[wirrbel]

Let's say you perform a maximum-likelihood estimate, you still have an assumption baked in, that maximizing the likelihood given the data is the right way to make your estimate.

In fact, it's very interesting to reconstruct a Bayesian prior for a maximum likelihood estimate. For example when you calculate probabilities for a binary event, 10 head flips, 8 tail flips. The ML estimate is 8/18 = 4/9. A Beta-Binomial bayesian model leads to a posterior distribution of Beta(a=8, b=10) with a mean of (8+a0)/(10 + 8 + a0 + b0), with a0 and b0 representing the prior distribution Beta(a0, b0). Now you can see that the maximum likelihood estimate is identical in this case to assuming a bayesian Prior of Beta(0, 0).

I am not saying by this that frequentism is Bayesian inference in disguise, rather, you cannot escape the assumptions.

Also, frequentism is not that straightforward, there are many kinds of frequentist estimators and it can be complicated to choose among them.

[zozbot234]

The ML estimate is a posterior mode, assuming a flat prior. It's not immediately clear that it will always be possible to find a corresponding posterior mean. (From a Bayesian point of view, this is a difference in loss functions as opposed to priors over the parameters. With a posterior mean, you're making the optimal inference assuming a quadratic loss; a posterior mode is appropriate for a 0-or-1 loss.)