Lesson 6 of 6 · Detection bias
Detection bias
10 minute lesson · 3 checks along the way
Your goal for this lessonCorrect a deliberately simple planet count for geometry and recovery, and explain why the result applies only to its stated population.
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Words with a dotted underline open a short definition right here in the lesson.
A discovery catalog is a selected sample
Different search methods favor different signals. A needs a favorable alignment and enough brightness measurements during the event. more readily detects stronger stellar reflex motion, all else equal. Direct imaging favors adequate separation and contrast, often making young warm giants accessible. Microlensing depends on a transient source–lens alignment. These selection effects mean the easiest planets to discover need not be the most common planets.
The target list matters too. Nearby bright stars, cool stars, crowded fields, or stars observed for many years are not interchangeable samples. Before comparing two catalogs, identify their stars, time coverage, methods, and acceptance rules. A count without that denominator measures what was reported, not automatically the underlying abundance of planets in the Galaxy. An impressive collection of discoveries can still miss an entire region of planet properties.
Separate geometry from recovery
For circular orbits with random orientations and planets small relative to their stars, the geometric transit probability is approximately Rstar/a. Express stellar radius and orbital radius a in the same units. A star of radius 0.005 au with a planet at 0.1 au gives 0.005/0.1 = 0.05, or 5%. At 1 au the probability becomes 0.5%. This is an alignment probability, not a planet-occurrence estimate.
Even an aligned transit can be missed because of noise, gaps, shallow depth, or too few repeated events. Injection-and-recovery tests add simulated signals to data and ask how often the search retrieves them. That measures for the tested signal population and pipeline. asks a different question: how many accepted candidates are actually planets? More permissive detection rules can increase recovery while admitting additional false alarms.
Check 1 of 3
10 pointsUse the reading above. You can try again without losing points.
Work through a decision
Undo two specified selection steps
Consider an invented survey of 1,000 comparable stars. In one narrow planet-size and orbit bin, each star has either zero or one planet. Every planet has a 5% transit probability, and 80% of the aligned transits are recovered. Assume all eight recovered objects are genuine planets and these efficiencies are exact. The overall detection probability is 0.05 × 0.80 = 0.04. The estimated underlying count is 8/0.04 = 200 planets.
Under the one-planet-per-star-in-this-bin assumption, that corresponds to 200/1,000 = 20% of the sampled stars. Eight divided by 1,000, or 0.8%, is only the detected fraction. Treat 200 as a model-based estimate, not an exact census: actual counts fluctuate, efficiencies have uncertainty, and stars differ. If some candidates were false positives, the inferred planet count would need a reliability correction too.
Survey selection
Original instructional expectation model, not observed catalog counts. Boxes are labels, not area-scaled population marks. Real counts fluctuate and geometry, recovery, and reliability have uncertainty; the 20% refers only to this specified stellar sample and planet bin.
Open full-size diagram in a new tab: Survey selectionCheck 2 of 3
10 pointsUse the reading above. You can try again without losing points.
Make an honest population claim
Kepler’s published completeness and reliability products let researchers examine these corrections rather than treating every missed event or false alarm as unknowable. Their use still requires a specified population, stellar properties, and analysis model. It is especially difficult to infer abundance where the search has very low sensitivity: dividing by a tiny, poorly known recovery probability can produce a large and unstable estimate.
A defensible conclusion names its domain, such as a chosen radius and period range around a defined stellar sample. It does not extend the toy survey’s 20% to every orbit, star, or planet type. Multiple methods can fill different gaps, but combining them requires their separate selection functions. The aim is to understand a population through a measured observing process, while keeping individual detections and population estimates as distinct scientific achievements.
Check 3 of 3
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Put it together
Your lesson progress
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Go to the source
Explore the evidence behind this lesson. These optional readings and videos open in a new tab.
- Read: Kepler completeness and reliability productsOfficial data products for testing search and vetting performance.
- Read: Reliability correction and occurrence ratesOriginal research showing why recovery and reliability both matter.
- Read: Geometric transit probabilitiesSection 2.2 derives the circular, small-planet approximation used here.