Around 1960, Ray Solomonoff founded the theory of universal inductive inference, the theory of prediction based on observations. Given is the beginning of some sequence of symbols. Which symbol will be next? Solomonoff's theory provides an answer that is optimal in a certain sense. Unlike Karl Popper's informal theory of inductive inference, Solomonoff's is mathematically sound. Ray Solomonoff (born 1926) invented the concept of algorithmic probability around 1960. ... Sir Karl Raimund Popper, CH, FRS (July 28, 1902 – September 17, 1994), was an Austrian and British philosopher and a professor at the London School of Economics. ...

Fundamental ingredients of the theory are the concepts of algorithmic probability and Kolmogorov complexity. The universal prior probability of any prefix p of a computable sequence x is the sum of the probabilities of all programs (for a universal computer) that compute something starting with p. Given some p and any computable but unknown probability distribution from which x is sampled, the universal prior and Bayes' theorem can be used to predict the yet unseen parts of x in optimal fashion. Around 1960, Ray Solomonoff invented the concept of algorithmic probability. ... In computer science, the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity) of an object such as a piece of text is a measure of the computational resources needed to specify the object. ... A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ... The Turing machine is an abstract machine introduced in 1936 by Alan Turing to give a mathematically precise definition of algorithm or mechanical procedure. As such it is still widely used in theoretical computer science, especially in complexity theory and the theory of computation. ... Bayes theorem is a result in probability theory, which relates the conditional and marginal probability distributions of random variables. ...

See also

• Algorithmic probability
• Kolmogorov complexity
• Confirmation bias
• Language identification in the limit

Skepticism?? Around 1960, Ray Solomonoff invented the concept of algorithmic probability. ... In computer science, the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity) of an object such as a piece of text is a measure of the computational resources needed to specify the object. ... Confirmation bias is a type of statistical bias describing the tendency to search for or interpret information in a way that confirms ones preconceptions. ... Language identification in the limit is a formal model for inductive inference. ...