This week resumes a brief introduction to differential geometry, before going on to define the notion of a metric on a statistical manifold and the Rao distance between probability distribution functions. We continue on to introduce the concept of sufficient statistics before introducing alpha-connections and various families of information geometries, concluding with a derivation of the Cramér-Rao bound. Next week’s lectures will start to pick up applications in physics and beyond. N.B. there was an issue with the audio for the recording of the second lecture. This will be re-recorded and posted in the coming days. In the meantime, I have posted links to the relevant sections of recordings of a previous iteration of this course covering the same material.
Lecture IV (part I) , (part II)