Purpose: Machine learning is broadly used for clinical data analysis. Before training a model, a machine learning algorithm must be selected. Also, the values of one or more model parameters termed hyper-parameters must be set. Selecting algorithms and hyper-parameter values requires advanced machine learning knowledge and many labor-intensive manual iterations. To lower the bar to machine learning, miscellaneous automatic selection methods for algorithms and/or hyper-parameter values have been proposed. Existing automatic selection methods are inefficient on large data sets. This poses a challenge for using machine learning in the clinical big data era. Methods: To address the challenge, this paper presents progressive sampling-based Bayesian optimization, an efficient and automatic selection method for both algorithms and hyper-parameter values. Results: We report an implementation of the method. We show that compared to a state of the art automatic selection method, our method can significantly reduce search time, classification error rate, and standard deviation of error rate due to randomization. Conclusions: This is major progress towards enabling fast turnaround in identifying high-quality solutions required by many machine learning-based clinical data analysis tasks.