Bayes’ Theorem and Testimony


Where I actually am while writing this as a Boltzmann Brain

When I was younger there was a chain of thought I had regarding my testimony that hinged on Bayesian logic (although I didn’t know the term at the time). 

Bayesian statistics and logic is a field that incorporates prior probabilities into current probabilities. For example, I heard (I don’t know if this is true) that most positive HIV tests are false positives, even though the false positive rate is low, say 5%. This is because, while the false positive rate is low, the chance that somebody actually has undetected HIV is quite a bit lower. Therefore, while the chance of you getting a positive HIV test when you don’t have HIV is low, the chance of you getting a positive HIV test when you don’t have HIV conditional on you already having a positive HIV test is high.  

In terms of testimony. For me personally I haven’t had one huge Moroni’s promise experience, but rather a lot of accumulated ones and the occasional big one (usually when things are hitting the fan). Of course, motivated reasoning and feeling is a thing, so there is always the possibility that since I have been raised to believe that I would feel spiritual confirmations of the truth claims of the Church, then in some subconscious level I produced such confirmations. 

(Of course, if that were the case my testimonial route would have probably been the more expected route of finishing the Book of Mormon, closing it, praying in my knees, then feeling a lifted up burning in the bosom. I don’t begrudge others having had that experience, it just hasn’t happened to me.)

Where Bayes comes in is when I incorporate the prior of me being a member. 

If the Church is true, the chance that I happened to be born into the One True and Living Church is quite small given the billions of people on the earth. Even if I think that the chance that my spiritual experiences were subconsciously generated is quite small, the chance that I have generated subconscious support for the spiritual paradigm I was raised in could arguably be seen as having a higher probability than the idea that I was born into the One True and Living Church.

A couple things though:

  1. At some point we just have to run with what we feel. There is no math equation for why slavery is wrong. For the vast majority of human history slavery has been a-okay socioculturally. I happened to luck out and be born in a time period when it isn’t–but it’s still wrong and I’m going to trust my feelings on that. 
  2. There’s a limit to how powerful the subconscious is. People leave religions all the time. If we start going down the rabbit hole of thinking all of our conclusions are based on subconscious wiring and aren’t based in anything substantive, that extends to a lot more than just religious beliefs. 
  3. I’ve already demonstrably won a lot of lucky die rolls. Of the 100 billion or so humans who have ever lived I (and you, probably) won the roll of a 300-sided die when it comes to quality of life. If we start considering the chance that my particular chain of ancestors and their gametes came together to form me then the chance becomes infinitesimally small. Of course, there is a gigantic number of rolls, so I’m not sneaking an intelligent design argument in here, but for my particular conscious self I already won the lottery multiple times while being hit by lightning so that knowledge gets me used to the idea of winning the die roll of being born in the Church. 
  4. And then if we start thinking deeply about those really small probabilities, that leads us to rather bizarre places like the Boltzmann Brain and the simulation hypothesis. (Indeed, one of the issues with Bayesian logic is that if you fiddle with the priors you can get it to say anything including; for example, defending the reality of the Resurrection but also the idea that Jesus Christ never existed as a historical person). 

So I could be a Boltzmann Brain floating in a multiverse with false spiritual memories, or I could be in the matrix, or I could just have a lot of internally consistent spiritual experiences generated by subconscious triggers embedded in me during my childhood, but as with a lot of other beliefs it just makes sense to, in the absence of disconfirming empirical evidence, take at face value the sensory experiences I’ve had and live life accordingly.

14 comments for “Bayes’ Theorem and Testimony

  1. This is a pretty accurate description of my own experience too. “At some point we just have to run with what we feel” – I said something like that in a conversation last week.

  2. Great post. I left the church many years ago and some of these sorts of probabilistic ways of thinking were at play.

    It is dangerous to approach the gospel through the same probabilistic lens that we may apply to other decision-making endeavors in life. God operates in the space of seemingly low-probability events, and we may lose Him in the mindset.

    To me, the question is never, “What are the odds?” Rather, I ask myself as Alma encourages, “What do I desire to be true?” Then, I allow that desire to work in me to experiment upon the word. And through experimentation, the fruit of Alma 32 is undeniable.

  3. In response to your final paragraph: the process of coming to know God shatters all solipsistic constructs of reality. There will come a time (if we’re faithful) when we will know what the Sacred Other knows–and that will give as a sure knowledge of who and what we are relative to God and other intelligent beings.

