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.
- 27 March 2014