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Classical statisticians as Unitarians

[cat picture]

Christian Robert, Judith Rousseau, and I wrote:

Several of the examples in [the book under review] represent solutions to problems that seem to us to be artificial or conventional tasks with no clear analogy to applied work.

“They are artificial and are expressed in terms of a survey of 100 individuals expressing support (Yes/No) for the president, before and after a presidential address (. . . ) The question of interest is whether there has been a change in support between the surveys (…). We want to assess the evidence for the hypothesis of equality H1 against the alternative hypothesis H2 of a change.”

Based on our experience in public opinion research, this is not a real question. Support for any political position is always changing. The real question is how much the support has changed, or perhaps how this change is distributed across the population.

A defender of Aitkin (and of classical hypothesis testing) might respond at this point that, yes, everybody knows that changes are never exactly zero and that we should take a more “grown-up” view of the null hypothesis, not that the change is zero but that it is nearly zero. Unfortunately, the metaphorical interpretation of hypothesis tests has problems similar to the theological doctrines of the Unitarian church. [emphasis added] Once you have abandoned literal belief in the Bible, the question soon arises: why follow it at all? Similarly, once one recognizes the inappropriateness of the point null hypothesis, we think it makes more sense not to try to rehabilitate it or treat it as treasured metaphor but rather to attack our statistical problems directly, in this case by performing inference on the change in opinion in the population. . . .

All this is application-specific. Suppose public opinion was observed to really be flat, punctuated by occasional changes, as in the left graph in Figure 3. In that case, Aitkin’s question of “whether there has been a change” would be well-defined and appropriate, in that we could interpret the null hypothesis of no change as some minimal level of baseline variation.

Real public opinion, however, does not look like baseline noise plus jumps, but rather shows continuous movement on many time scales at once, as can be seen from the right graph in Figure 3, which shows actual presidential approval data. In this example, we do not see Aitkin’s question as at all reasonable. Any attempt to work with a null hypothesis of opinion stability will be inherently arbitrary. It would make much more sense to model opinion as a continuously-varying process.

The statistical problem here is not merely that the null hypothesis of zero change is nonsensical; it is that the null is in no sense a reasonable approximation to any interesting model. The sociological problem is that, from Savage (1954) onward, many Bayesians have felt the need to mimic the classical null-hypothesis testing framework, even where it makes no sense.

This quote came up in blog comments a few years ago; I love it so much I wanted to share it again.

P.S. I also like this one, from that same review:

In a nearly century-long tradition in statistics, any probability model is sharply divided into “likelihood” (which is considered to be objective and, in textbook presentations, is often simply given as part of the mathematical specification of the problem) and “prior” (a dangerously subjective entity to which the statistical researcher is encouraged to pour all of his or her pent-up skepticism). This may be a tradition but it has no logical basis. If writers such as Aitkin wish to consider their likelihoods as objective and consider their priors as subjective, that is their privilege. But we would prefer them to restrain themselves when characterizing the models of others. It would be polite to either tentatively accept the objectivity of others’ models or, contrariwise, to gallantly affirm the subjectivity of one’s own choices.

62 Comments

  1. Elin says:

    This is actually a good companion piece to the sociology one. Why find it necessary to use some inaccurate just weird metaphor? Only one portion of Christians believe in the “literal” Bible. Unitarians reject the Trinitarian doctrine, but that has nothing to do with literalism. Further, Unitarians have an internally consistent set of understandings that someone might not like or think are funny, but they are very real. Unfortunately as usual we find that people practicing outside their area of study, just like physicists talking about magnetism and voting and sociologists talking about genetics, it ends up making the argument less coherent and weaker rather than interesting or stronger.

    • Andrew says:

      Elin:

      Fair enough. I don’t really see the purpose of my analogy as making our argument stronger; it’s more of an (imperfect) way to connect to other topics that we think about. This is my general view of analogies: they’re not part of the chain of reasoning but rather a hook to connect to other ways of thinking.

