Computer - Intensive Statistics in Mathematical Astronomy

这项研究将确定适当的新的和创新的计算机密集统计程序，并将它们应用于由客观标准定义的离散河外源样本，以及它们与数学宇宙学预测的关系。假设样本是无偏的并且公认的宇宙学是正确的，那么可以观察到的这种偏差的概率将用蒙特卡罗方法估计出来。时间学和弗里德曼宇宙学假设在统计上的可接受性将通过将它们预测的可观测关系与在完整的或其他统计上客观描述的已发表样本中观察到的关系进行比较来检验。本文将研究几种频率下光度函数的多变量估计。这项研究是跨学科的，涉及统计学与计算宇宙学的共生。统计学、李群、现代分析、几何、相对论和宇宙学等领域都与红移本质及其客观统计含义的宇宙学理论的测试、验证和形成有重要的科学关系。这些领域的资深科学家通常不会相互作用，他们将结合他们的专业知识，重新分析河外数据并重新测试红移理论。

This research will determine appropriate new and innovative computer-intensive statistical procedures and apply them to samples of discrete extragalactic sources defined by objective criteria, and to their relations with the predictions of mathematical cosmologies. The probabilities of such deviations as may be observed, assuming the sample is unbiased and accepted cosmology is correct, will be estimated by Monte Carlo methods. Statisical acceptability of the chronometric and Friedman cosmological hypotheses will be tested by comparison of their predicted observable relations with those observed in complete, or other statistically objectively delineated, published samples. Computer applicable multivariate estimation for luminosity functions at several frequencies will be investigated. This research is cross-disciplinary, involving a symbiosis of Statistics with Computational Cosmology. The fields of Statistics, Lie Groups, Modern Analysis, Geometry, Relativity, and Cosmology are all scientifically relevant in an essential way to the testing, validation, and formulation of cosmological theories of the nature of the redshift and its objective statistical implications. Senior scientists from these fields, which are normally non-interacting, will combine their expertise in re-analyzing extragalactic data and retesting the redshift theory.