Testing a Hypothesis about the Supernatural

[SteveII]

But the fact remains that the supernatural either exists or does not and science has no standing in making that determination.

I agree that it exists or it doesn't. And no matter how much we choose to believe or not believe in it, it makes it no more or less real.
But, if we have no way of testing for the supernatural, how can we even determine that it exists in the first place?
If 'Event A' happens, and it's claimed to be supernatural, there must be something about that event that gives you reason to believe that it is "supernatural" and not just "unknown". Supernatural is not synonymous with unknown, which is what a lot of people seem to be doing.

Okay, but context is important. I said earlier that when discussing Jesus' miracles, the context that strengthens the claim might include:

1. Timing
2. Illustrating a particular point. 
3. Reinforce teachings with some authority. Example feeding 5000, Matt 9:35
4. So that people might believe (specifically stated). Example Lazarus (John 11)
5. Reward for faith.
6. Theologically significant. example virgin birth, baptism, tearing of the veil in the temple, resurrection.

So let's stick with the example I have above. So as not to get sidetracked on a debate about the NT, let's just say for the sake of this discussion you were present and you knew the man to be paralyzed. 

Luke 5:17 On one of the days while Jesus was teaching, some proud religious law-keepers and teachers of the Law were sitting by Him. They had come from every town in the countries of Galilee and Judea and from Jerusalem. The power of the Lord was there to heal them. 18 Some men took a man who was not able to move his body to Jesus. He was carried on a bed. They looked for a way to take the man into the house where Jesus was. 19 But they could not find a way to take him in because of so many people. They made a hole in the roof over where Jesus stood. Then they let the bed with the sick man on it down before Jesus. 20 When Jesus saw their faith, He said to the man, “Friend, your sins are forgiven.”

21 The teachers of the Law and the proud religious law-keepers thought to themselves, “Who is this Man Who speaks as if He is God? Who can forgive sins but God only?” 22 Jesus knew what they were thinking. He said to them, “Why do you think this way in your hearts? 23 Which is easier to say, ‘Your sins are forgiven,’ or, ‘Get up and walk’?

24 “So that you may know the Son of Man has the right and the power on earth to forgive sins,” He said to the man who could not move his body, “I say to you, get up. Take your bed and go to your home.” 25 At once the sick man got up in front of them. He took his bed and went to his home thanking God. 26 All those who were there were surprised and gave thanks to God, saying, “We have seen very special things today.”

Present in the series of events is 1, 2, 3, 5, and 6. That's a lot of context. 

Now, using Bayes Theorem and especially Bayesian Inference, we can examine the probability of seeing the paralyzed man walk given the overall context. 



R = A Miracle Having Happened (the man walks due to supernatural causes)
B = Background information (the supernatural exists)
E = Evidence (paralyzed man walking in the context of being commanded to for the reasons mentioned)

The way you read this is 
Pr="The probability of" 
| = "given"
& = "and"

So the probability of a Miracle Having Happened given the Evidence and The Supernatural Exists OVER the probability of a Miracle Having NOT Happened  given the Evidence and The Supernatural Exists
=
The probability of Miracle Having Happened given The Supernatural Exists OVER the probability of Miracle Having NOT Happened given the The Supernatural Exists
X 
The probability of seeing the Evidence given a Miracle Having Happened and The Supernatural Exists OVER the probability of seeing the Evidence given a Miracle NOT Having Happened and The Supernatural Exists

Notice this last part of the equation. It is the probability of seeing the evidence given no miracle, no supernatural. A low value here significantly increase the overall probability of a miracle having happened.