      It is true, though, that in our culture it’s considered kind of ok to make fun of Unitarians in the way that we’re not supposed to make fun of Jews, Muslims, Mormons, Southern Baptists of any ethnicity, etc. And that is a little bit wrong.

    • In some sense, my guess is that the two of you are actually talking about separate groups of people. See below: http://andrewgelman.com/2017/07/13/classical-statisticians-unitarians/#comment-524419

      Believers in the doctrine of “Unitarianism” as established in the 1500’s to 1700’s are one fairly serious group of Christians https://en.wikipedia.org/wiki/Unitarianism , whereas “Unitarian Universalists” which is almost surely the group that Andrew is considering because it’s by far the most common thing that “Unitarians” means in the US are a group of what you might call “seekers” or “personalistic” religious people. From the wiki https://en.wikipedia.org/wiki/Unitarian_Universalism

      “Unitarian Universalism[2][3][4] is a liberal religion characterized by a “free and responsible search for truth and meaning”.[5][6] The Unitarian Universalist (UU) Church does not have a creed. Instead, UUs are unified by their shared search for spiritual growth”

      In this sense they seem similar in spirit to people who’ve rediscovered the concept of “seeking enlightenment” that led the Buddha to his Bodhi tree (though, perhaps through different methods than the Buddha’s). Buddhism would categorize people such as this as “seekers of enlightenment” or loosely Bodhisattva. https://en.wikipedia.org/wiki/Bodhisattva

      The thing is, the analogy really doesn’t work well at all. Because Andrew asks: “Once you have abandoned literal belief in the Bible, the question soon arises: why follow it at all?” but it seems clear enough that the Unitarian Universalists indeed *don’t* “follow the bible” and so he is in essence making fun of them for having an irrational doctrine… that they don’t actually have Whereas the Unitarianism-ists reject the Trinity, predestination, and the infallability of the bible, but still accept that the teachings of Jesus are divinely inspired, and believe in fundamental christian ideas such as the teachings of “the golden rule” and “turn the other cheek” and soforth. The rejection of the idea that a book is “infallable” doesn’t lead you to reject the truth of every teaching in the book. Think of BDA for example, hardly infallable, but a terribly useful thing full of individual truths about data analysis.

      So, the only thing I can say about this analogy is that, at least it led me to look at the wiki and get a sense of what the heck unitarianism is… perhaps bad analogies well studied are better than good analogies in the end.

    • jrkrideau says:

      I was going to point out that the Catholic Church never seems to never have been committed to a literal interpretation of the bible if other evidence was sufficient to show that the Bible’s wording should be interpreted figuratively.

      One must to have very strong evidence.

      • Martha (Smith) says:

        My grandfather was trained as a Methodist minister in a Methodist theological seminary over a hundred years ago. Part of the training was learning Latin, Greek, and Hebrew well enough to read the various parts of the Bible in those original languages, rather than relying just on English translations when preparing a sermon.

  2. Jonathan (another one) says:

    A word for the Unitarians…. Stock prices look a lot more like the right panel than the left panel. The event study methodology for whether or not a particular new event materially impacted the stock price fits a model to stock prices (say, based on the returns to a portfolio of similar stocks — depends on the particular event) and then looks for a residual two standard deviations outside the underlying standard deviation of the model. Granted, this is then all mucked with NHST garbage talk, but if you want to know whether the stock move that day was unusually large (and, by implication and rhetorical exhortation, the result of the news at issue, but this is always potentially in dispute if there were other news as well.)

    I don’t see anything wrong with this method (beyond the inability to ascribe causality in any way but rhetorically.) But it’s just a classical stats test and it is indistinguishable from the Aitkin method above. The null hypothesis of no change is just the expected value of the model, just as it is if the Presidential approval process above is a random walk. So it’s not that we think that it’s no change, it’s just that no change, and the associated standard deviation of expected changes is the appropriate comparison point against which to assess data we suspect was affected.

