This is Leo.
Explanation or explanatory modeling can be considered to be the use of statistical models for testing causal hypotheses or associations, e.g. between a set of covariates and a response variable. Prediction or predictive modeling, (supposedly) on the other hand, is the act of using a model—or device, algorithm—to produce values of new, existing, or future observations. A lot has been written about the similarities and differences between explanation and prediction, for example Breiman (2001), Shmueli (2010), Billheimer (2019), and many more.
These are often thought to be separate dimensions of statistics, but Jonah and I have been discussing for a long time that in some sense there may actually be no such thing as explanation without prediction. Basically, although prediction itself is not the only goal of inferential statistics, everything—every objective—in inferential statistics can be reframed through the lense of prediction.
Hypothesis testing, ability estimation, hierarchical modeling, treatment effect estimation, causal inference problems, etc., can all be described in our opinion from a (inferential) predictive perspective. So far we have not found an example for which there is no way to reframe it as prediction problem. So I ask you: is there any inferential statistical ambition that cannot be described in predictive terms?
P.S. Like Billheimer (2019) and others, we think that inferential statistics should be considered as inherently predictive and be focused primarily on probabilistic predictions of observable events and quantities, rather than focusing on statistical estimates of unobersvable parameters that do not exist outside of our highly contrived models. Similarly, we also feel that the goal of Bayesian modeling should not be taught to students as finding the posterior distribution of unobservables, but rather as finding the posterior predictive distribution of the observables (with finding the posterior as an intermediate step); even when we don’t only care about predictive accuracy and we still care about understanding how a model works (model checking, GoF measures), we think the predictive modeling interpretation is generally more intuitive and effective.
Leo:
In this post, you’re saying something that Don Rubin used to always say, that statistical inference is all about missing data.
For sampling, the missing data are the observations for the people who are not in the sample.
For causal inference, the missing data are the outcomes under the treatment (for people who were exposed to the control) or the outcomes under the control (for people who were exposed to the treatment) or both (for people not in the study).
For measurement problems, the missing data are the latent or underlying quantities.
For prediction, the missing data are future potential observations.
For Bayesian inference, the missing data are all the unknown parameters.
One way I like to put it is that, even if all you care about is prediction, we can still be interested in parameters in a model, because parameters can generalize to new settings in a way that pure phenomenological prediction cannot. This is related to modeling and poststratification.
You missed the least controversial one that ‘For missing data problems, missing data are the missing data.’
Thanks Andrew, I like a lot this missing data perspective from Don Rubin.
> One way I like to put it is that, even if all you care about is prediction, we can still be interested in parameters in a model, because parameters can generalize to new settings in a way that pure phenomenological prediction cannot.
Yes, and I feel this is much connected with the statisticians’ modeling awareness, which is not always shared, in my opinion, by some deep/machine learning modern researchers.
Yeah, if you have a good explanation then it seems by necessity it should produce a good prediction. It is possible for a bad explanation to also produce a good prediction, but it shouldn’t be possible for a good explanation to produce a bad prediction (on average).
>rather than focusing on statistical estimates of unobersvable parameters that do not exist outside of our highly contrived models
>we also feel that the goal of Bayesian modeling should not be taught to students as finding the posterior distribution of unobservables
>we think the predictive modeling interpretation is generally more intuitive and effective
I don’t know about in every scenario. Let’s say you have a serial dilution lab experiment where you start with some large number of bacteria that are placed into a test tube solution and then serially dilute samples from the solution by 0.1 fraction for several dilutions. You then plate the bacteria at the final dilution, count the number, and want to infer the starting number of bacteria. You might write something like
target += poisson_lpmf( plate_count | 0.0001 * lambda );
in Stan with the goal to estimate lambda, the starting amount. Yes the model makes assumptions about the sampling error at each dilution etc, but it doesn’t really seem “highly contrived”, and the intuitive goal does seem to be to find the posterior distribution of unobserved lambda. Obviously a good estimate of lambda should be able to provide good predictions of plate counts. But from the educational standpoint, I don’t really see how the predictive modeling interpretation is more intuitive than finding the unknown parameter.
I agree with this. The same thing is true for example when you drop balls in a vacuum chamber to estimate the gravitational acceleration at a point on the surface of the earth, or you drain fluid through a hole in the bottom of a cup to estimate viscosity of a fluid, or you load a load cell with different weights to calibrate the load vs voltage curve or you break bolts to find the yield strength… There are lots of cases where the goal is to find the parameter. Admittedly these often are so you can publish the parameter and people can know what to predict in the future, but the parameter is fairly real in these cases.
