I wanted to know about how empirical works are done in Linguistics. I have very little idea about this field, but I am interested to know.
I know many empirical "facts" about languages and their families, like my first language, Assamese is an Indo-Aryan language, part of the Indo-European family. My hometown has a lot of people whose first language is Mising, which comes under the Tani languages, of the Sino-Tibetan family. So my language is linguistically closer to German, a language native to a place thousands of miles away, than to Mising, spoken by people living next door. And the classification makes sense: I can understand a little bit of Gujarati or Punjabi spoken 1000+ miles away, because of similarities between Assamese and Gujarati/ Punjabi (both Indo-Aryan languages), but I can't understand my neighbour languages like Mising, Bodo, Mizo etc. at all. This fascinates me a lot!
What is the empirical methodology to construct language-trees like that?
And as the title of the question suggests, while the fascination with language families is one of the primary reasons I want to learn this, firstly, I understand that directly jumping to language-trees may not be possible, and secondly, a general overview of the methods would also be helpful. I have many other questions that interest me, for example, how are two languages considered different (why are Assamese and Bengali different languages, how do we know that Cachar is a dialect of Bengali and not Assamese etc.), how are languages classified as endangered etc.
So maybe a general introduction to statistical methodology in linguistics would help? Maybe an introductory textbook and then an advanced one would help? I have a fair amount of knowledge of statistics, econometrics and psychometrics. I would love a rigorous mathematical treatment, along with say software implementation etc. If there is no comprehensive textbook, a series of textbooks/ articles etc. would also help.