    • Carl says:

      Jonathan –
      I agree, that like an event study, the question here seems to be not a literal change/no-change one, but a causal/counterfactual one. But I think it’s still even an ill-posed question in that form. Stock event studies and are a good analog, since they’re both basically the aggregation of a bunch of underlying dynamic opinions. If some news about a company causes one investor to sell, then there’s clearly some causal effect of the news, just as a debate might cause one person to disapprove of a candidate.

      But a 2-sigma test has no power to detect that, and really isn’t even looking. It can only answer something very narrow: after controlling for all things I think might predict my series, is there a >= 2-sigma residual that I’m confident could be from no other cause but the event (debate, SEC filing, etc)? That then disqualifies from my study and < 2-sigma sized effects, which might be important and interesting! And it also leans a lot of causal inference on a given forecast model — once you factor in model uncertainty your power for identifying interesting effects is pretty much nil. So you not only don't get to phrase your question as an NHST problem, you don't even get to phrase it as a causal inference or counterfactual problem. Then what are you doing?

      Without recourse to the CLT by looking at lots of identical debates or corporate news events, I don't think even the barest dressings of reject/accept logic are very useful for these situations.

      • Jonathan (another one) says:

        I’m not sure we disagree, except as to the conclusion!
        (a) Smaller effects might well be interesting, but that’s just the point Andrew has made many times: against a noisy background, there’s no chance to pull out a small signal. The signal might be interesting if you could prove it existed, but you can’t.
        (b) Model uncertainty is less of a problem for stock market models because we have strong reasons to believe that something like the standard market model works. That said, there can be issues with that model, but all that will do is raise the boundary on big movements.
        (c) I’m not even sure what it would mean to call a debate or corporate news event “identical.” No such beasts.
        All that said, I still don’t see what’s wrong with phrasing this as a causal/counterfactual problem. “This is the sort of move that occurs 1 day in 300 in the market after adjusting for the sort of news that affects stocks generally. I claim that this day was unusual because the following thing was reported widely. Without arguing I’ve proved causality, I claim to have least shifted the burden to you to show some other reason the price change was this big.”

        • Carl says:

          Yeah, I think we agree except for some points of interpretation, very likely coming from experience with different use cases.

          We agree low power is a problem if your goal is to accept or reject “no effect.” I think my only point here is, especially with these one-off events, that you’re throwing away a lot of useful information. Indeed the measured residual *may* be all noise and no effect, but I would still like to use my model(s) to learn about more-and-less plausible values of the effect.

          The fact that they’re unique (as you say, and I meant to imply, these events are never really identical), means that you need to thoughtfully combine evidence from “similar” events to say answer questions. E.g.: Are stock-split announcements more meaningful for some companies than others? Do bad debate performances matter more for front-runners? Just making some binary decision and moving on doesn’t help you accumulate any knowledge. The situation is different when you do have repeatable experiments, because you have some hope of a single, well-defined signal coming through.

          My problem with calling it a causal inference test is that it’s not. All stock announcements and all debates have some causal effect on the mechanisms that drive stock prices and approval rates: they always change somebody’s mind. So there is for sure a non-zero causal effect of these things. You can have a test for “small enough to matter,” I don’t think n-sigma is a good way to do that, and I think you’re really forced to talk about plausible effect sizes. Your burden-of-proof formulation isn’t wrong per se, I just think it’s very limiting.

          • Carl says:

            A somewhat concrete example that may better explain what I’m getting at:

            Suppose I’ve measured the residual returns on a bunch of stocks on the days of their stock-split announcements. All of these fail to reject 0 for some n-sigma test, either individually or averaged over stocks, or both.

            But, I then regress these statistically insignificant residuals on market cap. I find a strongly significant relationship between the stock-split residuals and market cap. Well, that’s weird: didn’t I just decide these announcements were all just draws from random noise?

