Various research applications suffer from small data sets and require highly predictive models. For instance, a major challenge in predicting the recovery rate of communities after disasters is that recovery data are often scarce due to the nature of extreme events. To address this challenge, we propose a new model called the Hierarchical Bayesian Kernel Model (HBKM). This model integrates the Bayesian property of improving predictive accuracy as data are dynamically accumulated, the kernel function that can make nonlinear data more manageable, and the hierarchical property of borrowing information from different sources in scarce and diverse data samples. The proposed model is applied to estimate the recovery from power outages of a community in Shelby County, Tennesse after the most severe storms since 2007. HBKM is compared to other statistical methods for validation, such as the Hierarchical Bayesian Regression Model (HBRM) and the Poisson Generalized Linear Model (GLM). The predictive accuracy of the models is evaluated using log-likelihood and Root Mean Squared Error. Preliminary results show that HBKM yields the highest average value of the out-of-sample predictive accuracy.