  4. Here is a source for your example of false positive HIV tests –

    Measured false positive rates from the references is close to 4% of tests. False negative rates are significantly lower. And actual misclassified samples from a huge number of blood samples in this study were extremely low – like 1/250,000.

    Applying Bayesian logic to your testimony though would require updating your prior probabilities with the observed data. There are many datapoints that challenge whether LDS church ever was the “one true and living” church that you have to ignore or be ignorant of to stay in and believe that. Plus there are many forces pushing you not to change those assumptions about the truth claims of the church including your family situation and past and present relationship with the church and so I think it makes sense that when you say that you stay because in the end it feels like the right thing to do. That it is consistent with the childhood and adult spiritual experiences you may have had.

    The church isn’t “true” but it can be a good place. That is why you stay presumably. At some point you may change your mind and leave.

    I may have left the church but the stats classes at BYU were excellent. One thing I have learned from them and applied throughout my career is that Likelihood is a much better statistical and philosophical framework than Bayesian logic that is often misinterpreted and wrongly applied. I highly recommend A. W. F. Edward’s classic book on Likelihood of you haven’t read it. Or Owen’s updated Emperical Likelihood (2001). I find likelihood estimation and testing approaches to better reflect the information content and hypothesis testing of data than either frequentist or Bayesian approaches.

  5. It’s always curious to me when people make the “you stay because it’s easier” argument. That may be true for some people (and is one reason why I am *very* suspicious of Mormon bluebloods who are in the Church and comment on it but probably wouldn’t personally sacrifice much for it), but for most people in terms of stress and the like our hedonic quality of life would increase if we left. Now, not having stress is not the end-all of our existence, so that’s fine, but still, the Church asks a lot, and some awkwardness in family reunions is definitely worth not getting up on Sundays as well as all the other lifestyle parameters the Church requires of us.

    You can do that kind of armchair Freudianizing of others with any belief. You think that we should impose tariffs on Japanese cars, but is it really because of the reasons you state, or is it because of a deep-seated fear of Japanese people from your great-uncle WWII vet? Maybe? But still, that’s as empirically non-verifiable as Russell’s teacup if we’re going to adopt the all-beliefs-must-be-empirically-verified-to-be-believed framework.

  6. Stephen,

    your response is very difficult to parse. Generously, if try my best to make any sense of it, I guess you think I said that you stay because it is easy and you don’t like that I analyzed your comments to mean that. Maybe I misinterpreted your writing. It isn’t clear what your original thesis is and so I did the best I could.

    Well, in your post you said at some point you run with what feels right and that it isn’t based on a Bayesian update on prior assumptions from your childhood upbringing. The rest of the post was kind of mumbo jumbo after that about being in the matrix or some other intellectual babble that was not clear to me what you meant.

    I will not try to psychoanalyze what you mean by Mormon blue bloods or why you think not being in the church is hedonic or what tariffs on Japanese cars or Russell mean to you. Or that Sunday attendance is such a hard sacrifice. It is not clear to me what point you are making. Just questions from me that I won’t ask.

    I was just trying to be generous and acknowledge your whole Bayesian framework argument means that the church works for you whether or not your feelings and experiences are a false positive. That seemed to be the thesis and point you were making.

    I wasn’t trying to make any argument about staying being easy. It was hard to leave. It took me 40 years to finally step away. The culture and teachings of the church actively try to discourage you or me or anyone from making that choice. Life is hard either way. Stress abounds. I am not sure there are any hedonic pleasures besides a good cup of coffee that I have fallen for since leaving. You are right about having extra time on Sunday as an added pleasure as well. The rest of the world that never was Mormon is also just trying to do the best they can.

    If I misinterpreted you, my apologies. Not sure what you are really trying to say. The intellectual examples are not clear.

  7. “Your whole Bayesian framework argument means that the church works for you whether or not your feelings and experiences are a false positive.” That might be the misunderstanding. Nothing in the OP implied that; this is not remotely a “well, it works for me even if it’s not true” argument. I’m making a hard truth claim. And the updating the prior in light of new historical knowledge is a take on Bayesianism and the gospel that I didn’t even address in the OP.

    Ergo I read your “Plus there are many forces pushing you not to change those assumptions about the truth claims of the church including your family situation and past and present relationship with the church and so I think it makes sense that when you say that you stay because in the end it feels like the right thing to do. That it is consistent with the childhood and adult spiritual experiences you may have had” as armchair fruedianising because it seemed like you were projecting that on me when I didn’t say that.

