Dr. James A. Lindsay's Definition of Faith

Faith, he argues, is "a form of cognitive bias that tends to overestimate the probabilities that the hypotheses in which faith is placed predict the evidence (of the world) while underestimating the probabilities that alternative hypotheses predict the evidence we have." Or, in other words he says:
Faith (n.): A cognitive bias in which a person overestimates the prior probability, overestimates the positive consequent, and/or underestimates the negative consequent in a Bayesian analysis.
"Indeed" he continues,
I argue that "overestimating the positive consequent" and "overestimating the prior probability" are technical ways to say "believe without evidence" and that "underestimating the negative consequent" is likewise a technical way of saying "believe in the face of contradictory evidence," although it's certainly not so cleanly cut since these categories overlap somewhat.

(Though the overestimate of the prior is more obviously the way to go with "believe without evidence," overestimating the positive consequent means "believing on false evidence," which is seeing evidence that isn't actually evidence, which implies of believing without actually having evidence since belief follows what is believed to be evidence.)
The effect, he says, "is pretty straightforward" since,
  1. Overestimates to the positive consequent will have the effect of overestimating the posterior probability, which measures the likelihood that the hypothesis is true after evaluating the body of evidence.
  2. Underestimates to the negative consequent will also have the effect of overestimating the posterior probability.

(Incidentally, overestimating the prior probability also overestimates the posterior probability.)

If someone were to approach a hypothesis entirely without bias, the posterior probability should tell them the actual degree of confidence upon which they can proceed with in terms of accepting the hypothesis. Faith, by this definition, then, overestimates the actual degree of confidence that one can have in a particular hypothesis.

The advantage of this definition is that it puts the cognitive bias of faith into clear contrast in terms of how it impacts the reasoning capacity of a person that holds it. In this light, it makes it very difficult to accept, at least in general, that this cognitive bias can be considered a "virtue." See here.
Make sure you get Dr. Lindsay's book, God Doesn't; We Do: Only Humans Can Solve Human Challenges.