            • Jonathan (another one) says:

              This can clearly happen if, for example, you get 12 insignificant positive residuals and no negative ones. My methodology in that case is to run a Kolmogorov-Smirnov test for the hypothesis that the p-values of these residuals is uniform. If it’s not, then I can say something is up about the distribution of these residuals even if none of them look particularly odd against background noise.

              Generally, though, I suspect you’re right about use case. I am in the unfortunate business of trying to use statistics to actually say *something* about one-off events. I have the further problem of trying to say something about them while maintaining some integrity. With sufficient modesty in the claim, I can do both, but I’m inherently limited by noise.

  3. Dan C says:

    The last point about likelihood and priors reminds me a bit of McElreath’s ‘modest proposal’ in his recent talk on “bayesian statistics without the frequentist language’, where he lightly suggests we simply refer to likelihood and priors as distributions and drop the likelihood/prior language when teaching/using the terminology. Curious about others’ thoughts on that and whether it would ever catch on?

    (link here: https://www.youtube.com/watch?v=yakg94HyWdE the slide at 48.07 in particular sums it up)

    • Carlos Ungil says:

      Calling then both “distribution” doesn’t change the fact that one of them is a “distribution which doesn’t depend on the data” (a.k.a. Prior) and the other is a “kind-of-distribution which is conditional on the data” (a.k.a. Likelihood)… (I’ve not seen the talk, maybe he doesn’t really suggest they are equivalent.)

      • Richard McElreath says:

        Dan’s phrasing is excellent. Maybe Carlos doesn’t recognize the term “modest proposal”?

        Likelihoods and priors are different. But they are also alike. Since the same probability assignment can serve as both “prior” and “likelihood” in the same model, depending upon whether a case is observed or not, clearly they have a lot more in common than the usual teaching approach suggests. Presenting them as different animals blocks solutions, I argue.

        For applied mathematicians, maybe these issue of terms aren’t important. But students from the sciences, in my experience, aren’t served when we use frequentist terms to describe Bayesian concepts. It leads to common conceptual errors.

        The same holds in reverse, I think: describing frequentist inference with Bayesian concepts distorts learning.

        Ultimately, I think the words we use to describe the math are always going to have flaws. If the words were sufficient, we wouldn’t need the math. So multiple, shifting frames are often needed to make sense of complex topics.

        • Laplace says:

          Another good reason to get rid of the word “prior” is that it’s not really a definable mathematical quantity. I suppose you could define it as any term takes the “prior” position in any equation/expression that looks like Bayes theorem. That’s operationaly how people do define it.

          But there are a mass of distributions which satisfy this definition for “prior” which have very different properties from what people intuitively expect. For example, it’s possible for a “prior” according to this definition to depend on the number of data points.

          None of this would be an issue if statisticians could think their way out of a paper bag. It would be sufficient to just say “prior” makes sense in some instances, but in most cases you need to examine the equations to see what’s what and think things through each time. But they obviously can’t think their way out of a paper bag, so controversies that what be trivially solved in other communities become century long debates that show no sign of ever being resolved.

          A good first step in cleaning house in statistics though would be to get rid of anything that can’t be given a precise mathematical definition. What ever monumental problems p-values have they can at least be given a precise definition. “Prior” distributions can’t. So get rid of the term.

        • ojm says:

          But a likelihood as usually defined is not a probability distribution, it’s a function of a parameter (or at least of the variable on the RHS of the conditioning), right? So a likelihood doesn’t integrate to one for example.

          See also my comment just below on y free vs y0 fixed etc. I don’t object to eg calling p(y|theta) a data model and p(theta) a parameter model, but I do object to the confusing misuse of the term ‘likelihood’.

          • Keith O'Rourke says:

            Might be good place to put in Mike Evans’ take to just get rid of likelihoods (functions of a parameter or really an equivalence class of functions of a parameter) by starting with a joint model (prior and data generating model) conditioning to get the posterior and then defining the effect of conditioning as a ratio posterior/prior.

