For the present work, we introduce and evaluate a novel Bayesian syntactic shallow parser that is able to perform robust detection of pairs of subject-object and subject-direct object-indirect object for a given verb, in a natural language sentence. The shallow parser infers on the correct subject-object pairs based on knowledge provided by Bayesian network learning from annotated text corpora. The DELOS corpus, a collection of economic domain texts that has been automatically annotated using various morphological and syntactic tools was used as training material. Our shallow parser makes use of limited linguistic input. More specifically, we consider only part of speech tagging, the voice and the mood of the verb as well as the head word of a noun phrase. For the task of detecting the head word of a phrase we used a sentence boundary detector. Identifying the head word of a noun phrase, i.e. the word that holds the morphological information (case, number) of the whole phrase, also proves to be very helpful for our task as its morphological tag is all the information that is needed regarding the phrase. The evaluation of the proposed method was performed against three other machine learning techniques, namely naive Bayes, k-Nearest Neighbor and Support Vector Machines, methods that have been previously applied to natural language processing tasks with satisfactory results. The experimental outcomes portray a satisfactory performance of our proposed shallow parser, which reaches almost 92 per cent in terms of precision.