, or may produce invalid results. I use what is known as the "Bayesian'" approach to statistics to tackle such problems. In this approach, we first must formulate an appropriate model, that defines all the possibilities for what the underlying phenomenon is like, and how likely we think each is. We must then perform the computations needed to integrate the information from the observed data into this model, in order to reach conclusions or make predictions. Much of my research will be on improved methods for performing such computations, mostly based on the method of "Markov chain Monte Carlo". My aim is, on the one hand, to make it possible to tackle problems that could previously not be solved, and on the other hand, to make it easier for statisticians to routinely solve simpler problems, allowing them to concentrate on statistical issues without being distracted by computational issues. I also plan to work on improving the Bayesian approach in general, as well as on Bayesian methods that are specific to particular applications, such as analysis of the human genome.

从市场营销到人类基因组分析，再到宇宙学，统计学在各个领域的大量应用涉及大量数据和复杂现象。 分析这些数据在统计和计算上具有挑战性-幼稚的方法可能无法从这些数据中获得可能的益处，或者可能产生无效的结果。 我使用所谓的“贝叶斯”统计方法来解决这些问题。 在这种方法中，我们首先必须制定一个适当的模型，定义潜在现象的所有可能性，以及我们认为每种可能性有多大。 然后，我们必须执行所需的计算，将来自观测数据的信息整合到这个模型中，以便得出结论或做出预测。 我的大部分研究将是改进的方法来执行这样的计算，主要是基于“马尔可夫链蒙特卡罗”的方法。 我的目标是，一方面，使解决以前无法解决的问题成为可能，另一方面，使统计学家更容易解决更简单的问题，使他们能够专注于统计问题，而不会被计算问题分散注意力。 我还计划在总体上改进贝叶斯方法，以及针对特定应用（如人类基因组分析）的贝叶斯方法。