标题： 物理推理的数学基础 显示英文标题

标题： Mathematical Basis for Physical Inference

摘要： 虽然在空间上引入概率分布的公理化方法很常见，但其在利用物理理论和先验知识进行预测时，由于缺乏形式化而存在不足。 我们提议在所有概率分布的空间中引入两种运算，即或运算和与运算，这些运算是使空间具备对物理参数可能值进行推理所需结构的方法。 虽然物理理论通常被假定为解析的，但我们认为一致的推断需要将解析理论替换为参数空间上的概率分布，并且我们提出了一种系统的方法，通过物理实验结果的或运算来获得此类“理论相关性”。 预测实验结果或解决“反问题”是与运算使用的例子。 这为一般的物理推断提供了一个简单而完整的数学基础。 显示英文摘要

摘要： While the axiomatic introduction of a probability distribution over a space is common, its use for making predictions, using physical theories and prior knowledge, suffers from a lack of formalization. We propose to introduce, in the space of all probability distributions, two operations, the OR and the AND operation, that bring to the space the necessary structure for making inferences on possible values of physical parameters. While physical theories are often asumed to be analytical, we argue that consistent inference needs to replace analytical theories by probability distributions over the parameter space, and we propose a systematic way of obtaining such "theoretical correlations", using the OR operation on the results of physical experiments. Predicting the outcome of an experiment or solving "inverse problems" are then examples of the use of the AND operation. This leads to a simple and complete mathematical basis for general physical inference.