Very nice overview of Bayes Theorem and Historical Jesus

[_Mary]

- assemble the basket of all of the evidence we have

Analytics, what would you count as evidence? How would you weight it in the first instance?

[_Analytics]

Hi Analytics,

I am confused by your use of a priori assumption. What is the assumption that is a priori your referring to? Or an example.

I'm talking specifically about the "a priori" assumptions in Bayes' Theorem. "a priori" is Latin and means "from the earlier." In this context, it is an explicit assumption you must make and assign a number to before you actually perform the analysis. This is the concept that Kishkumen was mocking, and is the controversial aspect of Bayes' Theorem.

In my specific example, before I can answer the question, "how likely is it that Jesus existed?" I must first take a stab at answering the exact same question: "how likely is it that Jesus existed?"

So, I might say that I thought there was a 20% chance of Jesus existing before I looked at the data. That is my a priori, but after looking at the data I might change that to, say, 10%. The key is that mathematically, you can't calculate the 10% from the data without first taking a subjective a priori guess about it. And yes, changing my a priori from 20% to anything else changes the final result from 10% to something else.

Can you see why that is troubling? Can you see why some historians probably don't want to say that is what they are doing?

Does Philo or yourself really believe historians don't weigh evidence in the same rigorous mathematical/logical way Carrier espouses? Take my example above. No matter how you slice it or dice it, if you call it applying Baye's theorem, or if you call it historical criticism, source criticism, redaction criticism etc.. you apply reasoning and weighing of evidence towards the best explanation. That's what historians do. ....

I'm not prepared to make blanket statements about what historians do and don't do. However, if Kishkumen's comments on this thread are any indication, Bayesian analysis isn't universally held in high regard by historians.

Bayes' Theorem is somewhat paradoxical. On the one hand it's intuitive and implicitly present in all valid analysis of things involving evidence and uncertainty. But on the other hand, it can be confusing and troubling--do we really want to "decide in advance how likely it is something will happen by spitballing," and have that be an explicit, necessary component of the subsequent scientific, data-driven analysis?

Bayesians such as myself confidently say yes. But in most fields, we are probably in the minority.

[_Analytics]

We have a P&C actuary (me - light) vs life actuary (Analytics - darkness).
Take an example from P&C. Let's assume that the a priori assumption is that a given line has a 10% frequency based on prior experience. New data is that the frequency is 6%. The claim count for the new experience indicates that it has a credibility of 50%. The Bayes indicated frequency is 8% = 10% x 50% + 6% x 50%. Unless new evidence is uncovered about the historicity of Jesus, I'm not sure how you use Bayes Theorem. Perhaps the evidence for Pilate uncovered in the 1960s could be weighted with prior skepticism about his existence.

One of my employees is a member of the Casualty Actuaries Society (like RichardMdBorn). Once she said in all seriousness that the Society of Actuaries (my clique) is a "terrorist organization." lol.

Anyway, what you are describing is credibility theory more than a true Bayesian analysis.

Bayes theorem is:

[_kairos]

Can someone calculate the probability that jesus lived(existed as human on earth) given the conditional probability ,certainty , pb=1 that God does exist

and then calculate the same with pb=0 god exists

and separately calculate the pb God exists given the conditional probability pc=.5 that intelligent design is necessary for the world/creation to have come into being.


probability of the above items being stupid ps=.75

just calculatin

k

[_Analytics]

- assemble the basket of all of the evidence we have

Analytics, what would you count as evidence? How would you weight it in the first instance?

I don't have any insights into this that are very specific or interesting--just that the evidence and weighting needs to be done in each competing scenario on its own terms.

[_Analytics]

Bayes theorem is:

Fleshing this out:

A is the proposition that Jesus exists, and B is the sum-total of the evidence. So:

P(A|B) is the probability that Jesus exists, given the evidence
P(B|A) is the probability of getting this entire basket of evidence, given that Jesus really existed
P(A) is the a priori probability that Jesus existed--the spitball
P(B) is the probability of getting this basket of evidence under all scenarios put together (e.g. P(B) = P(B|A) + P(B|~A))

So, to calculate the probability that Jesus exists, you need to calculate P(B|A) and P(B|Ã). AND, you need to come up with the a priori P(A). Putting that last piece into the equation is what people are uncomfortable with. However, mathematically it is necessary. Understanding these relationships and addressing them directly promotes clear thinking.

[_Analytics]

Philo,

Why don't you just show us? Take just one example of the critical method as I'll introduce below and then you apply Baye's probability to it.....

For illustrative purposes, I'll lay out a few points of evidence and apply Bayesian analysis. I'll keep it simplified--the point isn't to settle the matter, but rather to illustrate the thought process.

The Theories
There are two theories.

