Some examples of confirmation bias are a bit more complicated than others and people typically mix together several different fallacious forms of argument. Here's an example from Denis Alexander's book Creation or Evolution (p. 213) that combines begging the question and confirmation bias.
Certainly God's great work in creation is distinct from his wonderful plan of redemption but the point here is that the whole book [the Bible] is God's book. The various narratives running through the book all stem from the same author. The evolutionary creationist1 is one who has a very firm belief in God's sovereignty over the whole created order, worked out in his plan and purposes for both creation and redemption. [my emphasis, LAM]Denis Alexander assumes that the Bible is the inspired word of God and he spends a great deal of time explaining how the stories of Genesis actually conform to what science has discovered in the past 150 years. For example, Adam and Eve are not the first humans but the first couple to see God. The deluge was probably a local event. The opening verses of Genesis are allegory meant to convey an impression of God the creator rather than scientific fact.
Once we have baptised evolution into our Christian worldview, just as countless Christians have been doing ever since the time of Darwin, then of course we will see no need to view evolutionary theory as the sinister intruder or 'universal acid' that the Dennetts and Dawkins of this world appear to imagine, but rather as the process that God has chosen by his sovereign will, to bring into being all the amazing biological diversity that we see all around us.
But it's also begging the question since the real question is not why God was so ambiguous when writing his book but whether God even wrote it—or whether he even exists. That's the real conflict between science and religion but Denis Alexander ignores that question.
A few paragraphs later he brings up the idea of confirmation bias in a different context.
I am not suggesting for a moment that adopting the position of evolutionary creationism resolves at a stroke all the problems, and we shall be considering some of those in the next few chapters, but I would suggest that it provides a well-justified framework for continuing to hold together the book of God's Word and the book of God's works in a way that does justice to both.I don't think Denis Alexander sees the irony in his criticism. He criticizes Dawkins for confirmation bias but his crime is much greater and much more obvious.
Once we adopt this position, the ruse of annexing 'evolution' in support of ideological agendas loses its power to persuade. For example, there is nothing I can see in evolutionary theory that supports atheism. Of course, if we view evolution through an atheistic lens, we shall inevitably interpret it within an atheistic framework, as Dawkins does when he writes that in evolution he sees 'no design, no purpose, no evil and no good, nothing but blind pitiless indifference.' How could it be otherwise? The conclusions are built into the starting presupposition. This is what the atheistic worldview delivers; it is not what evolution itself delivers.
If you were to believe Denis Alexander's description of atheism then there might be a kernel of truth in his criticism. But here's the problem. The question before us is whether science reveals a world full of purpose and design as the belief in Alexander's God requires. That's a scientific question. Dawkins says that the evidence does not support such a claim and I agree. (Alexander thinks that atheism is the metaphysical denial the gods exist—that's part of his problem.)
Thus, scientists such as Richard Dawkins see no reason to believe in creator gods. Neither do I. We don't initially start with the presupposition that gods exist nor do we start with the supposition that they don't exist. We are looking for evidence one way or the other.
The default position is that gods don't exist. That's the only way you can fairly examine the evidence. It's not confirmation bias, in my opinion, when the evidence doesn't support the claim of existence. The burden of proof is on the believers who are making an extraordinary claim.
Look at it this way. Imagine that you find no evidence whatsoever to support the existence of Santa Claus or the tooth fairly therefore you don't believe in them. Is that confirmation bias because you started out being skeptical of their existence? I don't think so.
We can argue about whether the universe shows evidence of purpose but that's a different issue. If it turns out that there's abundant evidence of purpose and scientists are ignoring it in favor of other evidence for lack of purpose, then that's confirmation bias (if they are atheists). But in this case, you can only accuse Dawkins of confirmation bias once you've established that he is biased in selecting his evidence. That requires a discussion about purpose but Denis Alexander doesn't go there in this chapter. You have to wait until page 424.
When you get to that page you'll discover that his arguments for purpose are very weak2 so he has no case when he accuses Dawkins of confirmation bias. There is a case, on the other hand, for accusing Denis Alexander of seeing only what he wants to see.
1.Denis Alexander describes himself as an evolutionary creationist.
2. He thinks the tape will replay in the same way and the evidence of convergence (Simon Conway Morris) proves it.