Objectives and context: The research objective of this proposal is to build inference algorithms in the Bayesian non-parametric (BNP) framework and study fast alternatives for a large dataset , especially in the case of grouped data and sequential data. Model selection generally measures how well the model fits the data. and it also has a complexity penalty to favor the simplest model. BNP offers an alternative way to solve the model selection problem, while the traditional method first fits several models and then applies certain criteria to select the optimal one. Additionally, BNP adapts to the model by adapting its complexity to the data, and the complexity can increase when more data is available. In the case of a mixture model, the BNP modeling approach automatically estimates the number of mixture components from the data and also allows the number of mixture parts to be increased when more data is observed. BNP modeling is now experiencing a revolution in statistics and machine learning over the last decade. Neal (2000) summarized and developed a number of Gibbs and other MCMC algorithms for the Diriclet Process Mixture (DPM) model, and then a huge amount of work and extensions were established. Rasmussen (2000) provided a detailed derivation of the Gaussian DPM model, called the infinite Gaussian mixture model, and then Beal et al. (2002) applied the BNP concept to learn the infinite hidden Markov model (iHMM), whose number of transition and emission states is not determined in advance to learn the parameters, and the paper constructed the hierarchical Dirichlet process (HDP) to model the structure. transition and emission scheme. Then, HDP was formally defined by Teh et al. (2006), and it showed that the HDP defined in the article is equivalent to the coupled...... middle of article...... the basic knowledge of the above preliminaries, I need to review BNP model building and their inference algorithms for some classic models from the last decade, for example, the specific model structure I am interested in is Bayesian hierarchical modeling for clustered data and HMM for time series data/ sequential data, and inference methods for these models always have two options, where BNP inference always provides a valuable comparison with classical. Finally, there are to be extensions and new algorithms for BNP modeling during my doctoral research, although the appropriate methodology and context of application will be discussed with my supervisors. Furthermore, it is very likely that I will research fast computational approaches on BNP configuration during my research, because large data size and high dimensionality problems always push us to find inference algorithms alternatives..