But if you do find an estimate of the parameter , if it’s the correct, it should be useful in making predictions about the princess from which the parameter was derived.
I find myself agreeing with the original poster. It’s not enough that we can find estimate of a parameter that fits existing data, we should be thinking of it as finding an estimate that fits existing data while allowing us to make predictions about future state. Lots of things can fit the past and be correct, the usefulness of something is still it enables us to say something meaningful about the futur future.
Being able to estimate gravitational g isn’t enough. Can we then use that g to predict the speed of a falling mass in a vacuum. So the problem becomes, finding the best estimate that fits data and makes verifiable predictions
For teaching, I think the word “prediction” has to be handled carefully. In normal conversation, a prediction means a statement about something in the future. Here it is about something outside the knowledge of the statistician. Leo has been careful to define it this way, so I’m just saying this might need some emphasis. A prediction might be about the past or an alternative universe. For example, jd doesn’t know the original number of bacteria in their test tube, so it makes sense to “predict” that. They could have counted the original bacteria in various ways rather than performing dilutions.
Exactly.
Briggs, W. (2016) “Uncertainty. The Soul of Modeling, Probability and Statistics”, cited in Billheimer’s paper, also takes this position and is a great read.
I wonder whether people interpret the word ‘prediction’ differently. In an industrial / manufacturing setting there are a lot of tools marketed as ‘predictive’ and the underlying impression that is given is that once you get to predictive this is superior to explanatory, ie if you can predict the output then the system is inherently understood. This is the age old conflation of cause and correlation, but with a shinier marketing gloss.
I need a definition of “prediction”. I certainly don’t think that all statistics problems are prediction problems using the usual meaning of “prediction”.
Great point, different fields have a different understanding or use of “prediction”.
I’ve thought about this issue a fair bit in relation to survey sampling, and even here it seems to me that there are subtle problems that I have not seen clearly discussed.
For example, even within survey sampling we might have subtly different aims. When we canvass people in election polling the immediate aim is apparently descriptive, but really we are probably more interested in predicting the outcome of an election. It seems to me that this directly motivates the use of things like MrP, where we take advantage of shrinkage in various ways in order to reduce predictive error. However, in other survey sampling cases we may only be interested in the instantaneous state at the time of sampling. One example of this might be the construction of indicators, e.g. ecological indicators that use information on species’ abundances or distributions to show the state of the environment. In this case it seems to me that justifying methods that take advantage of bias/variance trade-offs is more difficult, because the aim is not to minimise predictive error, but just to give descriptions of populations with full uncertainty. At the least the effects of these approaches on things that purport to be pure descriptions should be clearly discussed by practitioners.
Interesting post. I don’t have an answer to its specific question. Just wanted to say though that this argument (i.e., everything is prediction) was also brought up by Brad Efron when commenting Leo Breiman’s “The Two Cultures” paper (see here: https://projecteuclid.org/journals/statistical-science/volume-16/issue-3/Statistical-Modeling–The-Two-Cultures-with-comments-and-a/10.1214/ss/1009213726.full). Always nice and funny and stimulating intellectual exchange to read.
I do not agree with your proposition. And I believe those cited texts present good enough arguments to keep these two goals (causal explanation vs. out-of-sample prediction) separated. In short, (a) explanation =I am looking back in time at a realized intervention (be it result of manipulation/exogenous variation in a lab or another source of variation based on “as-if random” assumption) and estimate it’s effect on Y in a given population of units in time and space, traspontability of this estimated effect to other setting (even the same setting in future) is not guaranteed; (b) prediction = I want to get as close as possible to Y given whatever data I have in my setting of interest.
You are predicting the effect of an intervention. It is prediction but for an intervened upon population…
Am I understanding things correctly by summarizing this all as follows:
Researcher A: We have investigated whether listening to Bananarama’s 80’s smash hit “Venus” results in eating more bananas. We’ve used hypothesis testing and a sample of 2.423.569 people, and found a suuuuuuuuuuuuper tiny effect size and a “statistically significant difference”.
We think “that inferential statistics should be considered as inherently predictive and be focused primarily on probabilistic predictions of observable events and quantities, rather than focusing on statistical estimates of unobersvable parameters that do not exist outside of our highly contrived models.” and we also think like W. Edwards Deming and think that “The only useful function for a statistician is to make predictions, and thus provide a basis for action.”
