Arguments Against Bayesian Inference
- Bayesian Inference
Whereas frequentist methods derive solutions via inventing estimators (a multitude of them may exist) and computing a likelihood function, Bayesian methods only offer one answer to a well-posed problem.
The Bayesian inference method is conditioned on assumptions (for example, the prior). Some say the prior introduces subjectivity. But how can one make inferences without assumptions? Bayesian methods force us to make these assumptions explicit.
Once the assumptions are made, the inferences are objective, unique, and can be agreed upon by everyone. These assumptions are easy to modify, and we can quantify the sensitivity of our inferences to our assumptions. It also quantifies the uncertainty in our inferences.
There is a common misconception that the aim of inference is to find the most probable explanation for some data. While the most probable explanation may be of some interest, this is only the peak of a probability distribution, and it is the whole distribution of explanations itself that is of interest. The most probable outcome from a source is often not a typical outcome from that source.