The two PDF's - Page 1 and Page 2 are the equations from the book "The Resurrection of God Incarnate" by the Philosopher Richard Swineburne. The pages are the actual steps taken to run the calculation. This is my handwriting. I found my ability to follow the equation much easier as I wrote through the steps multiple times and with variations. The book is of course a fuller view of the matter. My interest in this particular post is the insights that I gained from building a calculator to run the numbers much faster and in various ways.
The calculator/s, for those who wish to run them yourselves in a python interpreter, can be found on my github here https://github.com/apept/apept
Swinburne's original estimates get us a likelihood of 97% that Jesus was God incarnate and rose from the dead. The first two numbers he gives for the likelihood of the existence of God and the that God would incarnate/reveal, he set at 50%. Thus, he was mathematically avoiding biasing his initial start. Even with that initial start we get to 97% likely.
One's initial estimate of God's existence and incarnation can go rather low assuming that we keep the other number estimates of Swinburne's the same. By "go rather low" I mean that we can estimate the likelihood of God's existence and that he would reveal himself both, as low as only 10% likely, and we still end up just barely over 50% likely that Jesus is God incarnate and rose from the dead. Thus, even here it is still rational enough to believe in it, assuming +50% should count as rational. The starting points are fairly low indeed. Assuming the atheist doesn't say "0% likely" the theist has some good grounds to reason with them on the resurrection.
Swinburne's "Evidence" which he spends the majority of the book seeing if they are in fact true, is where a lot of the assessment comes down to. One can simply say, "I don't think such long ago past events can actually be known. If someone holds such a view, then they will not agree to the evidence Swinburne Still, one could reason with them that certain past events can be known, and there are good books on past knowledge that could be read to overcome that difficulty. Either way though, a lot hangs on "E" in the equation.
One can go through from the perspective of different belief systems, assuming you know a thing or two about other worldviews. Running the numbers this way can bring forth some interesting insights. For instance, running the calculator from a Muslim mindset will not bring results that are favorable to the incarnation/resurrection. The main reason for this has to do with a very strong prior belief that God will not associate himself with a man. Thus, the whole concept of incarnation is a no go. I ran the numbers from a strong belief in God (99%) but an almost non-existent chance that God would reveal himself as a human (.001). Some of the other inputs were adjusted too. The final result was a maximum of a 10% chance for the final conclusion.
This study shows that value in understanding how weighty prior beliefs can be in assessing a topic. Moreover, if we can focus in on beliefs that are causing the difficulty in someone's thinking on any given topic, we will be able to narrow down the work we are doing to help someone see a particular truth or hypothesis.