I write this post mostly to show that this blog is still alive ... and still asking the same question(s).
Recently, I read this paper about a numerical study in lattice gravity, trying to distinguish 1st and 2nd order phase transitions. They use and refer to the methods I am familiar with, but I do wonder if this is really the best one can do nowadays.
If one does e.g. fit the location of the critical coupling as a function of lattice size, one has to deal with two big problems: First, the location of the critical coupling is not so well defined (e.g. due to the metastable states associated with 1st order transitions) for a given lattice size; there are limits on computation time and resources (*).
Second, how can one be sure if the lattice is big enough to be in the 'scaling region', i.e. big enough that small size corrections can be neglected (if the typical size of the 'bubbles', which come with a 1st order transition, is n and the lattice size N is smaller than n one has a problem).
So what is the current state-of-the-art and where are the professional statisticians and their Bayesian stochastic network thingy-ma-jiggies when we need them (x)? Please let me know if you know something.
(*) A related question for the practitioner: Is it better to spend the available computation power on a small number of iterations on a large lattice or is it better to do many iterations on a small lattice?
(x) Speaking of Bayesian thingy-ma-jiggies ...