That’s why we work for the government of course. We have been asked by the government to investigate how to get more people to eat bananas, because reasons. So, in our official role as scientific government advisers, we propose that every work and school-day should start with blasting Bananarama’s “Venus”. Science rocks!!
Researcher B: Uhm, couldn’t you further investigate whether other variables might be way more important concerning the eating of bananas. And, shouldn’t people decide for themselves whether they want to eat a banana. And, why does the government get to decide that I have to listen to Bananarama’s “Venus”. And can you please ask Deming whether he thinks that there might be other factors involved in “providing a basis for action”.
As a side note: I don’t like bananas myself for instance. And I like to listen to my own music in the morning, thanks. I am currently listening a lot to “Cigarette Machine” by Fred Eaglesmith in the morning with my first cup of coffee for instance.
Researcher A: Science rocks!! Prediction man, prediction. Follow the science! Carrot-stick. Incentives. Government!
Anon:
I don’t think your scenario is realistic. The usual setting is the opposite:
I’ve long felt the mantra, “statistical significance is not the same thing as practical significance,” while completely true, is misleading, in that it evokes images of silly studies such as you evoke with huge sample sizes and tiny but statistically significant estimated effects. What I’ve mostly seen in the press is the opposite sort of silly study, with small sample size and lots of noise, resulting in large and statistically significant estimated effects. The estimates are large because, given the level of noise, the estimate has to be large to reach the threshold of statistical significance, and the result is statistically significant because systematic errors and forking paths enable researchers to find statistically significant patterns at a rate much higher than would be expected from simple theory.
Quote from above: “I don’t think your scenario is realistic.”
Please keep this comment in mind in the coming 10 years or so. Especially perhaps in relation to large “collaborative” efforts and how the data is collected and the studies designed in these projects, the topics and conclusions of these types of studies, and ideas and thoughts like “The only useful function for a statistician is to make predictions, and thus provide a basis for action.”
I might not be around here to comment on such things in the coming years. I may just be listening to Fred Eaglesmith and doing other stuff.
Anon:
Here’s a discussion of a recent large meta-analysis of “nudge” intervention, and here’a discussion of a recent large collaborative study the same area. In both cases, there were inflated estimates of effect sizes and a big push to interpret the data to make effects seem large.
I have the impression that a lot of researchers working on “nudges” are good people, sincere, trying their best, and wanting to do good science. Unfortunately, honesty and transparency are not enough. All the good intentions in the world won’t help you if you’re studying highly variable effects with noisy measurements and using sloppy statistical methods.
What if the megastudy concerning fitness only tested 5 possbile ways to increase going to the gym?
And what if those 5 ways only came from a certain kind of researcher (e.g. the ones who participate in a megastudy or the ones who even perform this kind of research on this topic)?
And what if those 5 ways are way less useful than 5 other ways which are not researched?
And what if people say that “well, we’ve investigated that one of these 5 ways we investigated is the best way of these 5 ways to increase going to the gym so we should be doing that because that’s the best data we have. Follow the science!”
And what if people say that we should really view this megastudy as “predictive” because that’s kind of what statistics might be all about in a way, sort of.
And what if policy makers sort of take this as a reason for action, maybe nudge members of society because the government knows best and the data analyses can be interpreted as being “predictive” and not merely “explanatory” or “descriptive”?
And what if those megastudies lead to such large projects that they can never be replicated by someone else, or at a different time, due to their size?
And what if those megastudies lead to some sort of centralized orginazation that “facilitates” all these megaprojects, because that’s just how nice they are? They can come up with the 5 options to increase going to the gym for instance, just because they are nice!
And what if those megastudies involve a centralized data collection method, in which one mistake or “mistake” somewhere might lead to influencing all the data from all the independent labs?
Anonymous
I guess I am missing your point. Any research project that omits important factors – whether accidental or by design – will produce poor models, perhaps dangerous ones. This is true regardless of whether the model is being used for prediction, for causal inference, or some combination of the two. Now it might be true that a model designed only for prediction might be more prone to discovering spurious relationships than a model designed for inference. But I think that is debatable – the opposite might even be true. So, I’m not understanding how your comment relates to the issue raised in the post.
