Determining the probability of future events based on past events
Inductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical basis for learning and the perception of patterns. It is a source of knowledge about the world.
There are three sources of knowledge: inference, communication, and deduction. Communication relays information found using other methods. Deduction establishes new facts based on existing facts. Inference establishes new facts from data. Its basis is Bayes' theorem.
Information describing the world is written in a language. For example, a simple mathematical language of propositions may be chosen. Sentences may be written down in this language as strings of characters. But in the computer it is possible to encode these sentences as strings of bits (1s and 0s). Then the language may be encoded so that the most commonly used sentences are the shortest. This internal language implicitly represents probabilities of statements.
Occam's razor says the "simplest theory, consistent with the data is most likely to be correct". The "simplest theory" is interpreted as the representation of the theory written in this internal language. The theory with the shortest encoding in this internal language is most likely to be correct.
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Inductiveprobability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical...
conclude with a general statement, the inductive prediction concludes with a specific statement about the probability that a single instance will (or will...
inductive interpretation (Ramsey, Cox) and the logical interpretation (Keynes and Carnap). There are also evidential interpretations of probability covering...
different reason: inductive reasoning. A single universal prior probability that can be substituted for each actual prior probability in Bayes's rule was...
Inductive logic programming (ILP) is a subfield of symbolic artificial intelligence which uses logic programming as a uniform representation for examples...
fundamental results in probability and statistics such as the moment-generating function, method of least squares, inductiveprobability, and hypothesis testing...
modern meaning of probability, which in contrast is a measure of the weight of empirical evidence, and is arrived at from inductive reasoning and statistical...
philosophy concerning knowledge Inductive reasoning – Method of logical reasoning Inductiveprobability – Determining the probability of future events based on...
observations. This inference from the observed to the unobserved is known as "inductive inferences". Hume, while acknowledging that everyone does and must make...
information theory that includes quantum information Formal science Inductiveprobability Info-metrics Minimum message length Minimum description length Philosophy...
different probabilities. This raises the broader question of the relation of probability theory to inductive reasoning. Karl Popper argued that probability theory...
unknown but computable probability distribution. It is a formal inductive framework that combines two well-studied principles of inductive inference: Bayesian...
mathematician who invented algorithmic probability, his General Theory of Inductive Inference (also known as Universal Inductive Inference), and was a founder...
anthropologist (1904–1980) Heuristic – Problem-solving method Inductiveprobability – Determining the probability of future events based on past events Logical reasoning –...
Studies in Inductive Logic and Probability. Vol. 1. The University of California Press. Jeffrey, Richard C., ed. (1980). Studies in Inductive Logic and...
frequentist statistics (so-called probability matching priors). Such methods are used in Solomonoff's theory of inductive inference. Constructing objective...
paradox Forecast verification Inductiveprobability § Removing theories without predictive power Predictive probability of success § Relationship with...
forms of inductive reasoning is denied. Some forms of deductivism express this in terms of degrees of reasonableness or probability. Inductive inferences...
segmentation, etc. Algorithmic probability Algorithmic information theory Grammar induction Inductive inference Inductiveprobability Kolmogorov complexity –...
using data analysis to infer properties of an underlying distribution of probability. Inferential statistical analysis infers properties of a population,...
Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability as the limit of its relative frequency in...
idealized form, the data-generating process. When referring specifically to probabilities, the corresponding term is probabilistic model. All statistical hypothesis...
An appeal to probability (or appeal to possibility, also known as possibiliter ergo probabiliter, "possibly, therefore probably") is the logical fallacy...
relational model ProbabilityProbability bounds analysis Probability box Probability density function Probability distribution Probability distribution function...
conventional quantified classical probability. Here Keynes considers under what circumstances conventional inductive reasoning might be applicable to both...
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