            It avoids a lot of complications (and is one member of equivalence class of functions of a parameter) so you just lose the complicated math. No one is likely to think the ratios of probabilities should integrate to one?

            Maybe just the joint model before and after the data with the ratio of (marginal over possible data) joint model before divided by the (conditional) joint model after the data – to display the effect of observing that data in that joint model.

            • Martha (Smith) says:

              Starting with a joint model (prior and data generating model) makes the most sense to me.

            • Carlos Ungil says:

              Does he really “get rid of likelihoods”? In simple cases at least he seems to end up with a likelihood under another name. And I find strange that he considers that “the best estimate of ψ is the value for which the evidence is greatest” (i.e. the MLE), completely ignoring the prior distribution.

            • ojm says:

              From a Bayesian point of view, sure, fine don’t use the term likelihood. Introduce relative belief or Radon-Nikodym derivatives or whatever.

              Call p(theta) a parameter model instead of a prior, cool.

              Just don’t call p(y|theta) a likelihood and confuse everyone.

        • Carlos Ungil says:

          The term “modest proposal” makes me think of child-eating, so I watched your talk to be sure that’s not what you’re advocate for either. It seems to me that you go too far on mixing data and parameters, but I guess I’m not the target audience. Prior distributions for the parameters represent the state of knowledge about the model before taking the data into account. You can construct a predictive distribution for the data but it’s just a consequence of the former.

          You can update your state knowledge using the data/likelihood to get the posterior distributions for the parameters. You don’t update your distributions for the data but now you have an updated model so you can produce a new predictive distribution for the future data. It’s not clear what does it mean to have a joint generative model of all variables. Let’s say I’m doing a regression of height on age, do I have to be able to generate pairs (age, height)? To analyse the data I only need to model the height as a function of age, because everything is conditional on the age values (which are a given).

          Of course I can change the model to introduce latent variables (i.e. new parameters) where I had data before and say that now the data are the observed values which are noisy, censored, etc. And in that case you need to model the presence of the cat explicitly. But I would say that in the new model there are still parameters and data clearly identified as such. Maybe the distinction is not “deep”, though. I will be interested in seeing how you present this issues in the new edition of your book.

        • Dan C says:

          Thanks for your input on this Richard! Speaking as an applied (non-mathematician) researcher, it is sometimes exhausting trying to move others (including reviewers and editors) beyond a near-obsession with aspects of the prior and fear of its ‘subjectivity’ (even with running analyses under multiple priors and having large N’s!). I thought the idea, or at least having a serious conversation about shifting terminology, was a very good one. Your rethinking book has been an immense help to myself and as a resource to direct others to; looking forward to seeing what’s next!

    • ojm says:

      FWIW I find it superficially appealing but ultimately a bad idea. I also dislike what seems to be the casual equating of p(y|theta) where y is free with p(y0|theta) where y is fixed to y0 when Bayesian discuss ‘likelihood’.

      • Dan C says:

        Great points from both of you. McElreath is a very bright guy and I won’t attempt to speak for him; perhaps I’m also misrepresenting the roots (or not giving appropriate context) to his ideas. My broad guess is that he is just trying to think of different possible ways (hence ‘modest proposal’) as an instructor of trying to reshape how individuals new to bayesian stats think about priors (and in some cases seems to worry endlessly about them, such as happens in some of the anti-bayes discussion still occurring in areas of psychology, etc.).

  4. From their web site (in the UK), it sounds to me like they’re more like subjective Bayesians:

    It is impossible to give the Unitarian position on specific ethical and moral issues. First, there are too many to deal with. Second, Unitarians do not impose a moral orthodoxy any more than a theological one. Individuals are encouraged to arrive at their own conclusions.