Anon:
I don’t know. My point here is only that, as I see it, the problem is not reported effects that are statistically significant and tiny (in your words, “a suuuuuuuuuuuuper tiny effect size and a “statistically significant difference”), but rather reported effects that are statistically significant and large. I don’t think these apparently large and definitive results should be directly influencing policy or science, because I think these will generally be huge overestimates and will understate uncertainty.
Quote from above: “Any research project that omits important factors – whether accidental or by design – will produce poor models, perhaps dangerous ones. ”
I think that’s exactly part of the point I am trying to make! Or better, part of what I am wondering.
Additional points I am trying to make, or wondering about:
Is it possible to design certain research, e.g. by using only certain variables or constructs, to sort of paint a certain picture, or get a certain result one wants? And, does a focus on statistical significance and not effect size make it more possible to do this, and leave out important variables or constructs?
Does viewing statistical inference and/or research as “predictive” make this possibilty even more dangerous because it more implictly and/or explicitly connects statistical inference to decision making, policy, etc. (also in light of the quote “The only useful function for a statistician is to make predictions, and thus provide a basis for action.”)?
I am not a statistician, so I am still not sure what the point of the blogpost is exactly. That’s why I asked whether I understood things before writing my original post/scenario. I am also asking question mostly here.
Anon:
I don’t know what the point of the blogpost is either! I didn’t write it. In this little thread, I’m just commenting on your “suuuuuuuuuuuuper tiny effect size” example.
My (not carefully thought out) reaction is that it isn’t worthwhile pondering whether focusing on prediction vis a vis causal inference is more or less likely to result in poor analysis. Just as with statistical studies, there are many sources of variation and I’m not sure which are the most important ones (incentives, purpose of the research, capability of the researchers, outlet for publication/dissemination, etc.). But I think a key is domain expertise – an analyst who knows nothing about the domain is most susceptible to omitting important factors, misspecifying models, and being impressed by significant findings and/or large effects. I suppose the opposite is possible – subject matter experts may be more likely to have preconceived notions that blind them to more appropriate analyses. But I think the dangers with researchers who do not understand the subject are more pronounced.
These issues have come up often in discussions on this blog. To what extent is it necessary to have a background in a subject being studied? My own belief is that it is critical – at least, if a team effort, somebody on the team should understand the subject. I find much of the social psych literature devoid of value – but I’m reluctant to dismiss it too easily. Smart people have spent their careers working in that area, and it is too easy to just declare all their work as useless or misdirected. Of course I am tempted to do so anyway.
Quote from above: “My (not carefully thought out) reaction is that it isn’t worthwhile pondering whether focusing on prediction vis a vis causal inference is more or less likely to result in poor analysis.”
That’s not what I am wondering about mostly. As I wrote:
Does viewing statistical inference and/or research as “predictive” make this possibilty even more dangerous because it more implictly and/or explicitly connects statistical inference to decision making, policy, etc. (also in light of the quote “The only useful function for a statistician is to make predictions, and thus provide a basis for action.”)?
Now it sounds like your question is rhetorical. But I don’t think a focus on prediction makes things worse since it is more closely tied to decision making. By definition, decisions involve interests and interests introduce potential bias (both intentional and unintentional). So, in a sense, connecting prediction to decision making is bound to potentially lead to bias in the analysis. I don’t see that a focus on something other than prediction makes this any less likely. Such is the human condition.
One thing I think might help is detaching analysis from decisions. Too much published research attempts to advise decisions. The world may expect to demand that, but I think it also reflects a desire of researchers to be decision makers. I’d prefer to see a cleaner distinction between the two. As an example, think of all those medical studies. Clinicians want – and need – answers. But that is their job. The research should provide an improved basis for clinicians (or policy makers) to make decisions. Decisions are often binary (do X or don’t do X), but analysis should almost never be binary. I think confusing the two invites poor research practice.
I can to some extent identify with the emphasis on prediction and observables. At least it should remain a key challenge for any scientific work to make predictions that can be tested against observable outcomes.
I however believe that the attitude that “everything is prediction” severely underestimates that we do science not only for prediction of what happens in specific situations, but also to inform our general thinking with implications on communication, creativity, problem solving, and decision making in situations that go beyond the more narrow prediction problems that are usually addressed by specific studies (or resulting from reframing such studies as treating prediction problems if they don’t do that explicitly). Scientific work contributes to our general experience and world view in ways that are different from applying prediction machines to the situations for which they were built, and the current interest in “interpretable machine learning” should not surprise anyone. Often models involving unobservable or only indirectly observable parameters are a useful tool for such thinking and for transferring what is know in one situation to another situation at least as a starting point for developing ideas. One might argue that such considerations could be seen as an instance of a bigger more general prediction problem, but I don’t think we have effective methods for treating such problems, and I’m skeptical about how much could be expected from this.
