标题： 将错误聚焦 显示英文标题

标题： Bringing errors into focus

摘要： 本讲座介绍了误差传播理论的最新进展。 我们首先解释在哪些情况下可以使用一阶微分学进行误差传播，或者需要使用二阶微分学。 然后我们指出误差传播与微分几何中二阶向量概念之间的联系，并强调关于偏差算子存在一点模糊性。 第三部分致力于狄利克雷形式的强大框架，其主要特点是能够轻松应用于无限维模型，包括维纳空间（以误差的角度解释马里亚夫计算），泊松空间和蒙特卡罗空间。 在第四部分中，我们展示了通常数学意义上的误差，即一个近似量，可能会产生一个狄利克雷形式，并引入四个偏差算子。 最后，我们通过将场算子的平方与费舍尔信息矩阵的逆相联系，将狄利克雷形式与统计学联系起来。 显示英文摘要

摘要： This lecture presents recent advances in the theory of errors propagation. We first explain in which cases the propagation of errors may be performed with a first order differential calculus or needs a second order differential calculus. Then we point out the link between error propagation and the concept of second order vector in differential geometry, emphasizing the existence of a slight ambiguity concerning the bias operator. The third part in devoted to the powerful framework of Dirichlet forms whose main feature is to apply easily to infinite dimensional models including the Wiener space (giving an interpretation of Malliavin calculus in terms of errors), the Poisson space and the Monte Carlo space. In the fourth part we show how an error in the usual mathematical sense, i.e. an approximate quantity, may yield a Dirichlet form and we introduce the four bias operators. Eventually we connect the Dirichlet form with statistics by identifying the square of field operator with the inverse of the Fisher information matrix.