The result of a stochastic dynamic prediction is the expected values of the model parameters and the covariances among all the parameters. By adopting a Bayesian approach to the problem of analysis and making certain assumptions, one can utilize the vast amount of information in a stochastic dynamic prediction along with the information contained in observations. By making simulated observations of a pre-defined atmosphere, it is shown that the uncertainty in the analyzed values is substantially less than either the uncertainty in the forecast or in the observation. In addition, the results indicate that the effects of the limiting assumptions are minimal. Further experiments are performed in which only heights or only temperatures are actually observed, and in each case it is possible to obtain an analysis for all the parameters in the model. The method is particularly useful for assessing the value and impact of different amounts or types of data.