Reconstructions are probabilistic, and consequently some of our best tools are those of historical statistical inference. This is fortunate, since a great deal of fundamental mathematical research has already been done and we can now take advantage of it.
As an example, I introduce the AusPhon-Lexicon database, containing comparably phonemicized lexicons of 240 Australian languages: around 330,000 lexical forms, or 2 million segments. The database is generative, and can derive any number of datasets according to the research question of the user.
I show that the phonotactics of Australian laminal consonants, long thought to be distributed overwhelmingly according to areal / language-contact effects, can be shown in fact to harbour strong, vertical phylogenetic signal within the Pama-Nyungan language family, estimated to be on the order of 5,000 years old.