Meaningful visualizations of big data are crucial and can be misleading without including measures of uncertainty. We extend a method called Bayesian Visual Analytics (BaVA) to incorporate uncertainty as users explore data visually. BaVA relies on linear projections of data based on Weighted Multidimensional Scaling (WMDS) (Kruskal 1964). The direction in which data are projected in WMDS is determined by weights assigned to each variable. Visualizations are interactive in the BaVA framework, and possible interactions include manipulating variable weights and/or the coordinates of the two-dimensional projection (Endert et al. 2011; Leman et al. 2013). Uncertainty exists in these visualizations on the variable weights, the user interactions, and the WMDS projection. We aim to quantify these uncertainties using a probabilistic approach of WMDS under the BaVA framework (pWMDS) in order to aid users in exploration. We use posterior parameter estimates from pWMDS to assess model fit and uncertainty in the coordinates displayed. Lastly, we find an approximation to our pWMDS so that we reduce computation and enable real time data explorations that account for uncertainty.