Theology, philosophy, math, science, and random other things

Bayesian evaluation for the likelihood of Christ's resurrection (Part 14)

We are calculating empirical values for the Bayes' factor of a sincere, personal human testimony. Several lines of calculations have all converged around 1e8 as a typical value. In the last post, I gave some real-life examples that I have personally lived through and verified - and they validate the 1e8 value. But perhaps you're not convinced by the stories from my past. Fair enough - they're event that I have directly experienced, so they're empirical for me, but they're not empirical for you.

Here, then, is a calculation that anyone on the internet can verify to get an empirical value for the Bayes' factor of a human testimony.

Go on LinkedIn, and search for "PhD physics Harvard". You'll find many people who claim to be in the PhD program at Harvard University. You may need to upgrade your LinkedIn account to see the profiles for these people, if they're outside your network. Now, are these people telling the truth? And what ought we make of their claim that they're getting the most advanced degree in the most challenging field from the most prestigious university in the world? And what is the Bayes' factor for that claim?

To address this, we first need to find the prior probability for someone on LinkedIn being in the Harvard physics PhD program. For this, we'll need to gather up some numbers - all of which are readily available online.

First, let's get the number of people in Harvard's physics PhD program. This is easy enough - their department's webpage tells you that they have about 200 graduate students.

It's also easy to find the number of people on LinkedIn. Their website will tell you that they have more than 128 million registered members in the United States.

Now, we'll make the generous assumption that all 200 people in Harvard's physics PhD program are on LinkedIn. This means that the prior probability for someone on LinkedIn actually being in the program is about 200/128 million, or about 1e-6.

What about the posterior probability? Well, we can take the people on LinkedIn who claim to be in the Harvard physics PhD program, and actually investigate them one by one. Many research groups have their rosters published online, so you can easily find out whether someone really is in a physics research group at Harvard. You may also find their scientific publications or teaching records online, all of which can confirm their status in the program.

So, I searched on LinkedIn for "PhD physics Harvard". I spot checked more than a dozen people from the search results who claimed to be in the Harvard physics PhD program. I chose my sample over many pages across the unfiltered LinkedIn search results, so that the "relevance" of the search results to me will not influence my sampling.

What was the result? I found that every single person I checked was telling the truth. I could verify each of their claim independently from the LinkedIn page, nearly always from an official Harvard physics department page. Since I had checked over a dozen people, this represents a posterior odds of 1e1 at a minimum for these people really being in the Harvard physics PhD program.

This means that, at a minimum, the mere claim of these individuals on LinkedIn changed the odds for that claim, from a prior value of 1e-6 to a posterior value of 1e1. Therefore, the Bayes' factor for these claims have about 1e7 as a lower bound. The actual value is therefore well within range of the 1e8 value that we've been using.

It's also important to note how weak a claim on LinkedIn is compared to the kind of earnest, personal testimony that we're interested in. Anyone can get a LinkedIn account; they just have to sign up for it. They can then say whatever they want in that account. Furthermore, there is not much concrete negative consequences for lying, while the incentive of getting a job or a business contact can be quite appealing. But even with all this going against it, the people on LinkedIn turn out to be quite trustworthy, with the Bayes' factor for their claims having a value near 1e8.

The Bayes' factor for the disciples testifying to Christ's resurrection must be at least that much. Therefore, Christ almost certainly rose from the dead.

More evaluation for the Bayes' factor of a typical human testimony are coming next week.

You may next want to read:
How to think about the future (Part 1)
On becoming a good person
Another post, from the table of contents

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