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Likely

See probability, likeliness, likelihood, tendency, future, What the future holds (See also: The Dangers of Technology)

Snippet from Wikipedia: Probability

Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.

Snippet from Wikipedia: Likelihood function

The likelihood function (often simply called the likelihood) is the joint probability mass (or probability density) of observed data viewed as a function of the parameters of a statistical model. Intuitively, the likelihood function L(θx){\displaystyle {\mathcal {L}}(\theta \mid x)} is the probability of observing data x{\displaystyle x} assuming θ{\displaystyle \theta } is the actual parameter.

In maximum likelihood estimation, the arg max (over the parameter θ{\displaystyle \theta }) of the likelihood function serves as a point estimate for θ{\displaystyle \theta }, while the Fisher information (often approximated by the likelihood's Hessian matrix) indicates the estimate's precision.

In contrast, in Bayesian statistics, parameter estimates are derived from the converse of the likelihood, the so-called posterior probability, which is calculated via Bayes' rule.

Snippet from Wikipedia: Central tendency

In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution.

Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s.

The most common measures of central tendency are the arithmetic mean, the median, and the mode. A middle tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution. Occasionally authors use central tendency to denote "the tendency of quantitative data to cluster around some central value."

The central tendency of a distribution is typically contrasted with its dispersion or variability; dispersion and central tendency are the often characterized properties of distributions. Analysis may judge whether data has a strong or a weak central tendency based on its dispersion.


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likely.txt · Last modified: 2023/09/15 13:41 by 127.0.0.1

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