<p>With the development of big data techniques, the difficulty that streaming longitudinal data lack theoretical support in modeling has become increasingly prominent. This paper proposes a two-layer Gaussian mixture model within a Bayesian framework to theoretically fit such data by characterizing their nature, such as being correlated, time-varying, and velocitous. Under the assumptions of first-lag autocorrelation and dependency, the conditional posterior probability, posterior distributions of the parameters, and posterior expectations are estimated for the purpose of statistical inference. These theoretical results are effectively validated through simulations under different hyper-parameter values, model estimation structures, as well as in a real data where real-time classification is conducted for heart disease diagnosis using heart sound signals. The model performance is also explored in cases where assumptions are violated in the simulation. The results show that the estimated theoretical statistical inference is precise under the assumptions. Specifically, the proposed model structure is more effective in characterizing the data compared with structures that do not consider their autocorrelation. Data with different location parameters are classified with high accuracy compared with those with differences only in scale parameters. The model performance is generally guaranteed under appropriate noise level. In contrast, the parameter estimation performance is suboptimal when the stated assumptions are violated by the data.</p>