Furthermore, the concept of “observability” isn’t without its problems. We’re talking about measurements here, and most measurements are based on theory that comes with its own assumptions, which can often themselves not be verified by observation.
By the way, for some reason this thread looks different on the main page than others. I can’t type in a comment directly but have to click on “x replies” instead (I saw it on both a Mac and a Linux machine). Not that this is a big problem, but something that should maybe be checked.
>the goal of Bayesian modeling should not be taught to students as finding the posterior distribution of unobservables, but rather as finding the posterior predictive distribution of the observables (with finding the posterior as an intermediate step); even when we don’t only care about predictive accuracy and we still care about understanding how a model works (model checking, GoF measures), we think the predictive modeling interpretation is generally more intuitive and effective.
I have held a similar “easier to interpret” hypothesis for a while, which I’ve tried to apply to my research on communicating/visualizing uncertainty. It’s often easier for people to reason in data space.
On the more general point that we can always cast explanation as prediction, I’m reminded of stuff like Yarkoni and Westfall, “Choosing prediction over explanation…” and Hofman, Watts, etc “Prediction and explanation…” and “Integrating explanation and prediction…” Here I’m not quite sure if you are repeating a similar message (i.e, we have to care about prediction when doing explanation) or saying something new?
Jessica:
Interesting connection. This reminds me of the work of Gigerenzer et al. on thinking about probabilities in terms of natural frequencies (for example, instead of saying that 2% of people have a disease, saying that, in a room of 100 people, we’d expect 2 of those people to have the disease). Arguably, natural frequencies are a predictive framework, whereas probabilities are a modeling framework. The advantage of natural frequencies is that they have a direct interpretation; the advantage of probabilities is that they generalize more easily (for example, “2%” doesn’t depend on the size of the room).
Looking at it this way, the point is not that predictions are a “better” or “worse” way of thinking than probabilities or models, but rather that there is a duality between predictive and parameter-based frameworks.
>there is a duality between predictive and parameter-based frameworks
Yep, and in communicating statistical results we often completely forget this
> It’s often easier for people to reason in data space.
But, not always.
Consider sports ratings (table tennis, chess, etc.). The data is the result of player A vs. player B. Do you want to say it is easier to reason about the probability that A beats B than about the probability of A’s playing strength?
Suppose we want to rank players according to their performance in 2023. I suppose you could consider this a prediction problem: Predict the probability that the 2023 version of A would beat the 2023 version of B. But, it seems more natural to consider this an estimation problem: How good was each player in 2023?
Another example is Kalman filter (state space) models for guidance/navigation. These models may have a hundred states. The data is the position (and maybe velocity/attitude) error. The latter depends on the particular scenario (course, target, etc.). We are interested in predicting how the system will work for other scenarios, but we are also interested in estimating the model parameters because they are properties of the hardware. You could claim the latter is really about predicting how the hardware will work in the future, but how does that help clarify things?
I said often, not always.
I don’t quite understand your first example – if the goal is to convey something we’ve learned from historical plays about player A vs B, I would say its easier for people to think in terms of how many games A would win versus B than the probability that A beats B. This is similar to what Andrew is mentioning above about frequency versus probability.
Your second example seems like a comment on the original post, not on my comment!
> everything—every objective—in inferential statistics can be reframed through the lense of prediction.
For example, the determination of the mass of Saturn can be reframed as the prediction of what the mass of Jupiter will happen to be when we know it more precisely. Actually this works beyond inferential statistics: every question and problem can be reframed as the prediction of its answer. That’s why ChatGPT can do anything just by guessing the next token!
I’m not sure what the mass of Saturn has to do with the mass of Jupiter but I’m thinking maybe you just accidentally switched planets mid analogy?
Determining the mass of Saturn can be reframed as predicting what the future more correct answer to “What is the Mass of Saturn?” yes. This is why I don’t think much is going on in this “reframing as prediction”.
Determining the gravitational constant of the earth at Caltech’s quad can be reframed as predicting the rate at which a dropped steel ball will accelerate in a vacuum tube placed in the quad… it’s trivial and not very interesting to say this. I think that was your point?
> maybe you just accidentally switched planets mid analogy?
