We study the Latent Dirichlet Allocation model, a popular Bayesian algorithm for text analysis. We show that the model's parameters are not identified, which suggests that the choice of prior matters. We characterize the range of values that the posterior mean of a given functional of the model's parameters can attain in response to a change in the prior, and we suggest two algorithms that report this range. Both of our algorithms rely on obtaining multiple Nonnegative Matrix Factorizations of either the posterior draws of the corpus' population term‐document frequency matrix or of its maximum likelihood estimator. The key idea is to maximize/minimize the functional of interest over all these nonnegative matrix factorizations. To illustrate the applicability of our results, we revisit recent work studying the effects of increased transparency on the communication structure of monetary policy discussions in the United States.