Bayesian stopping rule in discrete parameter space with multiple local maxima

summary:The paper presents the stopping rule for random search for Bayesian model-structure estimation by maximising the likelihood function. The inspected maximisation uses random restarts to cope with local maxima in discrete space. The stopping rule, suitable for any maximisation of this type, exploits the probability of finding global maximum implied by the number of local maxima already found. It stops the search when this probability crosses a given threshold. The inspected case represents an important example of the search in a huge space of hypotheses so common in artificial intelligence, machine learning and computer science