The main challenge in developing soft sensors in process industry is the existence of irregularity of data, such as measurement noises, outliers, and missing data. This paper is concerned with a comparative study among various data-driven soft sensor algorithms and the Bayesian methods. The algorithms to be considered for a comparative study in this paper include ordinary least-squares, robust regression, error-in-variable methods, partial least-squares, and the Bayesian inference algorithms. Methods for handling irregular data are reviewed. An iterative Bayesian algorithm for handling measurement noise and outliers is proposed. Performance of the Bayesian methods is compared with other existing methods through simulations, a pilot-scale experiment, and an industrial application.