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Solar coronal seismology is based on the remote diagnostics of physical conditions in the corona of the Sun by comparison between model predictions and observations of magnetohydrodynamic wave activity. Our lack of direct access to the physical systems of interest makes information incomplete and uncertain so our conclusions are at best probabilities. Bayesian inference is increasingly being employed in the area, following a general trend in the space sciences. In this paper, we first justify the use of a Bayesian probabilistic approach to seismology diagnostics of solar coronal plasmas. Then, we report on recent results that demonstrate its feasibility and advantage in applications to coronal loops, prominences and extended regions of the corona.