Can't prove the supernatural God

[SteveII]

The very definition of a supernatural event make detecting and investigating the cause logically impossible. So we are only left with the result and the context. 

Continuing to ignore the validity of the events for the purposes of a philosophical discussion...

Perhaps you are right for one event. If there were hundreds of similar events and other events that illustrated power over matter, life and death, knowledge that should not have been available, etc., the contextual interpretation becomes become stronger and the probability increases that supernatural forces are at play. This would all be in addition to the fact that Jesus clearly explained the source of this power--which at the very least lends additional context clues.

I'm sorry, but you're simply wrong here: increasing the number of events in which a given cause is asserted in no way influences what the cause of those events actually is. Allow me to demonstrate: here's a magician, and he says he's doing magic. Do you believe him? He just sawed that woman in half!

Except isn't that is how we arrive at all sorts of beliefs and theories?  We are talking about a series of unique but similar/connected events. We look for context and patterns in cause and effect, we look for exceptions, and we look for a theory that fits the data. More data strengthens the theory. 

You say a time traveler fits the theory just as well as does supernatural causation. Since time travel has its own problems, it isn't a viable option (causal loop paradox, grandfather paradox), it seems supernatural causation is still a leading contender (Occam's razor and all). 

You asked: "how do you ascribe a higher probability to a cause you cannot detect or even show is possible, over those other ones?" Why do you say we cannot detect the cause? We have the effect. Why aren't we justified in inferring supernatural causes as the best explanation? 

From Wikipedia: Inferring the cause of something has been described as

• "...reason[ing] to the conclusion that something is, or is likely to be, the cause of something else".[3]
  
• "Identification of the cause or causes of a phenomenon, by establishing covariation of cause and effect, a time-order relationship with the cause preceding the effect, and the elimination of plausible alternative causes."[4]