Karl Popper is famous for declaring that theories can never be confirmed, only falsified. It seems to me he is wrong about this, and his error turns on viewing falsification and confirmation as all or nothing affairs.
But they are not. As pointed out by Duhem, Quine, Lakatos, Feyerabend, and others, no theory is ever so thoroughly falsified that there is no way to rehabilitate it. The Duhem-Quine thesis notes that, given an experimental result that apparently refutes a theory, one can always change an auxilliary hypothesis instead of the central tenet of the theory, and so rescue the theory. For example, Copernicus did not regard the absence of observed parallax in the stars as refuting his heliocentric theory. Instead, he simply moved the sphere of stars ten times as far away as it was previously thought to be. As my history of science lecturer, John Milton, pointed out, in this respect a Popperian has to regard Ptolemy's model as scientific and Copernicus's as unscientific, since Ptolemy's would be falsified by observered parallax, while, if newer, more accurate instruments still failed to detect parallax, Copernicus could simply place the sphere of the stars even farther away!
And so it is for confirmation. It is true that no theory is ever completely confirmed. But each piece of evidence supporting the theory raises the degree to which it is confirmed. Let's look at a hypothetical example from historiography to see how the Popperian view fails to capture the true state of our knowledge of the world. Imagine that two historians present you with two theories: One of them tells you that Caesar crossed the Rubicon in a deliberate act of defiance of the Roman Senate and constitution. The second says that King Arthur took on a dozen wives in order to cement diplomatic relationships with neighbouring kingdoms.
From a Popperian point of view, we have no cause to consider either theory more or less confirmed than the other. Confirmation is impossible. All we can say is that neither theory has been falsified. But this is clearly absurd: there is abundant, indeed, overwhelming evidence that leads us to believe the first historian's theory, while no one is even sure if King Arthur was a real person. (And, not knowing if he ever existed, we certainly cannot falsify a theory that says he had a dozen wives as of yet.)
One need not be a naïve or even a strict Bayesian to suspect that Bayesians are on the right track in holding that hypotheses are more or less confirmed, and that positive evidence rightly up our degree of belief in them. Scientists may not really formulate numerical estimates of the prior probability of different hypotheses. It is enough, as noted by Paul Horwich, that we can use an idealized model of how they might do so to dispel certain common errors, such as the failure to recognize that different hypotheses are held with different degrees of belief, and that different pieces of evidence do offer varying degrees of confirmation for a theory. Per Horwich, if Bayesianism can help in that process, it simply does not matter if it offers a complete, or even a very realistic, account of how scientists operate. Furthermore, if other models can also help to clear away the fog, there is no reason not to supplement Bayesianism with such models.