Activity data of individual users on social media are easily accessible in this big data era. However, proper modeling strategies for user profiles have not been well developed in the literature. Existing methods or models usually have two limitations. The first limitation is that most methods target the population rather than individual users, and the second is that they cannot model non-stationary time-varying patterns. Different users in general demonstrate different activity modes on social media. Therefore, one population model may fail to characterize activities of individual users. Furthermore, online social media are dynamic and ever evolving, so are users' activities. Dynamic models are needed to properly model users' activities. In this paper, we introduce a non-parametric hidden Markov model to characterize the time-varying activities of social media users. An EM algorithm has been developed to estimate the parameters of the proposed model. In addition, based on the proposed model, we develop a clustering method to group users with similar activity patterns.

The self-similarity of network traffic has been convincingly established based on detailed packet traces. This fundamental result promises the possibility of solving on-line and off-line traffic engineering problems using easily collectible coarse time-scale data, such as simple network management protocol measurements. This paper proposes a statistical model that supports predicting fine time-scale behavior of network traffic from coarse time-scale aggregate measurements. The model generalizes the commonly used fractional Gaussian noise process in two important ways: (1) it accommodates the recurring daily load patterns commonly observed on backbone links and (2) features of long range dependence and self-similarity are modeled only at fine time scales and are progressively damped as the time period increases. Using the data we collected on the Chinese Education and Research Network, we demonstrate that the proposed model fits 5-min data and generates 10-s aggregates that are similar to actual 10-s data.

We investigate the estimation of the size of a broadcast audience. We give the maximum likelihood (ML) estimators for different scenarios. Using a Poisson approximation we obtain upper and lower bounds for the audience size. The ML estimators has closed-form expressions, so do the bounds. We treat the problem of a malfunctioning feedback flow control, where the sender is overwhelmed by feedback messages. The ML estimate of the audience size is obtained using the expectation-maximization (EM) algorithm, even under such conditions as censored values due to feedback implosion. Quantifying the influence of feedback implosion on the loss of information for the audience estimation, we further investigate the choice of the parameters in order to optimize estimation results.