BAT 2.0: Development and applications

统计数据分析是科学研究各个方面的核心工具。贝叶斯定理允许在数据分析，特别是参数估计和模型比较中提出的典型问题的一致制定。然而，评估相应的关键量，例如后验概率和证据，是具有挑战性的，特别是对于科学研究中经常遇到的具有许多参数的复杂模型。后者通常只能在定制的软件工具中访问。随着科学实验产生的数据量不断增加，科学家需要匹配的解释和工具的统计方法。该项目的第一个目标是建立一个强大的和可维护的软件工具贝叶斯推理，BAT 2.0，这是在不同的科学领域可用。该工具需要允许快速和可靠地计算与高维和复杂模型的贝叶斯推断有关的数量，并提供一个平台，以开发，比较和应用不同的算法，以便在相同和良好控制的条件下进行采样，优化和整合。它必须独立于平台，而不是针对特定研究领域的特定需求。该项目的第二个目标是将最佳可得技术2.0应用于一类具体问题-复杂物理模型的参数估计-以展示该工具的全部潜力并提供基准应用。具体的物理案例来自粒子物理领域，将进一步开发EFTfitter工具，以执行模型的全局拟合，特别是从有效场论导出的模型，以实验数据。这个应用程序被放置在科学建模，统计推断和数值方法之间的接口。它将作为在大多数科学研究领域遇到的问题的代理，因此它将显示跨学科研究的潜力。该项目的第三个目标是将EFTfitter应用于顶夸克物理领域。两个模型将被建立和比较：一个将单独基于SM，并包括与顶夸克物理相关的SM的自由参数。研究这样的模型将有助于约束这些参数，例如顶夸克质量或矩阵元Vtb。第二个模型将是一个有效的模型，包括额外的六维算子。该模型将面临广泛的顶夸克测量以及b-物理学的结果，例如B-强子的罕见衰变。

Statistical data analysis is a central tool in all aspects of scientific research. Bayes’ Theorem allows for a consistent formulation of typical questions raised in data analysis, in particular parameter estimation and model comparison. However, the evaluation of the corresponding key quantities, e.g. posterior probabilities and evidences, is challenging, in particular for complex models with many parameters often encountered in scientific research. The latter are often only accessible in custom made software tools. As the amount of data produced by scientific experiments is increasing, scientists need matching statistical methods for interpretations and tools. The first aim of the project is to build a robust and maintainable software tool for Bayesian inference, BAT 2.0, which is usable in different fields of science. The tool needs to allow for fast and reliable calculations of quantities related to Bayesian inference for high-dimensional and complex models and offer a platform to develop, compare and apply different algorithms for sampling, optimization and integration under the same and well-controlled conditions. It must be platform-independent and not tailored to the specific needs of a specific field of research. The second objective of the project is the application of BAT 2.0 to a specific class of problems – parameter estimation of complex physics models – so as to demonstrate the full potential of the tool and give a benchmark application. The concrete physics case comes from the realm of particles physics for which a tool, the EFTfitter, will be further developed to perform global fits of models, in particular those derived from effective field theories, to experimental data. This application is placed at the interfaces between scientific modeling, statistical inference and numerical methods. It will act as a proxy for problems encountered in most areas of scientific research and so it will show the potential of interdisciplinary research. The third aim of the project is to apply the EFTfitter to the realm of top-quark physics. Two models will be set up and compared: one will be based on the SM alone and include the free parameters of the SM related to top-quark physics. Studying such a model will help to constrain those parameters, e.g. the top-quark mass or the matrix element Vtb. The second model will be an effective model including additional dimension-six operators. The model will be confronted with a broad range of top-quark measurements as well as results from b-physics, e.g. rare decays of B-hadrons.