Reporting Uncertainty Honestly

Across six lessons you built machinery for honesty: a prediction interval that really covers 90% of the time, a conformal band with a guarantee, a recalibrated probability that means what it says, a bootstrap standard error for a statistic with no formula. You can now put a defensible number on what you do not know. This final lesson is about the last, most human step: carrying that number into a decision, and saying it out loud, without lying, either by sounding more certain than you are or by dressing a rough estimate in false precision.

Rohan the real-estate agent and Nadia the rain forecaster both come back, each holding an honest number and facing a real choice: what to quote, how much to stock, how to write it down. Getting from a correct interval to an honest decision turns on four ideas, and we take them one at a time.

By the end of this lesson you will be able to:

• Separate aleatoric uncertainty (the world's own irreducible noise) from epistemic uncertainty (what more data could still teach you), and see which part of a prediction interval each one is
• Match the uncertainty tool to the question, so you quote the interval a decision actually needs
• Weigh the asymmetric cost of over- versus under-covering, and pick the coverage level or quantile a decision's stakes call for
• Communicate an estimate without false precision: a point, a range, its meaning, and its assumptions

Prerequisites: Lessons 1 to 6 of this course, especially prediction intervals and coverage, calibration, and the bootstrap and jackknife+. Base R: lm(), predict(), quantile(), vectors, a small function. A residual is actual minus predicted. Every new term is defined as it appears.

Two honest questions, one hidden split

In Lesson 6 you handed Rohan two honest numbers by resampling: a standard error for his headline median, and a jackknife+ range for one new home. Both were correct. But before you can report a number well, you have to understand what its uncertainty is made of, because not all not-knowing is the same kind.

Let us rebuild Rohan's 50 recent sales so we have something concrete to take apart. Each lesson runs in a fresh R session, so we create the data right here (run this once). Sizes are right-skewed like a real market, and price climbs with size plus honest, even scatter.

Rohan's client is back with the same 1,500 square foot flat from Lesson 1. When Rohan predicts its price, his uncertainty comes from two completely separate places, and telling them apart is the first honest move.