Do Bayesians ever argue there are cases in which their approach generalizes/overlaps with the frequentist approach? Do Bayesians ever argue that their approach generalizes the frequentist approach, because one can use non-informative priors and therefore, can recover a typical frequentist model structure?
Can anyone refer me to a place where I can read about this argument, if it is indeed used?
EDIT: This question is maybe phrased not exactly the way I meant to phrase it. The question is: "is there any reference to discussion of the cases in which the Bayesian approach and the frequentist approach overlap/intersect/have something in common through the use of a certain prior?" One example would be using the improper prior $p(\theta) = 1$, but I am pretty sure this is just the tip of the tip of the iceberg.
 A: The short answer is probably "yes--and you don't even need a flat prior for this argument to hold."
For example, the Maximum A Posteriori (MAP) estimate is a generalization of maximum likelihood that includes a prior, and there are frequentist approaches that are analytically equivalent to finding this value.  The frequentist relabels "the prior" as a "constraint" or "penalty" on the likelihood function, and gets the same answer. So frequentists and Bayesians can both point to the same thing as being their best parameter estimate, even if the philosophies are different.  Section 5 of this frequentist paper is one example where they're equivalent.
The longer answer is more like "yes, but there are often other aspects of the analysis that distinguish the two approaches. Still, even these distinctions aren't necessarily iron-clad in many cases."
For example, while Bayesians do sometimes use the MAP estimate (posterior mode) when it's convenient, they typically emphasize the posterior mean instead. On the other hand, the posterior mean also has a frequentist analogue, called the "bagged" estimate (from "bootstrap aggregating") that can be almost indistinguishable (see this pdf for an example of this argument). So that's not really a "hard" distinction either.
In practice, all this means that even when a frequentist does something that a Bayesian would consider totally illegal (or vice versa), there is often (at least in principle) an approach from the other camp that would give nearly the same anser.
The main exception is that some models are really hard to fit from a frequentist perspective, but that's more of a practical issue than a philosophical one.
A: Edwin Jaynes was one of the best at highlighting the connections between bayesian and frequentist inference.  His paper confidence intervals vs bayesian intervals (google search brings it up) as a very thorough comparison - and I think a fair one.
Small area estimation is another area where ML/REML/EB/HB answers tend to be close.
A: Many of these comments assume that "frequentist" means "maximum likelihood estimation."  Some people have a different definition: "frequentist" means a type of analysis of the long-term inferential properties of any inference method -- whether it's Bayesian, or method-of-moments, or maximum likelihood, or something couched in non-probabilistic terms (e.g SVM's), etc.
A: I have seen two arguments advanced that Bayesian analysis is a generalization of a frequentist analysis. Both were somewhat tongue-in-cheek, and more getting people to recognize the assumptions about regression models by using priors as a context.
Argument 1: Frequentist analysis is Bayesian analysis with a purely uninformative prior centered on zero (yes, it doesn't matter where its centered, but ignore that). This provides both the context for which a Bayesian might extract the results of a frequentist analysis, explains why you can get away with using some "Bayesian" techniques like MCMC to extract frequentist estimates in situations where say, maximum likelihood convergence is tough, and gets people to recognize that when they say "The data speak for themselves" and the like, what they're actually saying is that beforehand, all values are equally likely.
Argument 2: Any regression term you don't include in a model has, in effect, been assigned   a prior centered on zero with no variance. This one isn't so much a "Bayesian analysis is a generalization" as much as "There are priors everywhere, even in your frequentist models" argument.
A: I would like to hear from Stephane or some other Bayesian expert on this.  I would say no because it is a different approach not a generalization.  In another context this has been argued here before.  Don't think that just because flat priors produce results close to maximum likelihood that a Bayesian method with a flat prior is frequentist! I think that would be a false presumption that would lead you to think that by making the prior arbitrary you are generalizing to other possible priors.  I don't think that way and I am pretty sure most Bayesian don't either.
So some people do argue it but I don't think they should be classified as Bayesians 
although Stephane has pointed out the difficulty with strong classification.  So strictly speaking if the word is ever then I guess it might depend on how you define Bayesian.