    If Unitarians don’t necessarily believe all the same things then why bother getting together at all? Because to us sharing experience, perspectives, differences and ideas is a powerful way to explore and expand our personal ideas of faith.

    Wikipedia quoting di Finetti:

    For subjectivists, probability corresponds to a personal belief.

    • The Wiki is useful, because it seems that “Unitarian” isn’t a single group of people really:

      https://en.wikipedia.org/wiki/Unitarian

      In particular, “Unitarian Universalism” is popular in the US (with a similar group called “The General Assembly of Unitarian and Free Christian Churches”), often referred to as “Unitarian”, but seems quite different from “Unitarianism” which is a distinctly Christian theology around since the 1500’s and established a church in England in 1774, that treats Christ similar to Mohammad in the sense of being a human prophet rather than a “Son of God” and specifically rejects the Trinity doctrine while accepting many other specific Christian ideas.

      https://en.wikipedia.org/wiki/Unitarianism

      I agree with Elin though, the analogy with Unitarianism is a distraction. The real question is “Why bother to NHST?” and the answer is “no good reason” most of the time.

    • Elin says:

      There are a number of Protestant denominations that do not mandate that you subscribe to a specific creed. These range from Unitarians, who are at one extreme, to Quakers at the other. The belief in not having a human written creed (and in the Quaker sense in the centrality of direct experience of spirit) is itself a statement of belief.

  5. David says:

    The analogy may be more apt than you know. One of the potential answers to your hypothetical about the Bible is that if most folk in society come from a place where their understanding of the religious and spiritual has been shaped by Bible and church, then creating a forum to discuss those that reflects and builds on non-literal understandings of the same is a bridge to connect with people who you might see as co-believers through the right frame.

    Given how the modern understanding of science and scientific progress has been informed by traditional statistics, and the desire to link with fellow believes in scientific method as well as lay public (like me) around research findings, it seems that there might be useful ideas to mine in terms of how to present a new understanding so that it makes sense. Folks not trained in statistics will still need some sense of when a finding has been meaningful and should drive changes in behavior, and if the only answer is to be initiated in the mysteries, I wouldn’t hold my breath for broad uptake.

    To be fair, I think you do a good job in doing this, just wanted to defend the value of bowing to irrational path dependency in a world where choices are not made from blank slate starting points.

  6. jrkrideau says:

    What is a Unitarian?

  7. Mike says:

    Regarding the second point: perhaps the ‘logical basis’ of the division of a model into likelihood and prior is the distinction between uncertainty and ignorance. In Bayesian inference, both are treated the same — quantities are given probability distributions — but it doesn’t hurt to make this explicit, right? Since the distinction between uncertainty (random variability) and ignorance (lack of knowledge) depends the level of analysis, separating them into prior and likelihood makes clear at which level of analysis your model operates.

  8. Jonathan says:

    1. You need to state conceptions like ‘garden of forking paths’ in model form so one can not only identify that people exercise a choice function, explicit or implicit, but what that choice function is, how it operates and if not why then at least where it comes from and thus how its operations become ‘why’. I know I mentioned choice function in a comment the other day. I forget how difficult these are and thus how they and the ideas/operations/states inherent to them tend to be glossed over, with the glossing becoming more unconscious as you move away from an area like set theoretical operations in which the assumption of choice is at least relatively clear. When it reaches analytical/applied systems like statistics or economics, the lack of understanding of choice seems to me a lot like a poisoned apple.

    2. I would bet that in 20 years papers with p-values and ideas of null will be viewed as quaint. I hope statistics is young enough to reconstitute itself. I would expect it will become much more visual as the application to geometry develops so you can see the potential and probable spaces. (I almost said the application of choice to geometry because all decisions within any model space are choices and thus ….) I wonder how long it will take people to grasp that 2D graphics aren’t good enough given the 3D rotational potential in any virtual space like a freaking web browser. By good enough, I mean, for example, that rotation reveals the distortions imposed by compressing complexity to a plane, same as a 3D scan of the liver versus a compressed planar view, and yet you have to spend so much time talking about bleep flat graphs and even charts that don’t show any recognition they’re something that maps to a probability space. I find, for example, a lot of the analysis through logarithms becomes more interesting when you see the pathway made by the application.

