Borrowing priors from a sister event to seed a new one

Two weeks into a launch edition's meeting programme, the show director asked whether 38 per cent acceptance was good. Nobody could answer. The number had no comparison in the building, and the platform's benchmark figure came from a customer base of unknown shows in unknown verticals.

The comparison existed one floor up. The same portfolio ran a mature event in an adjacent vertical with four editions of proposal history, and its category level acceptance rates were sitting in a warehouse nobody had queried. Priors from a sister event are the cheapest source of a starting estimate an organiser has, and using them well takes one piece of arithmetic that has been in the statistics literature since 1961.

What can you legitimately borrow?

Category level rates, and a handful of operational settings. Not the model.

Acceptance rate per product category is the useful one. If the sister event's labelling and coding category accepts at 46 per cent across 1,880 proposals over two editions, that is a real measurement of how buyers in that category behave when a proposal lands, and there is no obvious reason for a new show in the same industry to be wildly different.

Meeting quota sizes transfer reasonably too, along with the ratio of proposals to confirmed meetings, which tells you how many proposals to generate to fill a programme. Review thresholds transfer with care.

Two things do not transfer. Weights, because they encode what your show is for and the sister event's answer is about a different show. And calibration curves, because a curve maps scores to probabilities under one score configuration, and if the new show's sub-scores are built from a different taxonomy the mapping is meaningless. What a calibration curve is and how it is fitted belongs to match score calibration in I3.

Shrinkage, and the arithmetic of n over n plus k

The instinct with borrowed data is to use it until local data exists, then switch. That produces a cliff, and it wastes the borrowed information on the day after the switch when you have 14 local observations and a lot of confidence.

The better approach blends continuously. Give the local estimate a weight of n divided by n plus k, and give the borrowed prior the remainder, where n is the number of local observations and k is a constant that says how much local data is worth as much as the prior.

Work it with k at 50. A new category has 12 local proposals, 7 accepted, so the local rate is 0.583. The weight on local data is 12 divided by 62, which is 0.194. The blended estimate is 0.194 times 0.583, plus 0.806 times 0.460, which is 0.113 plus 0.371, or 0.484.

The blend sits close to the borrowed number, which is correct, because 7 acceptances out of 12 is consistent with anything between about 0.3 and 0.8.

Now a category where the new show has run 300 proposals with a local acceptance rate of 0.380. The local weight is 300 divided by 350, which is 0.857, so the blended estimate is 0.857 times 0.380, plus 0.143 times 0.460, which is 0.326 plus 0.066, or 0.392. The prior has almost stopped mattering, and it did so without anyone flipping a switch.

This is shrinkage estimation, and it comes from a specific result. James and Stein showed at the Fourth Berkeley Symposium in 1961, in their paper on estimation with quadratic loss, that when you are estimating three or more means at once, an estimator that pulls the individual sample means towards a common value has lower total squared error than the sample means themselves. Efron and Morris took it into applied work in the Journal of the American Statistical Association in 1975, using the batting averages of 18 major league players over their first 45 at-bats of the 1970 season to predict how each would bat over the rest of the season.

Your categories are those players. Each one has a noisy local average from a small number of proposals, and pulling all of them towards a common value beats trusting each thin average on its own.

How do you choose k?

Empirically, using the sister event, which is the only place you have enough data to check anything.

Split the sister event's history in half. For each category, compute the acceptance rate in the first half and the acceptance rate in the second half. Now treat the first half as your local data and the portfolio wide rate as the prior, blend at a candidate k, and measure how well the blended estimate predicts the second half.

Run it at three values. Suppose k of 20 gives a mean squared error of 0.0042 across categories, k of 50 gives 0.0031, and k of 100 gives 0.0036. The middle value wins, and 50 goes in the config with the date and the test that produced it.

The intuition behind the number is worth holding. A k of 50 says that 50 local proposals in a category are worth as much as everything the sister event knows about it. That is a strong statement about how different two shows are, and if your two shows are nearly identical, the right k is higher, since the borrowed data deserves more weight. If they share only an industry, k should be low.

Portfolios with several mature events face a prior choice question, and averaging everything is the wrong reflex. Pick siblings by taxonomy overlap first, since a category that exists at both shows with the same definition is the only thing you are really borrowing. Where two siblings both qualify, weight them by proposal volume, so an event with 4,200 proposals contributes roughly three times what one with 1,400 does. Where they disagree sharply on a category, say 0.52 at one and 0.31 at the other, treat the disagreement as information: something about that category depends on the show, and the safe move is to widen the shrinkage towards the portfolio mean instead of picking a side.

When two shows are not sisters

The whole method rests on the assumption that acceptance in a category means the same thing at both shows, and there are four ways that breaks.

• Hosted versus open. A hosted buyer has a contractual meeting quota and a paid flight, so their acceptance rate reflects an obligation. Borrowing hosted rates for an open registration show will overstate every category.
• Taxonomy mismatch. If the sister event's packaging machinery node covers what your show splits across three nodes, the rates are not comparable and any mapping introduces error you cannot see.
• Region. Buyer behaviour in a meeting programme varies by market, and a sister event in a different region carries that difference into every borrowed number.
• Format. A show with a dedicated meeting hall and scheduled slots produces different acceptance from one where meetings happen at stands between other commitments.

Where one of these applies, shrink towards the sister event's overall mean instead of its category rates. You lose the category detail and keep the level, which is the honest amount of information transfer available.

There is a fifth issue that is easy to miss: the same buyers may attend both shows, and if so, your borrowed prior and your local data are not independent. Working out how much overlap exists means linking people across two registration files, which is a piece of work in its own right and belongs to duplicate records across shows in J1.

Retiring the prior on schedule

The blend retires the prior automatically, but somebody should still watch it, because a prior that never fades is a sign the new show is not generating enough proposals per category to learn anything.

Report two numbers per category each edition: n, and the current local weight. When a category reaches n of about 150 with k at 50, its local weight is 0.75 and the borrowed number is contributing a quarter. At that point the category is standing on its own and the prior is a tie-breaker.

Categories that stay below n of 20 across a full edition are telling you something else, which is that either the category is too fine for your exhibitor base or nobody is proposing meetings in it. Both are floor plan problems wearing a data costume.

Where this stops

Borrowing assumes the sister event's rates are themselves worth something, and they carry whatever selection effects that show's own matching created. If the mature event has been proposing meetings with its own score for three editions, its category rates describe what its score chose to propose, and importing them imports its blind spots along with its knowledge.

The second limit is the one shrinkage cannot fix. Shrinkage improves total error across many categories and it can make any individual category worse. A genuinely unusual category at your new show, where local behaviour really does differ from the sister event, gets pulled towards a number that is wrong for it, and the pull is largest exactly when local evidence is thinnest. If a category matters commercially, override the blend for it and say so in the config.

Start by running one query against your portfolio's most mature event: acceptance rate and proposal count by product category, for the last two editions. That table is your prior. Then run the split half test to pick k, which is an hour of work, and the new show has a defensible starting estimate for every category on day one, along with an answer to whether 38 per cent is good, and something better than a vendor benchmark in your matchmaking reporting. If the new show has no sister at all, the position is different and scoring on declared attributes only in I17 is where to start.