A common way to model decision maker (DM) preferences in multiple criteria decision making problems is through the use of utility functions. The elicitation of the parameters of these functions is a major task that directly affects the validity and practical value of the decision making process. This paper proposes a novel Bayesian method that estimates the weights of criteria in linear additive utility functions by asking the DM to rank or select the best alternative in groups of decision alternatives. Our method computes the entire probability distribution of weights and utility predictions based on the DM's answers. Therefore, it enables the DM to estimate the expected value of weights and predictions, and the uncertainty regarding these values. Additionally, the proposed method can estimate the weights by asking the DM to evaluate few groups of decision alternatives since it can incorporate various types of inputs from the DM in the form of rankings, constraints and prior distributions. Our method successfully estimates criteria weights in two case studies about financial investment and university ranking decisions. Increasing the variety of inputs, such as using both ranking of decision alternatives and constraints on the importance of criteria, enables our method to compute more accurate estimations with fewer inputs from the DM.