Predictive inference
Encyclopedia
Predictive inference is an approach to statistical inference
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...

 that emphasizes the prediction
Prediction
A prediction or forecast is a statement about the way things will happen in the future, often but not always based on experience or knowledge...

 of future observations based on past observations.

Initially, predictive inference was based on observable parameters and it was the main purpose of studying probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

, but it fell out of favor in the 20th century due to a new parametric approach pioneered by Bruno de Finetti
Bruno de Finetti
Bruno de Finetti was an Italian probabilist, statistician and actuary, noted for the "operational subjective" conception of probability...

. The approach modeled phenomena as a physical system observed with error (e.g., celestial mechanics
Celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...

). De Finetti's idea of exchangeability–-that future observations should behave like past observations–-came to the attention of the English-speaking world with the 1974 translation from French of his 1937 book, and has since been propounded by such statisticians as Seymour Geisser
Seymour Geisser
Seymour Geisser was a statistician noted for emphasizing the role of prediction in statistical inference – see predictive inference. In his book , he held that conventional statistical inference about unobservable population parameters amounts to inference about things that do not exist,...

.
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