Bayesian-inspired is not Bayesian, and the difference matters

“Bayesian” has become a word people attach to anything that outputs a range instead of a point. It is worth keeping the meaning, because the difference between a posterior and an ensemble spread changes what you are allowed to say about the number.

BEACON contains both, deliberately, and calls them different things.

The one that is actually Bayesian

BEACON includes a Laplace-approximated Bayesian logistic regression. It has the parts the word implies: a Gaussian prior over the weights, a Bernoulli likelihood, MAP estimation, and a local Gaussian approximation to the posterior around that mode.

That gives you a posterior over parameters. You can ask what the model believes about a coefficient, propagate that belief into predictions, and get intervals that mean something specific under the model’s assumptions.

It is also not the strongest ranking model in the study. Which is fine — it is there as a probabilistic baseline, not a leaderboard entry.

The one that is not

The uncertainty signal that actually carries the results comes from somewhere else: a bootstrap ensemble of gradient boosting models. Train each member on a resampled version of the training data, then for each event record the mean prediction and the standard deviation across members.

That standard deviation is a genuinely useful quantity. It measures how much plausible re-draws of your training data disagree about an event, which is a reasonable proxy for “how much does this prediction depend on the particular data I happened to have.”

It is not a posterior. There is no prior, no likelihood over the gradient boosting model’s structure, and no inference procedure targeting a posterior distribution. Nothing is being conditioned on anything. It is resampling variance wearing a coat that looks similar from a distance.

So BEACON calls it Bayesian-inspired, and says why in the methods section rather than hoping nobody asks.

Why the label is load-bearing

This is not pedantry about naming. The label determines which sentences are legitimate.

With a posterior you can make calibrated probabilistic statements under the model — credible intervals mean a specific thing, and you can reason about how the prior influenced them. With bootstrap spread you can say “models trained on resampled data disagree more about this event than that one.” That is a comparative, ordinal claim. It supports ranking and escalation. It does not support “there is a 90% probability the true value lies in this range.”

The two claims sound similar in a talk. Only one of them survives someone asking what the interval is an interval over.

Practical note: pick the method that answers your question, then describe it in the weakest terms that are still true. The weaker description usually turns out to be all you needed.

What the weaker thing was enough for

The honest part of this is that the Bayesian-inspired signal did the job. BEACON uses ensemble disagreement as a human-review escalation policy: review the 10% of events the ensemble is least certain about, and see how many high-risk events that catches.

It catches 97.5% of them at the one-day horizon, against 8.3% for random escalation. For deciding where to send an analyst, an ordinal uncertainty signal is entirely sufficient. You need to know which events to look at first. You do not need a credible interval to sort a queue.

A proper posterior would have been more expensive to build, harder to explain, and no better at the task. The reason to keep the distinction is not that one method is superior. It is that the cheap method comes with a smaller set of legitimate claims, and you should know which set you are in.

A rough guide

Ranking, triage, or routing? Ensemble disagreement is usually enough, and it is cheap.
Reporting an interval someone will act on numerically? You want an actual posterior, and you should be able to state the prior.
Reasoning about parameters rather than predictions? Posterior, and the approximation matters — a Laplace approximation is local and can be poor if the posterior is skewed or multimodal.
Writing it up? Name the method precisely, even when the precise name is less impressive.

Both models, and the escalation experiment that compares them, are in the repository.