Actually I tried to reuse an example from an old discussion with Christian Hennig (about whether a posterior probability can have an epistemic interpretation relative to a real-world quantity or only to a parameter in a model which would be something completely different). I initially got the planet wrong and when I remembered it better I failed to make the correction everywhere.
I personally prefer “everything about statistics is finding the plausible value of unknowns”.
Some unknowns are “tools” in the model such as say the assumed constant gravitational acceleration, some unknowns are “not yet observed data” such as the time of flight of the ball in the next gravitometer drop.
In the language of Bayes, they’re all parameters.
Same.
I’ve tried to explain it before via analogy as a machine that runs forwards and backwards. Take some widgets and run the conveyer belt backwards into the machine and you can resolve the size of the gears needed for the machine to produce those widgets. Run the machine forwards with those gears and you can produce widgets that look like the other widgets. Sometimes the gears are unknown and you need to resolve the shape and size. Sometimes the widgets are unknown and you need to produce widgets given previously resolved gear size. Sometimes it’s a combination of both. Sometimes your widgets are funky looking and you need to change the layout of the machine itself.
In any case, it’s all about unknowns. But I do agree with the OP that ultimately you check the machine in widget space. The real trouble comes in that many variations of machines can produce the same widget.
Your “not yet observed data” reminded me of a thought I had at the beginning of this year. I wanted to wish everyone on this blog scientific wisdom and sound judgement for the coming year(s). I was pondering how to formulate this, and had something like your “not yet observed data” in mind.
I got stuck. But it was supposed to be something like: “I wish everyone on this blog a lot of scientific wisdom and sound judgement for the coming year(s) so certain research, hypotheses, and data might not be necessary and/or possible to design, propose, and/or gather.”
Still not sure if it makes sense, or whether folks reading it get the gist of what I am trying to say with the words, but I was reminded of it when reading your “not yet observed data”.
I won’t say there are inferential problems that are *impossible* to recast as prediction, but there are definitely cases where it is much more natural not to. One example might be Hidden Markov Models where the unobserved state probabilities themselves are of inferential interest. In fact, not only is it hard to reason about the state from the posterior predictive distribution of the data; it’s even hard to reason about the state probabilities from the posterior predictive distribution of the states! For example, when the states are binary, then the posterior predictive distribution of the states will in general be a continuous mixture of Bernoullis, but the mixing distribution (i.e. the posterior distribution of the Bernoulli probabilities) won’t be identifiable from the posterior distribution of the discrete state.
Jacob:
Agreed. That’s why I prefer the “everything is missing data” framework to the “everything is prediction” framework: “missing data” includes latent unobservable data, for which it’s awkward to speak of “prediction.”
I think this is an interesting topic and I also believe that prediction is undervalued in the social sciences. However, I am not sure I understand the post. Maybe someone can clarify.
1. As far as I understand, you are not claiming that every prediction is also an explanation.
2. Further, you are not claiming that every explanation can be thought of as prediction.
3. But are you claiming that every *statistical* explanation can be thought of as prediction? Statistical explanations I take to be a proper subset of all explanations.
Some thoughts regarding the three points:
In 1. and 2. explanation means explanation in a general sense: An answer to a why? question.
1. I believe is false. Consider predicting the height of a flagpole by the length of it’s shadow and the angle of the sun above the horizon.
Taken from this excellent article https://plato.stanford.edu/entries/scientific-explanation/ I can predict the height, but my model does not explain why the flagpole was constructed with this specific height.
2. Is also false, I believe. I can explain why 9/11 happened without being able to predict a new 9/11.
3. Might be right. I think it depends what you mean with prediction. Do you mean prediction of future observations? Or of unseen observations that you could have sampled? Also, what is a successful prediction? How low has the prediction error to be? How large has the estimated probability to be for the explanation to be successful? Consider some event in the future takes place and the outcome Y happens. Is it a successful prediction if my model says P(Y = 1) = 0.1? Is it a successful explanation?
this vision appeals to me quite a bit, and I am the longer the more inclined to think in this way. Causal inference could be viewed as prediction on an intervened upon population (see also Dawid’s decision theoretic approach).
Causal inference in observational studies can be reframed as a transportability challenge: finding a predictive model on a test set that is intervened upon using training data that was not intervened upon.
In the context of randomized experiments training and test data are both intervened upon, hence their special status.
The only question i can think of that seems to elude the predictive framing is that of attribution, which has value in and of itself (law) and which I can’t see how to frame as predictive.