Missing values exist in nearly all clinical studies because data for a variable or question are not collected or not available. Imputing missing values and augmenting data can significantly improve generalisation and avoid bias in machine learning models. We propose a Hybrid Bayesian inference using Hamiltonian Monte Carlo (F-HMC) as a more practical approach to process cross-dimensional relations by applying a random walk and Hamiltonian dynamics to adapt posterior distribution and generate large-scale samples. The proposed method is applied to cancer symptom assessment, and MNIST datasets confirmed to enrich data quality in precision, accuracy, recall, F1-score, and propensity metric.