I was wondering from the view of dividing the topics of statistical theory into inference part and non-inference part, what inference topics and non-inference topics statistical theory is covering?
By inference, I mean the task in logic to reach some conclusion from some premises. Probabilistic inference is a way of logical inference using probability.
Can we say statistical theory is just providing probabilistic ways to accomplish logic inference? Or statistical theory and logic inference are overlapping, but neither falls into the other?
Relating to my previous post regarding decision theory and statistical theory, how are logical inference, decision theory and statistical theory are related together and differ from each other?
Thanks and regards!