Zelophehad’s Daughters

Why Faith Transitions Need to Be Less Frequentist and More Bayesian

Posted by Mike C

I know. You are probably despairing to think that such a disputed area of statistical dogma could have anything to contribute to such a disputed area of religious experience. (If you are despairing about this post for other reasons, I apologize). I mean, not even Martin Luther would have had the nerve to nail 95 non-informative priors on R.A. Fisher’s door.

But English statistician Thomas Bayes was also a Presbyterian minister, so it is only natural that his statistical insight would have religious implications as well. And his insight is, in my view, the key to healthier faith transitions.

To understand why, you first need to understand the difference between frequentist statistics and Bayesian statistics. Now don’t pee (value) your pants. It’s not that hard. Just bear with me.

If you’ve ever had a statistics class or a class that had some statistics in it, then you’ve learned frequentist statistics. To boil it down, in this approach you assume a hypothesis (e.g., the world is flat), you collect some data (e.g., Magellan sails in one direction and ends up where he started), and then you decide whether or not the data are sufficient to reject your hypothesis (e.g., you reject the hypothesis because Magellan’s voyage makes it highly unlikely that the world is flat). In other words, you are asking: what is the probability of the data given the hypothesis? This is sometimes abbreviated as P(D|H).

A subtle yet important limitation of this approach is that it does not tell you the probability that the world is round, only that the data are incompatible with the world being flat. For example, Magellan could have carried out a similar voyage on an ellipsoid. Frequentist statistics is good at rejecting hypotheses, but not good at telling you which of several alternative hypotheses is the most probable.

Bayesian statistics, on the other hand, is well-suited to distinguishing between competing hypotheses. Bayesian statistics has a long history, but because of philosophical concerns, enemies in high places, and computational difficulties (see a fascinating history here), it has only come into its own in the last several decades. The Bayesian approach can be summarized as follows: you start with a hypothesis or prior belief (e.g., I believe the earth is flat because it looks flat), you collect new data (e.g., you observe that the sun is lower in the sky as you move away from the tropics and the earth throws a circular shadow on the moon during a lunar eclipse), and then you update your belief (e.g., I believe it is less probable that the earth is flat and more probable that the earth is round). In other words, you are asking: what is the probability of each hypothesis given the data? This is sometimes abbreviated as P(H|D).

Bayesian statistics starts with your prior beliefs, collects more data, and then updates your beliefs into what are called posterior beliefs. Bayesian statistics is more intuitive than frequentist statistics because it gets at what you really want to know: how likely is it that my hypothesis is true? How likely is it that the world is flat? How likely is it that the world is round? In contrast to a frequentist approach, Bayes also has a formal mechanism for combining past beliefs and current data to update your beliefs, hopefully making them better, more accurate.

OK, stand up and stretch. Splash some cold water on your face. Stay with me.

Why, then, is a Bayesian approach better than a frequentist approach for dealing with faith transitions?

What I often see happen is that people grow up with a fixed hypothesis, a fixed assumption about the truth of the Church. If you are at all like me, this hypothesis can be quite rigid. In all fairness, we come by it honestly. As President Hinckley once stated, “Either Joseph Smith was a prophet, or this work is the greatest fraud ever perpetrated on the human race.”

Typically, we never consider competing hypotheses for how the gospel works. We accept the straightforward, black-and-white, all-true-or-none-true hypothesis and go about our lives. As we do so, we accumulate data that may or may not contradict our hypothesis. Sometimes we ignore or disregard data because we do not wish to challenge our hypothesis. And why would we, if our hypothesis works in our lives? The problem occurs, though, when the hypothesis is not working so well for us–for example, when a wife has an overbearing husband who uses the temple language or Proclamation on the Family to assert control, or when a teenager comes to discover that he is gay, or when we discover that Joseph Smith had teenaged wives and sometimes hid this information from Emma. People in these situations begin to more fully consider the data in their lives.

And then it happens: our newly collected or newly considered data seem incompatible with our fixed hypothesis. The p-value goes below the conventional 0.05 (i.e., the probability of observing such data assuming our hypothesis is true becomes less than 0.05, or 1 in 20). Sometimes our data may drive our gospel p-value even lower, making it highly unlikely that our original hypothesis is true. Cue the faith crisis.

