A high quality toolbox of computational methods for statistical inference

在应用科学的许多领域中，通常使用数学，一些感兴趣的量没有解析表达式，即没有明确的公式。在这种情况下，人们通常采用数值方法来近似感兴趣的量。蒙特卡罗方法是一类已经在物理学中常规使用了60多年的数值技术，最近对统计推断的实践产生了深远的影响，特别是贝叶斯统计。在贝叶斯统计的背景下，感兴趣的数量不是直接观察到的，而是被“噪音”扭曲和破坏的。由于噪声带来的不确定性，人们不试图给出感兴趣的量的估计，而是试图估计一个概率分布，它反映了我们对感兴趣的量的各种可能值的信念。这种方法的优势是显而易见的，但也是有代价的：概率分布是一个复杂的数学对象，对于感兴趣的典型真实的情况，不存在代数表达式，需要数值近似。尽管他们的成功，蒙特卡罗技术仍然需要一定程度的专业知识和微调是必要的，他们表现良好。最近提出了一个自动调整这些算法的一般框架：主要思想是算法学习如何最佳地解决任务，同时解决它。在贝叶斯上下文中，算法探索概率分布的表面，并根据过去的经验调整探索表面的方式。本项目的目的是开发这项技术以及相应的工具箱，以便使这些新技术广泛提供给专家和非专家。

It is common in many fields of applied science, where mathematics is used, that some of the quantities of interest do not have analytical expressions, i.e. no explicit formula are available. In such situations one typically resorts to numerical methods in order to approximate the quantities of interest. Monte Carlo methods is a class of such numerical techniques that have been routinely used in physics for over 60 years and have more recently had a profound impact on the practice of statistical inference, in particular Bayesian statistics. In the context of Bayesian statistics, quantities of interest are not directly observed, but distorted and corrupted by `noise'. Due to the uncertainty brought in by the noise, and rather than trying to give an estimate of the quantity of interest, one instead seeks to estimate a probability distribution which reflects our belief in the various possible values of the quantity of interest. The strength of the approach is evident, but comes at a price: a probability distribution is a complex mathematical object, and for typical real cases of interest, no algebraic expressions exist and numerical approximations are needed. Despite their success, Monte Carlo techniques still require some degree of expertise and fine tuning is needed for them to perform well. Recently a general framework for the automatic tuning of these algorithms has been proposed: the main idea is that the algorithm learns how to optimally solve the task, while solving it. In the Bayesian context, the algorithm explores the surface of the probability distribution, and adapts the way it explores the surface in the light of past experience. It is the aim of the present project to develop this technology together with the corresponding toolbox in order to make these novel techniques widely available to specialists and non-specialists.