We introduce the notion of a maximum likelihood optimal decision alternative for the choice problem with a finite set of decision alternatives, assuming a general parametric preference model of the decision maker. We also develop an optimization-based method for the identification of such alternatives for the cases in which the parametric preference model is based on uncertain intervals for criterion trade-offs. The suggested approach can be seen as generalising stochastic multicriteria acceptability analysis (SMAA) to a wider modelling setting. It also provides a maximum likelihood interpretation of the SMAA acceptability index.