Glossary/Bayesian inference
What is bayesian inference?
Bayesian inference is a way of estimating an unknown quantity that produces a whole range of plausible values with their relative credibility, rather than a single best guess. It starts from a prior — what is believed before seeing the data — updates it with the evidence, and returns a posterior distribution. For marketplace sellers the practical significance is not philosophical: it is that a campaign with eleven orders and a campaign with eleven thousand should not be treated with the same confidence, and a method that returns only a point estimate has no way to express the difference.
01/Formula
Formula
posterior(θ | data) ∝ likelihood(data | θ) × prior(θ)
Read as: what you believe now = what the data says,
weighted by what you believed before.Example
Two Shopee campaigns, both showing a 4% conversion rate. A: 2 orders from 50 clicks → credible range roughly 1% to 13% B: 400 orders from 10,000 → credible range roughly 3.6% to 4.4% Same point estimate. A budget decision that treats them identically is making a large bet on campaign A that nobody chose to make.
02/In detail
Why does thin data need a different method?
Because a point estimate on thin data is mostly noise wearing a decimal point. A campaign with a handful of orders, or a product with three weeks of sales history, contains very little information, and any method that compresses it to one number throws away the most decision-relevant fact about it — that it could easily be much better or much worse than it looks. Bayesian estimation keeps that fact. It also lets a sparse product borrow strength from similar ones: if forty products in a category behave alike, the estimate for the one with three weeks of data can be pulled toward what the group does, which is both more accurate and more stable than fitting it alone.
What is a prior, and does it bias the answer?
A prior is what the model assumes before it sees this particular product’s data — for instance, that a conversion rate is somewhere in the low single digits rather than at 80%. It matters most when data is thin and matters progressively less as data accumulates, which is exactly the behaviour you want: it prevents a two-order campaign from claiming a 100% conversion rate, and it gets out of the way once a campaign has real history. A prior can bias results if it is chosen badly, and the honest defence is to make it explicit and check that conclusions do not hinge on it, rather than to pretend that methods without priors have no assumptions.
How does uncertainty change a decision?
It changes the question from “what is the best guess?” to “what happens across the range of things that could be true?”. Once an estimate is a distribution, you can ask how often an action beats the alternative, how bad the bad cases are, and whether the difference between two options is real or within noise. Those are different questions with different answers, and several of them can disagree — a campaign can have a positive average outcome and lose money on most days. Knowing which question a recommendation answered is usually more important than the recommendation itself.
03/Why it matters
The trap, in one paragraph.
Marketplace sellers make high-frequency decisions on thin, lumpy, noisy data: campaigns with single-digit daily orders, products with weeks rather than years of history, prices that changed while three other things also changed. A method that reports a single number for each of these implies a precision that does not exist, and the resulting decisions swing with the noise. Carrying the uncertainty explicitly is what allows a system to act confidently where the evidence is strong and hold back where it is not.
Common mistake
Reading a credible range as pessimism. A wide range is not the model hedging; it is an accurate statement about how little the data supports. The correct response to a wide range is usually to size the action to match it — a smaller budget change, a longer observation window — rather than to ignore the range and act on the midpoint.
04/In DataGlass
How Bayesian inference is used in DataGlass.
DataGlass estimates demand response, conversion, and cost parameters as distributions rather than point values, so recommendations can be scaled to the strength of the evidence behind them. Where a product or campaign is too sparse to support a confident recommendation, the surface says so rather than producing a number that looks authoritative.
05/Sources
- [1] Bayesian inference — overview
The prior-likelihood-posterior formulation and the role of the posterior distribution as the output of estimation.
- [2] Russo, Van Roy, Kazerouni, Osband & Wen — A Tutorial on Thompson Sampling (arXiv:1707.02038)
A readable account of why posterior uncertainty, rather than a point estimate, is what allows sequential decisions to balance learning against earning.