In this seminar, a novel concept in mathematical statistics is proposed. Ordinarily, some topological factors such as Gromov-Hausdorrf distance, dilatation and distortion are defined inside one metric space. The proposed idea puts a probability operator with some topological factors over different metric spaces which can project from these to one common measure space. By assuming a compact Polish space, first the original information is projected to a metric space. Then the projected information from the different spaces is mapped to one common space where some topological factors are applied. The inference and estimation can be calculated.
The merit of the proposed idea is to be able to compare values and some qualities of different fields with those for one metric space. This novel concept can let Information of post Big Data become more natural for people.
In the seminar, the situation of the Great Earthquake in Japan on 11 March 2011 is also introduced.