Journal of Data Science

We propose a simple mixed membership model for social network clustering in this paper. A flexible function is adopted to measure affinities among a set of entities in a social network. The model not only allows each entity in the network to possess more than one membership, but also provides accurate statistical inference about network structure. We estimate the membership parameters using an MCMC algorithm. We evaluate the performance of the proposed algorithm by applying our model to two empirical social network data, the Zachary club data and the bottlenose dolphin network data. We also conduct some numerical studies based on synthetic networks for further assessing the effectiveness of our algorithm. In the end, some concluding remarks and future work are addressed briefly.

Abstract: Early phase clinical trials may not have a known variation (σ) for the response variable. In the light of applying t-test statistics, several procedures were proposed to use the information gained from stage-I (pilot study) to adaptively re estimate the sample size for managing the overall hypothesis test. We are interested in choosing a reasonable stage-I sample size (m) towards achieving an accountable overall sample size (stage-I and later). Conditional on any specified m, this paper replaces σ by the estimated σ (from stage-I with sample size m) to use the conventional formula under normal distribution assumption to re-estimate an overall sample size. The estimated σ, re-estimated overall sample size and the collective information (stage-I and later) would be incorporated into a surrogate normal variable which undergoes hypothesis test based on standard normal distribution. We plot the actual type I&II error rates and the expected sample size against m in order to choose a good universal stage-I sample size (𝑚∗ ) to start