An accurate prediction of brain tumor progression is crucial for optimized treatment of the tumors. Gliomas are primarily treated by combining surgery, external beam radiotherapy, and chemotherapy. Among them, radiotherapy is a non-invasive and effective therapy, and an understanding of tumor growth will allow better therapy planning. In particular, estimating parameters associated with tumor growth, such as the diffusion coefficient and proliferation rate, is crucial to accurately characterize physiology of tumor growth and to develop predictive models of tumor infiltration and recurrence. Accurate parameter estimation, however, is a challenging task due to inaccurate tumor boundaries and the approximation of the tumor growth model. Here, we introduce a Bayesian framework for a subject-specific tumor growth model that estimates the tumor parameters effectively. This is achieved by using an improved elliptical slice sampling method based on an adaptive sample region. Experimental results on clinical data demonstrate that the proposed method provides a higher acceptance rate, while preserving the parameter estimation accuracy, compared with other state-of-the-art methods such as Metropolis-Hastings and elliptical slice sampling without any modification. Our approach has the potential to provide a method to individualize therapy, thereby offering an optimized treatment.