|In contrast to the situation in a laboratory, the study of the solar atmosphere has to be pursued without direct access to the physical conditions of interest. Information is therefore incomplete and uncertain and inference methods need to be employed to diagnose the physical conditions and processes. One of such methods, solar atmospheric seismology, makes use of observed and theoretically predicted properties of waves and oscillations to infer plasma and field properties. In this talk, we report on recent results from the application of Bayesian analysis techniques to quantify the plausibility of physical parameter values and alternative models in seismology. A number of examples are shown in which parameter inference, model comparison, and model averaging are used in combination with observations of wave dynamics to obtain information about physical conditions and models in coronal and prominence plasmas.