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  2. Divergence (statistics) - Wikipedia

    en.wikipedia.org/wiki/Divergence_(statistics)

    The only divergence for probabilities over a finite alphabet that is both an f-divergence and a Bregman divergence is the Kullback–Leibler divergence. [8] The squared Euclidean divergence is a Bregman divergence (corresponding to the function ⁠ x 2 {\displaystyle x^{2}} ⁠ ) but not an f -divergence.

  3. Convergence of random variables - Wikipedia

    en.wikipedia.org/wiki/Convergence_of_random...

    When X n converges in r-th mean to X for r = 2, we say that X n converges in mean square (or in quadratic mean) to X. Convergence in the r-th mean, for r ≥ 1, implies convergence in probability (by Markov's inequality). Furthermore, if r > s ≥ 1, convergence in r-th mean implies convergence in s-th mean. Hence, convergence in mean square ...

  4. Positive and negative predictive values - Wikipedia

    en.wikipedia.org/wiki/Positive_and_negative...

    The positive predictive value (PPV), or precision, is defined as = + = where a "true positive" is the event that the test makes a positive prediction, and the subject has a positive result under the gold standard, and a "false positive" is the event that the test makes a positive prediction, and the subject has a negative result under the gold standard.

  5. List of probability distributions - Wikipedia

    en.wikipedia.org/wiki/List_of_probability...

    This does not look random, but it satisfies the definition of random variable. This is useful because it puts deterministic variables and random variables in the same formalism. The discrete uniform distribution, where all elements of a finite set are equally likely. This is the theoretical distribution model for a balanced coin, an unbiased ...

  6. Statistical distance - Wikipedia

    en.wikipedia.org/wiki/Statistical_distance

    Jensen–Shannon divergence; Bhattacharyya distance (despite its name it is not a distance, as it violates the triangle inequality) f-divergence: generalizes several distances and divergences; Discriminability index, specifically the Bayes discriminability index, is a positive-definite symmetric measure of the overlap of two distributions.

  7. Bregman divergence - Wikipedia

    en.wikipedia.org/wiki/Bregman_divergence

    The only divergence on that is both a Bregman divergence and an f-divergence is the Kullback–Leibler divergence. [ 6 ] If n ≥ 3 {\displaystyle n\geq 3} , then any Bregman divergence on Γ n {\displaystyle \Gamma _{n}} that satisfies the data processing inequality must be the Kullback–Leibler divergence.

  8. Kullback–Leibler divergence - Wikipedia

    en.wikipedia.org/wiki/Kullback–Leibler_divergence

    In mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence [1]), denoted (), is a type of statistical distance: a measure of how much a model probability distribution Q is different from a true probability distribution P.

  9. Divergence - Wikipedia

    en.wikipedia.org/wiki/Divergence

    As an example, consider air as it is heated or cooled. The velocity of the air at each point defines a vector field. While air is heated in a region, it expands in all directions, and thus the velocity field points outward from that region. The divergence of the velocity field in that region would thus have a positive value.