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Probabilistic analysis of turbulent structures from two-dimensional plasma imaging

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Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.

Joint probability distribution

Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables. The joint distribution encodes the marginal distributions, i.e. the distributions of each of the individual random variables. It also encodes the conditional probability distributions, which deal with how the outputs of one random variable are distributed when given information on the outputs of the other random variable(s).

Probability theory

Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.

Probability density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.

Maximum entropy probability distribution

In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions. According to the principle of maximum entropy, if nothing is known about a distribution except that it belongs to a certain class (usually defined in terms of specified properties or measures), then the distribution with the largest entropy should be chosen as the least-informative default.

Indecomposable distribution

In probability theory, an indecomposable distribution is a probability distribution that cannot be represented as the distribution of the sum of two or more non-constant independent random variables: Z ≠ X + Y. If it can be so expressed, it is decomposable: Z = X + Y. If, further, it can be expressed as the distribution of the sum of two or more independent identically distributed random variables, then it is divisible: Z = X1 + X2. The simplest examples are Bernoulli-distributeds: if then the probability distribution of X is indecomposable.

Conditional probability distribution

In probability theory and statistics, given two jointly distributed random variables and , the conditional probability distribution of given is the probability distribution of when is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value of as a parameter. When both and are categorical variables, a conditional probability table is typically used to represent the conditional probability.

Marginal distribution

In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. This contrasts with a conditional distribution, which gives the probabilities contingent upon the values of the other variables. Marginal variables are those variables in the subset of variables being retained.

Plasma (physics)

Plasma () is one of four fundamental states of matter, characterized by the presence of a significant portion of charged particles in any combination of ions or electrons. It is the most abundant form of ordinary matter in the universe, being mostly associated with stars, including the Sun. Extending to the rarefied intracluster medium and possibly to intergalactic regions, plasma can be artificially generated by heating a neutral gas or subjecting it to a strong electromagnetic field.

Prior probability

A prior probability distribution of an uncertain quantity, often simply called the prior, is its assumed probability distribution before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable.