Parametrized families of Gibbs measures and their statistical inference

For Hölder continuous functions [Formula: see text], [Formula: see text], on a subshift of finite type and [Formula: see text] we consider a parametrized family of potentials [Formula: see text]. We show that the maximum likelihood estimator of [Formula: see text] for a family of Gibbs measures with potentials [Formula: see text] is consistent and determine its asymptotic distribution under the associated shift-invariant distribution. A second part discusses applications; from confidence intervals through testing problems to connections to Bernoulli distributions and stationary Markov chains.