Mathematical Sciences: Implementation of Accurate Methods for Practical Inference

数学科学：实际推理的准确方法的实现

• 批准号: 9625440
• 负责人: George Casella
• 金额: $ 33.62万
• 依托单位: Cornell Univ - State: AWDS MADE PRIOR MAY 2010
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9625440&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Implementation; Accurate; Methods

DMS 9625440 Casella Although much research effort has been expended on developing accurate approximation techniques such as saddlepoint and improved likelihood-based procedures, less effort has been devoted to assessing the types of inferences that can be achieved in practice by using these methods. When this assessment is made, it is seen that the available inferences are severely limited in scope by both statistical issues and computational complexity. These two sources of limitation are intertwined, as computational difficulties can arise from the inherent demands of valid frequentist procedures. Ensuring the correctness of frequentist inferences can be computationally intensive, requiring many cumbersome evaluations of the complex expressions that derive from higher-order asymptotic approximations. In this research, these difficulties are overcome by a synthesis of frequentist and Bayesian inference, as the latter approach is simpler in outlook and implementation. In particular, the computational problem is addressed by adapting sampling-based techniques, such as Markov Chain Monte Carlo, to attain the higher-order approximations. The result will be improved inferences in a wide variety of practical problems; examples include logistic regression, censored data models, and variance component estimation. %%% In more complicated statistical models, statisticians have typically relied on approximate methods of inference, primarily because exact methods can be both difficult to derive and complex to compute. However, the validity of these approximate methods rests on the sample size being large, which means that such methods may not be accurate in problems with small samples. Now that inexpensive computational power has become widely available, statisticians are attempting to use the more realistic and complex models. For example, models used in analyzing global environmental change, or DNA assessment, are quite complex. The focus of t his research is to develop statistical methods that offer both accuracy and computational tractability. This work necessarily blends high-performance computing with modern statistical methodology. ***

DMS 9625440 Casella 尽管在开发准确的近似技术（例如鞍点和改进的基于似然的程序）方面投入了大量的研究工作，但在评估使用这些方法在实践中可以实现的推理类型方面投入的精力较少。 当进行这种评估时，可以看出，可用的推论在范围上受到统计问题和计算复杂性的严重限制。这两个限制源是相互交织的，因为有效的常客程序的固有要求可能会产生计算困难。确保频率论推论的正确性可能需要大量计算，需要对从高阶渐近近似导出的复杂表达式进行许多繁琐的评估。在本研究中，这些困难通过频率论和贝叶斯推理的综合来克服，因为后一种方法在前景和实施上更简单。 特别是，通过采用基于采样的技术（例如马尔可夫链蒙特卡罗）来解决计算问题，以获得高阶近似值。其结果将是改进对各种实际问题的推论；示例包括逻辑回归、审查数据模型和方差分量估计。 %%% 在更复杂的统计模型中，统计学家通常依赖近似的推理方法，主要是因为精确的方法可能难以推导且计算复杂。然而，这些近似方法的有效性取决于样本量较大，这意味着这些方法在处理小样本问题时可能不准确。现在廉价的计算能力已被广泛使用，统计学家正在尝试使用更现实和更复杂的模型。例如，用于分析全球环境变化或 DNA 评估的模型非常复杂。 这项研究的重点是开发既具有准确性又易于计算的统计方法。 这项工作必然将高性能计算与现代统计方法结合起来。 ***