In Topic Modeling can I use Logistic Normal distribution as a prior distribution and instead of a Gaussian distribution replace it with the Gaussian mixture component?
Model Logistic Normal distribution, mean, that you are using generalized linear model (GLM) and assume that errors follows the Normal distribution.The model using a Gaussian mixture component is essentially different from using Logistic Normal distribution.
Model using a Gaussian mixture component is type of generative models, this mean you can't replace, Logistic Normal distribution with Gaussian mixture component, but you can have an entirely different model, with different (assumption, parameters and equations).