Wednesday, March 23, 2016

Exploring the Christian Way - Prolegmonea - Bayesian Statistics as Foundational to Theology

Finally, I feel that I am prepared to write a full blown prolegomena where I explain my method for developing theology. Reading Stanley Hauerwas' The Work of Theology and Lewis Ayres Nicea and It's Legacy has helped me sharpen my thinking. It's not that I have adopted their methods so much as they have stimulated my thinking in fruitful ways, while I won't discuss them explicitly, I think their contribution is worth mentioning.

How do we know anything? The leap forward that was the Wesleyan Quadrilateral was that realized that we needed more than Scripture and Tradition to discern theological truth. Reason and experience were viewed as additional authorities and we needed a "formal method" to adjudicate between these sometimes conflicting authorities. I think it was a nice try, but we can do better. As an aside, many would argue that Scripture alone is our highest authority, but in practice I don't think anybody actually always let's Scripture overrule the other three (who thinks slavery is ok?). Other authorities overrule Scripture at least some of the time. Let's turn to my formulation next by discussing how we gain knowledge in the general case, and then moving on to theological knowledge.

I would argue that we have three basic sources of knowledge: expert testimony, experience, and mathematics or logic. These sources work independently of one another to our own peril. The mathematical component is most often ignored formally, even though people subconsciously function in a probabilistic fashion (e.g., this is more likely than that)  Ideally, all three sources should formally work in concert, and I believe, with a growing number of statisticians, that Bayesian Statistics can draw on all three sources of knowledge to build the best approximation or estimate of the truth that also provides the best gauge of the level of uncertainty involved in the estimation process.

Let me briefly, and as simply as I can, explain Bayesian Statistics and what makes it so powerful, then I will apply the essence of the approach to theological knowledge. It will be easiest to explain by contrasting it with classical or frequentist statistics. Classically, if you wanted to know, say, how many people supported a particular presidential candidate, you would collect data by asking people. If 45% said they would vote for candidate X, then that would be your estimate for the percentage of all likely voters who would vote for candidate X in the election. Then based on how many people you asked, you would come up with an estimate for your error (e.g., +/- 4%). How accurate is your estimate? How likely is that to be correct? You have no way of knowing. You may have gotten a very good sample and you could be very accurate. You may have gotten a lousy sample and may be way off. What you can do is repeat the study repeatedly and see how you do. The theory is that 95% of the time your result will be within your margin of error (assuming it's a 95% confidence interval).

Bayesian statistics comes at this very differently. Before you field your study you elicit priors. What this means is that you ask experts what percentage they think will support candidate X and what the possible range of likely values is (or use previously published data). So an expert might say, 'I think 50% will support candidate X and I think it's almost certainly between 40% and 65%.'  You pool your expert opinions to form a prior distribution that encapsulates their beliefs about the truth as well as the uncertainty involved.

Now you collect your data just like you would have before but you combine the expert opinion with your data to get your final estimate. Generally, if you have a good expert, this method will result in more accurate estimates because it will pull your bad or even just mediocre samples away from bad results towards the truth. Your prior information will have very little effect on your estimates when the data are in agreement with them. However, the agreement you have will result in more confidence in your results. Additionally you can now say that with, say 95% probability my result is between two values (a much stronger statement than that about margins of error) and typically that interval will be shorter than if you only used your data using classical methods. However, we need to be careful to make sure that we cover the full range of possible outcomes with our prior. Otherwise your inference can be pulled unhelpfully away from the truth.

Hopefully this discussion was not confusing and you can start to see how one might apply it to the work of theology. We have data that we collect and we have priors. I would argue that we should see our experiences of God as data. We may have these experiences through the Bible, in prayer, service of others, conversation, etc. God speaks to us in many ways. We experience God speaking to us and we come to know him and understand his priorities as he speaks. However, if we're wise then knowing God isn't a solo effort. We seek expert opinion to protect us from improper inference and give us assurance when we're on the right path. This is where we need to elicit priors.

Our priors are expert witnesses from the past and present. The foremost expert witness are the witnesses to God's revelation in the past. This includes Scripture and the great theologians of the church. They heard God speak to them and they wrote as they understood. As a text has been influential over time it should be accorded a heavier weight. Additionally, we need to include secular disciplines when constructing our prior. This would include, but not be limited to, the biological sciences, physics, philosophy, sociology, and history.

Now it may seem odd that I include Scripture as a prior when I include our experience of God through the Bible as data. I need to make a very important clarification here. I do not believe that God speaks directly through Scripture, i.e., it is not God's Word or possessing divine ontology. However, when we read Scripture, it can come to life and become God's word through the agency of the Spirit. When I refer to Scripture as a prior I am referring to the historical voice of the apostle, prophets, poets, and others who wrote and edited the texts we find in the Bible. Thus historical study of Scripture is critical, but not necessarily to hear God speak. It's to calibrate what we believe we hear God saying when we encounter him. Though, certainly we can here God speak as we study historically. However, what we experience through the study and the actual historical reconstructions are not the same thing. The same applies to reading the works of the great minds of the history of the church.

How do we combine all of this to form our prior? We weight our expert voices according to their degree of expertise on the subject. We also need to make sure to cull from a wide variety of experts. In theology, it means we need to hear from a variety of voices in terms of era, geography or race, denominational affiliation, and when possible, gender.