At this point, we may completely reject our prior beliefs because the frequentist approach has no way to incorporate them when we receive new data. We can easily conclude that the opposite of our original hypothesis is true–Joseph was not a prophet, the Church was not inspired by God, etc. In fact, we may conclude that God does not exist because the god of our original hypothesis cannot exist. Our past spiritual experiences couldn’t have been real or meant what we thought they meant because we’ve been forced to reject the framework through which we received them. Reaching these conclusions would be a mistake, however, because the frequentist approach only suggests that we reject our hypothesis, rather than pointing us to the most probable alternative hypothesis.

Enter the Bayesian approach to the rescue. In this approach to a faith crisis, you start out with prior beliefs to which you assign a probability (subconsciously, in most cases). Depending on one’s experiences, this probability could be very high (e.g., because of strong spiritual witnesses) or relatively low (e.g., because of concerns caused by being a woman in the Church). Then you collect and consider more data, continually updating your beliefs. The value to this approach is that you don’t feel compelled to reject everything you once believed and you are able to incorporate new data to create better posterior beliefs. It is more incremental and therefore less shocking to the system.

With a Bayesian approach you can, if you decide to, migrate to a belief in the gospel that is more nuanced–for instance, that allows Joseph to be a prophet who also did evil things, that allows Brigham to be a prophet who also was blind to some of the pain the gospel caused black people and polygamous wives, that allows the Book of Mormon to have value whether or not it was historical, that allows the Church to have unique truth and goodness in spite of its flaws. In short, a Bayesian approach makes it easy to explore alternative hypotheses about the gospel, including hypotheses that maintain some overlap with your initial hypothesis.

So if you know someone who is at the start of a faith crisis, send them a copy of Bayes theorem and remind them of this quote by LaPlace, an early champion of the Bayes approach:

The most important questions of life are, for the most part, really only problems of probability.

12 Responses to “Why Faith Transitions Need to Be Less Frequentist and More Bayesian”

  1. 1.

    I’m not a statistician, but I like this. I’ve thought of writing something similar, but in terms of acid-base buffer solutions (grin).

    “Either Joseph Smith was a prophet, or this work is the greatest fraud ever perpetrated on the human race.”
    I agree that Hinckley presented this as a binary, and people read it that way. But I’d suggest that Hinckley’s understanding of “prophet” differs strongly from the lay, casual understanding, that verges on omniscience, de facto infallibility, and perfection. So I would agree with his formulation, provided that we follow it up with a well-informed discussion of just what it does and doesn’t mean to call someone a “prophet.”

  2. 2.

    Wow, Mike! I *love* this framing of the issue. Great post!

  3. 3.

    You are speaking directly to the heart of someone who feels compelled to reject the Emotive-Spiritual-Factual Complex.

    Hang on. You are speaking directly to the heart of someone who is gradually revising his views on the Emotive-Spiritual-Factual Complex into a form more consistent with data.

    (I didn’t know spiritual fruit could sound so technical and taste so sweet!)

  4. 4.

    I like this better than the innoculation metaphor. With that one, you are sick, or you aren’t. You can hang onto the truth or you can’t. And this suggests that maybe I did something right as I revised my views of the gospel over 25 years rather than having it all hit me when I was 35. Thank you Utah schools for requiring me to get permission from my parents to learn about Evolution! My life hasn’t been the same.

  5. 5.

    I am so grateful my faith transition took the Bayesian approach naturally.

    Great post.

  6. 6.

    I like this. Out of curiosity, (and remember I got a C in college stats), how do you assign initial probabilities in everyday Bayesian analysis?

  7. 7.

    I’m with Kristine (which is a great place to be).

    Please allow me to reiterate that I love ZD so, so much. Thanks for this Mike :)

  8. 8.

    This is by far the best post on ZD, Mike, and I say that with all due respect to other ZD posts which have been superb.

