I have a basic question about Bayesian statistics.
Lets say that I want to make forecasts of a certain response variable, based on explanatory variables and lagged responses variables, while I have no knowledge apart from the data. This means that under a Bayesian approach, I would specify a diffuse prior to obtain the posterior distribution of my parameters.
In this topic (Why I should use Bayesian inference with uninformative prior?) I read the following sentence: ''if you are interested only in point estimates, then it (frequentist and bayesian) is basically the same''.
I would now like to ask: Does forecasting in a 'Bayesian way', when using a diffuse prior, has any advantages over just using MLE to obtain estimates for your parameters and making forecasts in 'frequentist way'? I think that for obtaining a point estimate of your parameter, a Bayesian approach does not really have any advantages over a frequentist approach, but I was wondering if this also was the case from a forecasting perspective.