What, then, is proper theology? It's proper data analysis. The less data you have the less confident you can be in your data analysis. We need to recognize that speculative theology, like the doctrine of the Trinity is just that, speculative, and realize that we have a lot of uncertainty surrounding our doctrinal formulations because we do not have access into the divine interrelationships. Where we have more data, for example, the fruitfulness of women ministers, we can have more certainty.

Hopefully this is informative about the way I will be pursuing my theological project, Exploring the Christian Way of Life, and is provocative. One thing lacking from a lot of theological discussion is a sense of uncertainty in the results. Hopefully I can model proper humility in the process. If nothing else, we will be following a formal framework that models the way people behave implicitly anyways.

Monday, March 21, 2016

Orphan Black: I Don't Think Shay Killed Delphine

The big mystery at the end of season 3 of Orphan Black is the identity of the murderer of Delphine. They are off screen so it must be someone we have seen before. I've heard it suggested that Shay is the killer. Granted her military roots, I don't see it. I suspect it's a clone. Note only that, it's one we've seen before.

Image of Krystal taken from:
http://tiny.cc/8wk39x
Yeah, that's right. I think Krystal could be the killer. The rest of the post will establish that there's far more than meets the eye with Krystal and that she is not trustworthy. From there I will suggest why she fits as a potential killer of Delphine.

When we first actually meet Krystal, Delphine and Dr. Nealon converse about just how naive she is. Dr. Nealon declares her, 'not one to pierce the veil...' But when we meet her with Felix, she clearly has pierced the veil significantly. She's noticed a pattern in her life that is abnormal and she's written about it in a notebook with the Castor symbol on the cover. Of course Felix doesn't recognize it, but we the audience do. In fact, she doesn't begin to spill the beans about her trauma with Castor until Felix asks his suspicious question to try to steal her identity. She's not dumb and is more than capable. And Dr. Nealon certainly knows that if he's been overseeing her monitoring. Felix grasps it a bit, but doesn't realize that she may have caught on to him, Most importantly, Dr. Nealon already convinced Delphine that she's naive so he can execute his and Rachel's plan.

After Felix leaves, Dr. Nealon shows up at her nail salon. Clearly she's never met him, but he has a task for her. Now what did he say to get her to go along with his plan? Presumably he could have offered her answers to all of those questions she seemed to have from her journal (which Felix never really read by the way, it's more than possible that she's not naive at all) as well as a way to get back at those trying to steal her identity. That's plausible motivation. However, I think more has to be at play here. There's no way a Leda clone could just end up with a Castor emblem on her notebook accidentally (and it clearly predates her known encounter with Rudy and Seth). She must have some sort of ties to Castor or perhaps directly or indirectly into Neolution (we know Neolution is still guiding Castor and Leda from a distance). Either of those possibilities would provide stronger reasons for her cooperation with Dr. Nealon.

As an aside, I want to ask about the first time we see Krystal, to her earlier encounter with Castor. Why was her monitor killed? Was it perhaps a ploy to get rid of a monitor that she was having some sort of issues with? Was it helpful for Dr. Nealon and Rachel? Who knows, but it's pretty convenient. Why would Castor try to kidnap her? They needed a fertile clone, which she presumably isn't. And how likely is it that they would actually get stopped? It's too hard to believe. Add to that, when Seth rescues Rudy it almost seems like Rudy knows when to expect him. And Dr. Nealon is the one who finds out that they escaped. Again, how convenient. Did Marion set the whole thing up?

We next see Krystal lying on a hospital bed under sedation in Dyad. When she wakes she acts hysterical (in character) and she wants Delphine to think that Dr. Nealon abducted her and drugged her to take Rachel's place. It's all misdirection and Delphine has no idea. Rachel was long gone and Krystal was in on it. The question, is, when Dr. Nealon shows her Rachel on the screen, does Delphine understand that Krystal was in on the ruse? I think it's more likely than not, Delphine is quite sharp.

I tried to get a sense for who Delphine's shooter was by watching the brief glimpse we get repeatedly. I think it's too hard to tell. The shoes are very loud for men's shoes, but I don't know how much we want to press the details, and some men's shoes can be pretty loud. Obviously it's someone tied to Neolution. The only person we know has ties to anyone in Neolution is Krystal. Yes, she may seem too weak to be a killer, but Helena, Beth, Sarah, and Alison all had it in them (granted Alison's and Sarah's ties to death were not cold blooded). Cosima certainly is fierce and Rachel certainly has no issue with violence even if she would never pull the trigger herself. Why do we dismiss Krystal?

To go back to Shay. It's certainly possible she could be the killer. We know she can handle a gun and Delphine's last words, 'what will happen to her?' mesh nicely with that hypothesis. However, it does not rule out anyone else. Delphine's time of having to love all of the sisters was over since she was no longer in charge of Dyad. She could go back to just loving Cosima. That is the most natural thing for Delphine to ask for her last question. I also want to note that there is no surprise on Delphine's face as she's about to be shot, just disdain. Given that she has just given Shay a vote of confidence, I would expect more surprise from Delphine. Disdain is a very natural response if the killer is Krystal.

I realize this is a speculative argument, but any argument at this point is speculative. But given the evidence we have, I think there's a stronger case to be made for Krystal than for Shay or any other person, for that matter. Her ties to Neolution must run deep. Otherwise it's hard to imagine Dr. Nealon and Rachel betting so much if they didn't know her cooperation was in the bag. I can't wait til next season to find out for sure.