Scott wrote: You are saying that it is not delusional to believe something without any evidence at all but only with evidence to the contrary, and I am saying it is.
I think it depends on what weight you give to inductive evidence that is, whether you consider it evidence at all. By inductive evidence I mean the accumulation of prior experience of similar circumstances. If you consider your prior experience to be circumstantial evidence applying to a current situation, belief might be viewed as delusional. If you do not consider it to be evidence at all, then belief in a new and different experience would be faith.
Thus in the situation of your wife's non-appearance, some would say that you have no evidence whatever, that her previous habits do not even constitute evidence. To imagine something is in this case faith—faith in the notion that your wife would not fail to come home without calling unless something had gone wrong. Others might insist that people follow habits and that failing to keep a usual habit is evidence something has gone wrong and you would be deluding yourself not to be worried.
The evidence we have against miracles for example is inductive—previous experience indicates they do not occur and belief in them is delusional. However, a person of faith might argue miracles are quite rare and previous experience devoid of miracles is not evidence they do not ever occur, but merely evidence of infrequency.
The general question of whether faith is self-delusional seems to me to hinge on precisely this point. At the time natural processes were not well understood, belief they were caused by supernatural forces was faith. It arose from ignorance of how things worked. Now that we understand things better, to believe disasters are the result of God's anger is delusion. What has changed is: the gradual accumulation of inductive evidence has shifted the ground away from faith.