    3. As fun, I think the conception of Unitarian as mentioned misses a point and evidences an implicit choice function – as any implication/definition/implementation must. That is, Unitarianism was not a single but many choice interpretations of an inherently unstable synthesis. It may help to think of that as a field, the field being the relationship between at least Jesus, the Holy Spirit and whatever one labels ‘God’. This synthesis to me mirrors the Biblical conception of who begat whom, which Judaism picks up in Abraham, Isaac and Jacob and which generalizes to past, present, future and of course strings of choice (but that is harder to explain) or what I like to point out at Seders that we all eat the afikommen because we are all the middle matza, because we live and carry with us the past and potential for our own and others futures. The issue of stability is pretty basic: you can formulate a line of God-Jesus-Holy Spirit and even reverse that but then you are arbitrarily fixing the chain, much like when you impose a restriction or type or even an artificial ‘universal set’. One might hope ‘we all agree on this chain’ but understanding changes with context so as much as ‘we’ would try to hold on to the G-J-HS string questions would arise about G because G affects your understanding of J and you have to ask how much of HS is in this world now versus the G before the J and thus what is J in this world, etc. The straw man idea that one could have literal interpretation proves the impossibility of literal interpretation when one breaks the ideas of literal interpretation – of a specific Trinity, of a specific text, etc. – down to the choices implicit in the statements of these ideas. Or bluntly, you got to start counting and there’s always basic questions: where do you start from and what do you call start and where do you count to and how do you know you’re there? You could find in that statement the Ancient Greek paradoxes of motion, including what became infinitesimals into limits into transfinite numbers and Tom Stoppard’s rendition in Jumpers of the old joke that since the arrow first crosses half the distance and then half the distance that St Stephen died of fright. I would also quote the old camp song: we’re here because we’re here because we’re here because we’re here
    – which I find is one of the best statements of the halting problem. So you pick a ‘stable’ definition for the G-J-HR field and hope it lasts like a proton! It can’t because it ain’t a proton; it’s an unstable ‘molecule’ ready and willing to bond with any idea that comes along, from messianic claims to utter denials. I’m looking at a 10 week old puppy so I’m stopping now.

  9. ojm says:

    Beating a dead horse at this point but when you say

    > Once you have abandoned literal belief in the Bible, the question soon arises: why follow it at all?

    seems pretty hypocritical given your attitude to Bayesian foundations.

    • Burn….

      But seriously, I think I have a situation where I can call something, let’s label it A as a formal system with some very simple requirements… and then probability theory becomes a model of (a subset of) that formal system. It’s now safe to say that “probability is a kind of A”….

      I’m not giving away all of it yet, because I’m writing a paper basically as we speak, but the upshot is “A” is something that looks a lot more like “testing a model’s explicit assumptions” than “inferring a probability that statement X is true”

      I think at this point, it’s fair to say “I don’t want to do A” and then, you could go off and do something else, but A is a pretty simple thing in my conception, and it’s a fairly obvious thing for a scientist to want to do. The only thing I don’t have is a uniqueness. I’m not sure probability theory is isomorphic to A, only isomorphic to a subset of A.

    • Andrew says:

      Ojm:

      Setting aside the appropriateness of the Unitarian analogy, I disagree with your comment regarding Bayesian foundations. I take Bayesian foundations very seriously and have written a lot on the topic!

      • ojm says:

        How can you say ‘standard Bayes foundations are wrong…I have my own ideas but there are a number of gaps’ and then write a really long, somewhat uncharitable review of someone trying something else, where the gist of the review seems to amount to ‘he’s not doing real Bayes’?

