Over the past 10 years Bayesian methods have rapidly grown more popular in many scientific disciplines as several computationally intensive statistical algorithms have become feasible with increased computer power. In this paper we begin with a general description of the Bayesian paradigm for statistical inference and the various state-of-the-art model-fitting techniques that we employ (e.g., the Gibbs sampler and the Metropolis-Hastings algorithm). These algorithms are very flexible and can be used to fit models that account for the highly hierarchical structure inherent in the collection of high-quality spectra and thus can keep pace with the accelerating progress of new space telescope designs. The methods we develop, which will soon be available in the Chandra Interactive Analysis of Observations (CIAO) software, explicitly model photon arrivals as a Poisson process and thus have no difficulty with high-resolution low-count X-ray and γ-ray data. We expect these methods to be useful not only for the recently launched Chandra X-Ray Observatory and XMM but also for new generation telescopes such as Constellation X, GLAST, etc. In the context of two examples (quasar S5 0014+813 and hybrid-chromosphere supergiant star α TrA), we illustrate a new highly structured model and how Bayesian posterior sampling can be used to compute estimates, error bars, and credible intervals for the various model parameters. Application of our method to the high-energy tail of the ASCA spectrum of α TrA confirms that even at a quiescent state, the coronal plasma on this hybrid-chromosphere star is indeed at high temperatures (>10 MK) that normally characterize flaring plasma on the Sun. We are also able to constrain the coronal metallicity and find that although it is subject to large uncertainties, it is consistent with the photospheric measurements.