Regression analysis, a technique used for modeling the relationship between input and output data, is widely used for prediction and forecasting. But in most cases, especially the case for constructing the empirical model, it’s very hard to select the model for prediction among a set of model class candidate. Even for same set of data, different people may use different assumption and different model class to do the regression analysis. So, based on different selected model, it’s not surprising that people may get the prediction result with significant difference. There are two levels of regression problem to be considered although they are strongly related. The first level is parametric identification with a specified model class. A metric is defined to measure the distances between observed and predicted data, by minimizing this distances, the optimal parameter value can be obtained. The second level is on the selection of model class. Quite a number of techniques have been developed and used to select the model based on the data. In this thesis, Bayesian model class selection technique is used to identify the optimal parameter value as well as their uncertainty, and to select the most plausible model class based on the data. Two different methods developed from this technique will be adopted to analyze the regression problems. The first one is the discrete Bayesian model selection. The second one uses the machine learning theory, and performs continuous model class selection to the linear regression model. These two methods are used to analyze the strong-motion record of China.