Another response by Lydia McGrew that misses the point entirely

In #religion

Here's a response video by Lydia McGrew that misses the point entirely: https://youtu.be/yazFM_qlsHI?si=LX_ClYr4naTtSGkf

Maybe I have not been clear, so I feel I really need to correct the way Lydia McGrew is framing things. In the video she consistently states that the skeptic is demanding that one has to avoid using a partition. Or that the skeptic demands that one has to slice the ~H model into the p(data|~H)=0 part and the other part. This is just flatly wrong. You want to use a partition? No problem! You don't want to use a partition? Also, no problem. Well, in both cases, as long as you always work with posteriors and not Bayes Factors. In this video she repeatedly claims that the skeptics are demanding a particular approach, which just isn't the case.

My original observation was that Lydia McGrew was the person demanding that one has to use a partition to do the inference properly. Here are a few relevant quotes:

https://youtu.be/cb0Cwk7upxk?si=LczKI5IJSD0NGqNf&t=384

Because each of those sub hypotheses has a low probability conditional on his innocence, that is to say, if he's innocent, you don't expect to find his fingerprints on the murder weapon at all. The majority of the space under \(\neg H\) is a place where you don't find this evidence at all.

This is something that Tim and I emphasized in our article on the resurrection. What's taking up the majority of the \(\neg R\) space? Well, nothing..[...] You just don't get the evidence at all.

And that's part of why the Bayes Factor is so strong.

McGrew later criticizes me for not including what I am calling the "nothing model" -- the model where, in her words, "you don't find this evidence at all" or \(P(\text{data}|N)\sim 0\):

https://youtu.be/cb0Cwk7upxk?si=FNgqGeyNFbhMGY54&t=467

I think it's very clear that Brian Blais is not using a full partition, because Brian Blais keeps saying Than needs to say more about these alternatives and so forth that explain this just as well.

And again in a different video... https://youtu.be/y7umQEVtbx4?si=LsUpWRiOOW5RyzSs&t=743

There are huge amounts of that \(\neg R\) space in which none of those things happen. [...] The most probable thing to happen if Jesus did not rise from the dead is nothing. The vast majority of the probability space given that Jesus did not rise bodily from the dead, we don't have any of this evidence. It has something akin to zero probability, it just doesn't happen.

I agree with McGrew that using the partition -- and specifically including the part of the probability space that doesn't predict the evidence -- is "the reason the Bayes Factor is so strong". It's just irrelevant to the posterior, and so is irrelevant to the inference.

My entire point was that if you include the "nothing" model or not (i.e. with or without the partition) the posterior was identical (see the original post https://bblais.github.io/posts/2026/May/14/how-to-inflate-your-bayes-factor-with-nothing/ and the followup https://bblais.github.io/posts/2026/Aug/01/more-inflating-of-bayes-factors/), so the skeptic not using the partition was perfectly fine. But it'd also be fine (although needless) to use the partition -- as long as you focus on the posterior. If you focus on the BF (as Lydia McGrew does) then including the "nothing" model increases that value needlessly (because a factor is automatically inserted into the prior to cancel the increase).

Put another way. Is there any problem with looking at:

$$ \text{posteror ratio}=\frac{P(H|\text{data})}{P(\neg H|\text{data})} $$

No. No problem at all. How about this?

$$ \text{Bayes factor}=\frac{P(\text{data}|H)}{P(\text{data}|\neg H)} $$

You betcha! It's totally easy to make the BF as high as you'd like without changing the posterior ratio. One way is to accomplish this is to use a full partition, specifically including models that don't predict the data, i.e. \(P(\text{data}|N)=0\), although perhaps there are other ways to accomplish it. Best to always use the posterior.

In the current video (https://youtu.be/yazFM_qlsHI?si=LX_ClYr4naTtSGkf) McGrew uses counter examples from an alleged demon activity and a murder scene. What she includes as alternatives, however, are models that actually predict the data to some degree (e.g. radio alarm clocks, and lifting fingerprints)! This is irrelevant to my point. Of course, in any inference, you want to include as many informative models as you can, apply Bayes theorem for all of these models, and calculate the posterior probability for each. No one is contesting this. I am also not critiquing (in this part) the backsolving for the prior that McGrew refers to from the Blackwell paper, so that is also irrelevant1

If you look again at my post, and especially the follow up, you'll see my point has been that including as part of the \(\neg H\)-space, models that don't predict the data (i.e. \(P(\text{data}|N)=0\)) will not affect the final posterior in any way -- but will inflate your BF needlessly. In my followup, I add to my "nothing" model some level of predicting the data, and you can easily see that the only part of \(N\) which appears in the posterior is that portion that predicts the data -- the part that doesn't predict the data cancels out of the posterior by the end automatically. Look at the math -- I didn't just arbitrarily choose a prior to cancel the increase -- it happens as a consequence of the properties of the nothing model and the way Bayes theorem actually works.

So I repeat my challenge: show me an example where models or parts of models that entail that we didn't see the evidence we observed actually affects the posterior. Since the posterior is all we care about, if such a model doesn't exist, then (as opposed to what Lydia McGrew claims) we shouldn't care at all about models that entail that we didn't see the evidence.

  1. just FYI, my critique of the Blackwell paper is in three parts, while the "backsolving" is not something I have a problem with. First, the \(BF\sim 10^{40}\) I think is ridiculous, and I see no attempt to confirm this. Second, given others, like Swinburne, calculate a Bayes Factor \(BF\sim 10^{3}\) from the same data then something is clearly going wrong somewhere. Finally, in that paper, when supporting \(R\) the McGrews talk about likelihoods, but whenever they talk about the alternatives they consistently refer to "plausibility" or priors for the alternative, thus they are using a double standard. Again, this critique of the Blackwell paper has nothing to do with the complaints about the partition and the "nothing" model. ↩