  8. Your hard truth claim is very unclear. I reread the original post to see where it is and I still can’t see it. Maybe I was projecting in trying to understand how the Bayesian theorem and methods apply to your post.

    You really should read Edwards or Owen’s books on Likelihood. Lots of good explanations on the math and applications of likelihood and Bayesian approaches to estimation and hypothesis testing. Won’t help with your hard truth claims but very helpful for parameter estimation and hypothesis testing on actual data.

  9. You might be interested in this: “The Compelling Bayesian Case for Christ” at

  10. With regards to point 1:

    Thumbs up for going with your feelings on slavery. It’s not surprising that you and I, as denizens of the 21st century, feel that slavery is wrong. As appalling as it seems, we would likely feel differently if we were we born to plantation owners a few centuries ago. And if we were “normal-minded” people in 1947, we would find interracial marriage repugnant according the 1st Presidency at the time. Personally, in my younger years I felt that homosexual relationships were wrong, which I don’t anymore.

    The lesson we hopefully learn from all this is that, given the fickle nature of feelings regarding subjective claims, we probably shouldn’t be relying on feelings when it comes to objective claims, e.g. the BoM is true.

    With regards to point 3:

    It’s certainly true that you, and maybe everyone reading your post, are in a very high percentile for quality of life. Hopefully that reminder motivates us to share the wealth. But if it gets us “used to the idea of winning the die roll”, then that smells like the gambler’s fallacy. And the fact that your ancestry produced *you* is true for all 8 billion *you*s in the world. If we see that as significant, then that’s the Texas sharpshooter fallacy.

  11. The gambler’s fallacy is believing that one is “due” for a lucky hit after an unlucky streak (or vice-versa), so it’s actually the opposite of the point in the OP, which is that winning big on points A to C viscerally habituates you to the possibility that you won big on point D. Of course logically point C might be orthogonal to point D, but it’s a personal reminder that a low chance is not a no chance.

    And as far as slavery; yes, I think that slavery being wrong is an objective, not subjective, truth. It’s “written in the sky” as Richard Rorty would phrase it. Now, if you’re a naturalist that doesn’t believe that moral statements have the same validity as scientific claims, well, that’s a much bigger issue. I’m not saying that my testimony of slavery being wrong is the same feeling as the testimony of the Book of Mormon, just that the former grants credence to the general principle that metaphysical/ethical objective truths can be discovered outside of a lab. And yes, sometimes the metaphysical touches on the physical, like the gold plates, but as long as there isn’t empirical disconfirmation that’s fine.

  12. I think the fact that we claim to be dealing with real agents — and not merely physical causes and effects — plays a significant role in how we think about knowing with respect to testimony building. It’s one thing to know that I love my wife. It’s a bit different, albeit related, to know that she loves me. One could argue that knowing the latter is a result of reading her actions towards me on an instinctual level–and I think there’s some truth in that. However, my wife and I have come to know each other so well over the past 35+ years that our understanding of each other cannot be reduced to simple cause and effect. Over time our hearts have become knit together–and we identify with each other in ways that are akin to self-knowledge.

    So it is with God. Our personal witness of his reality hinges on more than how he interacts with his children–though, of course, that interaction can be quite miraculous and edifying. Even so, the knowledge that will anchor us most securely is actually knowing the sacred other; knowing God as an individual intelligent agent. And God knowing the importance of that knowledge will condescend and make himself known to every individual as fast as he or she is able to receive it.

    And so, when we’re talking about testimony — gnosis if you will — we have to add the factor of coming to know a Living God to the equation. Otherwise we’re not likely to get beyond haggling over the capabilities and limitations of our biological matrix.

  13. Stephen C, you’re right, that was a senior moment on my part. What I remembered as the gambler’s fallacy is actually the opposite. I guess it’s really the hot hand fallacy — we feel more optimistic about rolling winners after we’ve already rolled some.

    And, BTW, I’m not opposed to going with one’s feelings, even when the weight of evidence is against them. Sometimes that’s the pragmatically right thing to do.

  14. It’s always delightful looking at clashes between Bayesians, frequentists, likelihood estimators, and reflecting on the fact that the whole debate is hopelessly meta. How does one pick between the different schemas of determining what probability itself is? Surely one cannot say that one or the other is more likely without being self-referential? It’s the same feeling as when one gazes into the Münchhausen/Agrippa trilemma for too long. It’s intuition all the way down.

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