    Statistics is outside my comfort zone, but we have something like this in the philosophical and theological world, called Process philosophy or Neoclassical Metaphysics (which has its roots in Hartshorne and Whitehead, and before them the American Pragmatists, particularly C. S. Peirce). It’s an evolutionary approach to the big questions that rejects the absolutist claims of positivism (which, even in its mainstream forms, tends to be rigidly dualistic and certain about certainty), but also rejects the obscurantist narratives that seem to explain everything (such as, we’re all batteries linked up to a central computing unit, and all sensible reality is a virtual program designed by machines), but which are entirely untestable (i.e. no new data can ever make a difference, because it all gets absorbed by the master narrative). As its name designates, its a philosophical approach that relies on process, evolution, and progression, not an immutable or absolute either/or stance to the world (even in moral terms).

    Of course, even the scientific method as classically postulated by Bacon in his Novum Organum is centered on probability and nuanced alteration to existing beliefs (a priori belief in G-d, for example) through data collection and testing. It was the nineteenth and most of the twentieth century that saw us go down the dark path of dualistic scientism.

    This also gets to the full implications of believing in a philosophically materialist G-d. C. S. Peirce: “Faith requires us to be materialists without flinching” (“A Guess at the Riddle” 9.2). Hooray for Bayesian statistics! You’ve opened up a new area of obsessive research for me, Mike. Thank you.

  9. 9.

    Oh, I do have to say one more thing, as a word of caution. I’m not at all saying that you’re doing this, Mike, but I’ve seen other people who are certain about their own moral positions invoke this kind of system as a way of opening up space for their own beliefs against the ensconced traditional one. They do this without reflecting on the very real possibility that their own position is also entirely open to doubt, even on a moral level.

    In other words, it’s true that Joseph Smith can still be a prophet and do evil things, but it’s also true that what we consider to be evil in the early twenty-first century could also be mostly a matter of cultural conditioning and programming. The strength of the Bayesian system, as you’ve pointed out, Mike, is that it allows for that oft neglected avenue to truth, intuition. But the problem with intuition is that it is as programmable as anything else.

    Again, I’m not saying you’re guilty of this, but this word of caution needs to be considered too.

  10. 10.

    In the terms of formal logic and analytics, what the Bayesian system (and Process philosophy) adds to the equation is what Peirce called “abduction,” a logically valid and intuitive approach to knowledge that is no more but no less important than the classical methods of induction and deduction. All three are needed to process reality with adroitness, accuracy, and sensibility.

  11. 11.

    Thanks everyone for the thoughtful comments.

    Ben S, as a non-chemist I can’t even imagine what the framing would be for an acid-base buffer solution, but it sounds intriguing.

    Casey, I will confess that I don’t know a lot about Bayesian statistics. During the past couple of months I took a lunchtime class at work, so I know just enough to be dangerous. (I also read the book on the history of Bayes.) Anyway, my understanding is that you have various options. If you have a lot of pre-existing data on the topic you can choose an “informative” prior, which represents a relatively narrow range of possibilities for prior belief. This might be useful if, for example, you want to look at the impact of breast cancer screening and you have lots of prior studies to draw from and to which you want to add your latest results. On the other hand, if you don’t have much prior information you can choose a non-informative prior, where you basically let your prior belief have a very wide range of possibilities, each with equal probability of being true. You can also choose something in-between–for example, that constrains the possible benefit or harm of breast cancer screening to be between a five-fold benefit or five-fold harm, with a higher probability being placed on the impact being closer to zero. In any case, you can do sensitivity analyses to see how much your choice of priors influences your posterior belief.

    SeraphimChaser, thanks for your comments. Since philosophy falls outside of my comfort zone I don’t have much to add, though I think it is interesting that there are philosophical approaches that seem to parallel these approaches of frequentist and Bayesian statistics. Perhaps that is why there has been so much controversy about these approaches over the years–the differences are more fundamental and philosophical than they are statistical.

    Regarding your word of caution, I can understand how easy it is to be blind to our possibility of being wrong as we move from one moral position to another. We can see what is wrong with our first position, but we may not notice what might be wrong with our new position. However, I would say that a Bayesian approach to this issue would help protect against that, because this approach formally recognizes the need to use new data to continually update our position. In other words, such possibility for adjustment is baked into the approach, and that is a good thing, in my view.

  12. 12.

    […] “how to stay LDS” but then I realized that a lot of much wiser, more experienced, much more helpful people have already done that. Wish I’d found them […]

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