Theory A is the Historical Jesus theory. According to this theory, Jesus of Nazarath was a historical figure, and that as early as AD 30 when people called themselves Christians or said "Jesus the Christ," it was unambiguous to them that they were talking about the guy from Nazareth with the long hair and sandals that preached from AD 30 to AD 33, and was then crucified.

Theory ~A is the Jesus Myth theory. This is more-or-less Earl Doherty's beliefs about Jesus: when people before, say, AD 70 talked about "Jesus Christ" they were referring to a God that lived in the spirit realm, where he was crucified for mankind's sins. Folks self identified as Christians and believed in "Jesus Christ," but they didn't equate Jesus Christ with the guy with long hair and sandals from Nazareth--they were talking about the son of God--not a local kid. Around 70 a couple of compelling stories were written--the Gospel of Mark, and the Q Gospel. The Christians rightly found these stories moving, and coopted them into their beliefs about Jesus Christ, the Son of God so that by the year, say, AD 100, they identified Jesus of Nazareth with Jesus Christ.

The Evidence
b1: The Gospel of Mark. A written account of the life of Jesus of Nazareth that was written within, say, 50 years of Jesus’ alleged death.

b2: Jews in the 2nd to 6th centuries that were antagonistic to Christians yet didn’t deny the historical existence of Jesus (see mikwut’s post above).

b3: Conspiracy of Silence. We know that Peter and Paul existed and started Christianity, and we still have their writings. However, they talked about Jesus Christ resurrected, not Jesus of Nazareth, the celebrity that went around preaching, healing, feeding, and raising the dead. (see Earl Doherty for more details).

The weighting
We need to evaluate the likelihood of each piece of evidence being the reality under each scenario, and then combine them:
P(b1|A) = 0.99
P(b2|A) = 0.99
P(b3|A) = 0.01
P(B|A) = 0.99 * 0.99 * 0.01 = 0.0098

P(b1|~A) = 0.99
P(b2|~A) = 0.99
P(b3|~A) = 0.99
P(B|~A) = 0.99 * 0.99 * 0.99 = 0.9703

The a priori
Why seriously doubt Jesus existed? Most people think so. Let’s give it a 95% spitball probability Jesus existed:
P(A) = 0.95

Bayes’ Theorem (Math Is Fun!)
Chances we’d see this pile of evidence:
P(B) = P(A) * P(B|A) + P(~A) * P(B|~A) = 0.95 * 0.0098 + .05 * .9703 = 0.05783

So, what’s the probability Jesus existed?
P(A|B) = P(B|A) P(A) / P(B) = 0.0098 * 0.95 / 0.05783 = 16%

Discussion
According to this illustrative analysis, there is a 16% chance that when the earliest Christians referred to “Jesus Christ” they were talking about a guy from Nazareth with long hair and sandals and not about a God that they believed lived and died in the spiritual realm. This is despite the fact that the a priori that Jesus of Nazareth was historical was given very heavy weight (i.e. 95%).

The result was driven by the fact that all of the evidence was consistent with both theories, except one: the “conspiracy of silence.” If Jesus Christ really lived a life on earth, we’d expect the earliest Christian writings to talk about his life on earth. But they don’t. That seems very inconsistent with the historical Jesus theory—that’s why I give it a 1% probability that Peter and Paul wouldn’t think that the remarkable things that Jesus said did on earth were important enough to include in their epistles.

Of course more evidence could be thrown into these formulas, and historians could dispute the specific percentages I gave everything. The point here is to illustrate the thought process.

I wouldn’t expect professional historians to assign specific probabilities to various pieces of evidence the way that I did. However, their reasoning should follow this basic structure. I believe that’s Carrier’s basic point, which I agree with.

[_Mary]

But Analytics, again the inputs are arbitrary?

[_Analytics]

As a side-note, I think I heard an interview with Richard Carrier on NPR a year or two ago, but otherwise, never heard of him until this thread. He has a PhD in history from Colombia, so he needs to be taken seriously.

He has two books on Amazon relevant to this thread: Proving History: Bayes's Theorem and the Quest for the Historical Jesus, and On the Historicity of Jesus: Why We Might Have Reason for Doubt. Both look quite formidable.

I think I already get his point with regards to Bayesian analysis, so I'm going to skip that one for now, and instead jump right into On the Historicity of Jesus. It looks like his basic point is the same as Earl Doherty's The Jesus Puzzle, which has always been a compelling case for me. However, Carrier's credentials are better than Doherty's, and it also appears he examines everything in more detail. But still, he's telling me a message I already tend to accept. Would any believers in Jesus' historicity like to read the book too, so we could have some detailed discussions about it?

[_Analytics]

But Analytics, again the inputs are arbitrary?

The inputs hopefully aren't arbitrary--they ought to be based on rigorous historical analysis.

The one exception to that is the a priori input. That one is arbitrary, in the sense that it is set up before the evidence (or new evidence) is examined.