The heart is an important organ in the human body, and acute myocardial infarction (AMI) is the leading cause of death in most countries. Researchers are doing a lot of data analysis work to assist doctors in predicting the heart problem. An analysis of the data related to different health problems and its functions can help in predicting the wellness of this organ with a degree of certainty. Our research reported in this paper consists of two main parts. In the first part of the paper, we compare different predictive models of hospital mortality for patients with AMI. All results presented in this part are based on real data of about $603$ patients from a hospital in the Czech Republic and about $184$ patients from two hospitals in Syria. Although the learned models may be specific to the data, we also draw more general conclusions that we think are generally valid. In the second part of the paper, because the data is incomplete and imbalanced we develop the Chow--Liu and tree-augmented naive Bayesian to deal with that data in better conditions, and compare the quality of these algorithms with others.