The arguments of Richard Swinburne seem to be well known (and well debated) among professional philosophers of religion, but little known outside their ranks.

Swinburne’s Principle of Testimony:  “[T]hose who do not have an experience of a certain type ought to believe any others when they say they do -- again, in the absence of deceit or deception.  If we could not in general trust what other people say about their experiences without checking them out in some way, our knowledge of history or geography or science would be almost non-existent.”

His Principle of Credulity:  “Now it is a basic principle of rationality, which I call the principle of credulity, that we ought to believe that things are as they seem to be (in the epistemic sense) unless and until we have evidence that we are mistaken .... If you say the contrary -- never trust appearances until it is proved that they are reliable -- you will never have any beliefs at all.  For what would show that appearances are reliable except more appearances?  And, if you cannot trust appearances as such, you cannot trust these new ones either.  Just as you must trust your ordinary senses, so it is equally rational to trust your religious sense.”

Richard Swinburne, Is There a God? (Oxford, 2d ed., 2010), pp. 115-116.