BAT 2.0: Development and applications

统计数据分析是科学研究各个方面的中心工具。贝叶斯定理允许对数据分析中提出的典型问题进行一致的表述，特别是参数估计和模型比较。然而，后验概率和后验证据等关键量的估计是具有挑战性的，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，科学家需要匹配的统计方法来解释和使用工具。该项目的第一个目标是建立一个健壮的、可维护的贝叶斯推理软件工具BAT 2.0，该工具可用于不同的科学领域。该工具需要允许快速可靠地计算与高维和复杂模型的贝叶斯推理相关的量，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、优化和集成。它必须独立于平台，而不是为特定研究领域的特定需求量身定做。该项目的第二个目标是将BAT 2.0应用于一类特定的问题--复杂物理模型的参数估计--以展示该工具的全部潜力并给出基准应用程序。具体的物理案例来自粒子物理学领域，该领域将进一步开发一种工具，EFTfitter，以执行模型的全局拟合，特别是那些源自有效场理论的模型与实验数据的拟合。这一应用被放在科学建模、统计推理和数值方法之间的界面上。它将作为大多数科学研究领域遇到的问题的代理，因此它将展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。将建立两个模型并进行比较：一个模型将仅基于SM，并包含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素VTB。第二个模型将是一个包含额外的六维算子的有效模型。该模型将面临广泛的顶夸克测量以及来自b物理的结果，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.