In statistics, a selection effect exists when some property of a thing is correlated with its being sampled. The classic example is a phone poll, which necessarily only reaches people who have phones. If only wealthy people have phones, then being wealthy is correlated with ever being polled in the first place. Thus the opinions of wealthy people will be overrepresented.

An observation selection effect exists when some property of a thing is correlated with the observer existing in the first place. The study of such effects is sometimes called "anthropic reasoning" or "anthropics", after the anthropic principle.

For example, if intelligence hadn't evolved, we wouldn't exist, and couldn't evaluate the probability of intelligence evolving. In a big enough universe, intelligence could evolve somewhere even if the probability of it happening was arbitrarily low. Therefore we cannot just infer that because intelligence evolved here, evolution is common, or that designing intelligence is easy.

Recent approaches to such effects have focused less on "anthropic principles" and more on candidate assumptions such as:

The self-sampling assumption, which performs a Bayesian update on the fact that you were randomly chosen out of the set of all observers.
The self-indication assumption, which favors theories in proportion to the number of observers they predict, because with more observers, you're more likely to exist at all. (Sometimes, people take this to include the Self-Sampling Assumption, using "SIA" as shorthand for "SSA+SIA".)
Full Non-indexical Conditioning, which performs a Bayesian update on the fact that there exists someone with your exact experiences.

Such assumptions are needed to determine how we choose between theories predicting different sets of observers.

One approach to anthropic reasoning that has sometimes been attempted is to derive the right principles from decision theory.

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