        Again the religious analogy seems ironic since it comes across a little ‘we are the true priests of Bayes who decide what is and isn’t Bayesian’ despite not having a fully-formed/consistent definition of what is and isn’t Bayesian.

        If you can be eclectic when it comes to foundations why can’t others? Which is to say, I’m confused about why you wrote such a long, dismissive review in the first place?

        Disclaimer: I met Murray Aitkin once recently and, while I don’t totally buy his position (not that I buy many if any), this was (it seems to me) basically his complaint about your review and I had to agree.

        • Andrew says:

          Ojm:

          I guess we didn’t write that review article clearly, so let me explain right now: Our point was not “he’s not doing real Bayes.” One clue to this is that we never said such a thing! Our point in the quoted passage was that the work in question represented “solutions to problems that seem to us to be artificial or conventional tasks with no clear analogy to applied work.” The book could’ve been 100% Bayesian and we’d still have a problem if there were no clear analogy to applied work. Conversely, the book could’ve been 0% Bayesian and we’d have no problem if the models made sense.

          Also, we never said anything like, “we are the true priests of Bayes who decide what is and isn’t Bayesian.” Again, a useful clue here is that there was no such quote in our article; you had to make it up! I’m open to all sorts of philosophies of statistics and I think it’s best to evaluate them on how they work in real examples.

          As to why we wrote the article in the first place: I can’t remember. I think Christian received the book in the mail and then we discussed it with Judith, and we wrote down our thoughts.

          • ojm says:

            From the summary/abstract:

            > We analyze in this note some consequences of the inferential paradigm adopted therein, discussing why the approach is incompatible with a Bayesian perspective

            • ojm says:

              There’s a whole bunch of such quotes scattered throughout eg

              > We do not claim here that Aitkin’s approach is wrong per se, merely that it does not fit within our inferential methodology, namely Bayesian statistics, despite using Bayesian tools.

              Your inferential methodology is Bayesian but his is not? Who decides?

            • Andrew says:

              Ojm:

              The full sentence: “We analyze in this note some consequences of the inferential paradigm adopted therein, discussing why the approach is incompatible with a Bayesian perspective and why we do not find it relevant for applied work.”

              • ojm says:

                Yes, that sentence includes an ‘and’. It doesn’t qualify the other part of the sentence it makes an additional point.

              • ojm says:

                For example it could have said

                > We analyze in this note some consequences of the inferential paradigm adopted therein, discussing why the approach is incompatible with a Bayesian perspective but nevertheless is relevant for applied work.”

              • Andrew says:

                Ojm:

                Ahhh, but I don’t think the approach in that book is relevant for applied work! I do think that there are lots of non-Bayesian statistical ideas that are relevant for applied work. But I don’t think the ideas in that book fall into that category.

              • ojm says:

                Yes, sure I get that. But the point is you implied I shouldn’t quote one part without the other to support a point about Bayesian foundations or whatever (not a point about practice). I was just showing that the issues seem quite independent. See also the other quote above.

                If you just said – I don’t think Aitkin’s approach is practical/relevant to my work – in your review, fine. It would also be a much shorter review.

                The issue is all the other stuff about how it’s not Bayesian, we’re Bayesian etc. And the original bolded quote that I called (and still think is) rather hypocritical.

      • Carlos Ungil says:

        Miguel Servet also took theology very seriously and wrote a lot about the topic… and was burnt on a pyre of his own books not far from here for spreading Nontrinitarianism.

  10. Kyle MacDonald says:

    I know that Christians are divided in their support for evolution, as well as their reactions to the non-determinism of quantum mechanics. Do Unitarians believe in evolution but require it to be unitary?

    • Martha (Smith) says:

      ” …Christians are divided in their support for evolution…” But there may be some disagreement between some Christians who support evolution and scientists about just what evolution is — at least, there was about fifty years ago when I was taught that “Evolution is the slow and orderly process by which God has created all things and is still creating new things.”

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