In frequentist statistics, the validity of the inference depends on the assumption that the model is correctly specified as well as pre-specified. Violations of these assumptions (i.e. we only specify a linear relationship but the true relationship is non-linear or we perform model selection procedures) undermine the validity of inference. Are there similar assumptions in Bayesian statistics or how are they solved in Bayesian statistics? I assume the prior is our belief about the correct model and therefore there is no misspecification?
Model specification in the Bayesian paradigm is just as important and potentially just has harmful as in frequentist statistics. The main difference with Bayes is that you can incorporate uncertainties instead of picking a simple model and hoping you're right. Examples:
- Instead of assuming normality, include a non-normality parameter in the model (indicating skewness, excess kurtosis, etc.)
- Instead of choosing whether an interaction term is in or out of the model, put it "half in" by having a prior for the interaction that favors "no interaction" but allows larger samples to override this.