I have started to read the book Probability Theory: The Logic of Science, by the late E. T. Jaynes. From what I understand so far, I think there is a high plausibility that it will help me have a more unified and deeper understanding of probability (and hence statistics). In reading the preface, he makes some interesting observations about probability and human thinking, and it seems quite apropos, and relevant to the recent advances in the fields of artificial intelligence, such as the recent match of Go.
A quote from the book that particularly struck me was the following:
… it is clear that probability theory is telling us something about the way our own minds operate when we form intuitive judgments, of which we may not have been consciously aware. Some may feel uncomfortable at these revelations; others may see in them useful tools for psychological, sociological, or legal research.