Why visible assumptions may be more objective – and more useful – than models that claim to have none.
By Atul Mohan, PhD
For more than two decades, Atul Mohan, PhD, has worked where advanced analytics, AI, marketing measurement, and executive decision-making meet. A Princeton-trained data scientist with leadership experience across American Express, Interpublic Group, Omnicom, Teachers Federal Credit Union, and Brainlabs, he brings a rare combination of technical depth and practical judgment to one of analytics’ most misunderstood questions: where assumptions belong.
The Myth of Objectivity
The claim that Bayesian methods introduce subjectivity gets the situation exactly backwards.
There is a comfortable belief in a lot of analytics organizations that Bayesian methods are the subjective ones. You are putting your beliefs into the model, the reasoning goes, so of course you get your beliefs back out. Better to use a method that lets the data speak for itself.
I have heard some version of this from smart people for twenty years, and I think it is close to the opposite of the truth.
Take marketing mix modeling, where the problem is about as stark as it gets. You have maybe a hundred and fifty weekly observations. You have a dozen media channels whose spend moves together because a human being planned them together in the same meeting. And you are trying to estimate, for each channel, a coefficient, a carryover parameter, and the shape of a saturation curve.
The data cannot do that. There is not enough independent variation in it to identify that many parameters. Something has to narrow the solution space, and something always does.
In a Bayesian model you write that something down. You state that television carryover probably sits in a certain range, because you know how television is bought and how people watch it. You state that paid search has almost none, because someone searching for a product either converts or does not. You put a prior on saturation informed by where you have historically watched returns flatten out.
Every one of those statements is visible. Every one of them can be challenged by a colleague who knows the channel better than you do. And every one can be tested by rerunning the model under a different assumption to see how much the answer moves.
When Assumptions Go Underground
Now consider the alternative. In a vendor model those same constraints exist as defaults sitting in a codebase you are not permitted to inspect. In a regularized frequentist model they exist as a penalty term whose strength somebody selected, probably through cross-validation, probably without documenting why that particular procedure was appropriate for this particular problem.
The assumptions did not go away. They went underground.
This becomes concrete at the worst possible moment, which is when a model tells someone something they do not want to hear.
A channel owner looks at a result that undercuts their budget and asks why. If your assumptions are explicit, you now have a real conversation. Was the prior on their channel reasonable? Here is the posterior under a weaker one. Here is how much the data moved it. That is two professionals disagreeing productively about a parameter, and it is a conversation that can actually conclude.
If the assumptions are buried, the conversation is about whether the model is legitimate. Nobody wins that argument, because there is nothing specific to argue about. It gets resolved by seniority, which means measurement has quietly become politics with charts attached. I have sat in that meeting more times than I would like and the outcome is always the same. The model gets described as directional, which is corporate language for shelved.
Experiments Need Somewhere to Live
There is a second advantage I think gets underrated, and it has to do with experiments.
If you run a geographic holdout and learn something real about a channel’s incremental contribution, a Bayesian framework gives you somewhere to put that knowledge. It enters as a prior on the relevant coefficient. The posterior reflects both the experiment and the observational data, weighted by how precise each one is. The experiment changes the budget recommendation. It does not sit in a separate deck next to the model, waiting for someone to reconcile the two by hand and by instinct.
Without that mechanism, and most organizations do not have one, you end up holding two numbers and no procedure. The model says one thing. The test says another. Whichever has more institutional support wins, and the losing number gets filed away.
This is worth dwelling on because it points at something larger about how measurement functions inside companies. An organization that runs experiments and cannot systematically fold the results back into its models is not learning. It is accumulating facts that expire. Somebody remembers the holdout from eighteen months ago, roughly, and mentions it in a meeting, and it carries exactly as much weight as the confidence of the person remembering it.
A formal updating mechanism is not a statistical nicety. It is institutional memory with a procedure attached.
The Honest Objection to Priors
I want to give the honest objection its due, because it is a real one.
Priors can absolutely be abused. Set them tightly enough and you will recover whatever you assumed, wrapped in credible intervals that make an assumption look like evidence. I have seen this done, occasionally on purpose, more often through a kind of unconscious drift where a modeler tries several specifications and stops when the output stops causing arguments.
Which is why sensitivity analysis is not optional and should never be treated as an appendix. Report the posterior under a tight prior, under a weak one, and under a prior centered somewhere you personally find implausible. If the answer barely moves, the data is doing the work and you can say so with confidence. If it moves substantially, you have learned that your result is mostly an assumption, and knowing that is worth more than the result was.
A useful discipline is to decide your priors before you see the fit, and to write down why. It takes ten minutes and it makes it nearly impossible to quietly tune your way toward the answer you wanted. Preregistration is standard practice in clinical research for exactly this reason and there is no principled argument against applying a lighter version of it to commercial modeling.
What a Prior Really Represents
There is a further point about what priors are actually made of, which often gets lost in the methodological argument.
A prior is not a guess. At its best it is accumulated knowledge from outside the current dataset. It is what the last three years of testing told you. It is what somebody who has bought television for twenty years knows about how a flight decays. It is the published literature on category elasticities. All of that is real information, and a method that has no way to incorporate it is not being objective, it is being forgetful.
The best mix models I have worked on were the ones where the media planners were in the room while the priors were being set. Not because they understood the mathematics, but because they knew things about the channels that were not in the data and never would be. Cost curves that move seasonally. A creative refresh that landed mid-flight. A competitor who went dark for six weeks.
That conversation also had a side effect I did not anticipate the first time. Planners who help set the assumptions do not dismiss the output when it disagrees with them. They argue with it specifically, which is a far more productive place to be.
The Test for Analytics Leaders
If you are running an analytics function, the test I would apply is not whether your team uses Bayesian methods. Plenty of good work is done without them and plenty of bad work is done with them. The test is whether anyone in the organization can tell you what your models assume when the data is thin.
If the answer is no, you do not have an objective model. You have an opaque one, and those are not the same thing, though they can look identical in a presentation and produce identical numbers right up until the moment somebody needs to defend one.
I would rather work with an analyst who shows me a prior I disagree with than one who tells me their method has no assumptions in it. The first person is a colleague I can argue with. The second is either mistaken about how their own tools work, or selling me something.
About the author
Atul Mohan, PhD, is a data and AI executive whose work spans data science, marketing analytics, measurement strategy, and the translation of complex technical systems into business decisions.
