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  2. Equivalence test - Wikipedia

    en.wikipedia.org/wiki/Equivalence_test

    A very simple equivalence testing approach is the ‘two one-sided t-tests’ (TOST) procedure. [11] In the TOST procedure an upper (Δ U) and lower (–Δ L) equivalence bound is specified based on the smallest effect size of interest (e.g., a positive or negative difference of d = 0.3).

  3. Cramér–Rao bound - Wikipedia

    en.wikipedia.org/wiki/Cramér–Rao_bound

    [6] [7] It is also known as Fréchet-Cramér–Rao or Fréchet-Darmois-Cramér-Rao lower bound. It states that the precision of any unbiased estimator is at most the Fisher information; or (equivalently) the reciprocal of the Fisher information is a lower bound on its variance.

  4. Stirling's approximation - Wikipedia

    en.wikipedia.org/wiki/Stirling's_approximation

    The equivalent approximation for ln n! has an asymptotic ... The approximation may be made precise by giving paired upper and lower bounds; one such inequality ...

  5. Upper and lower bounds - Wikipedia

    en.wikipedia.org/wiki/Upper_and_lower_bounds

    The set S = {42} has 42 as both an upper bound and a lower bound; all other numbers are either an upper bound or a lower bound for that S. Every subset of the natural numbers has a lower bound since the natural numbers have a least element (0 or 1, depending on convention). An infinite subset of the natural numbers cannot be bounded from above.

  6. Limit inferior and limit superior - Wikipedia

    en.wikipedia.org/wiki/Limit_inferior_and_limit...

    Thus, the infimum or meet of a collection of subsets is the greatest lower bound while the supremum or join is the least upper bound. In this context, the inner limit, lim inf X n, is the largest meeting of tails of the sequence, and the outer limit, lim sup X n, is the smallest joining of tails of the sequence. The following makes this precise.

  7. Infimum and supremum - Wikipedia

    en.wikipedia.org/wiki/Infimum_and_supremum

    There is a corresponding greatest-lower-bound property; an ordered set possesses the greatest-lower-bound property if and only if it also possesses the least-upper-bound property; the least-upper-bound of the set of lower bounds of a set is the greatest-lower-bound, and the greatest-lower-bound of the set of upper bounds of a set is the least ...

  8. Evidence lower bound - Wikipedia

    en.wikipedia.org/wiki/Evidence_lower_bound

    In variational Bayesian methods, the evidence lower bound (often abbreviated ELBO, also sometimes called the variational lower bound [1] or negative variational free energy) is a useful lower bound on the log-likelihood of some observed data.

  9. Frame (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Frame_(linear_algebra)

    The optimal lower bound is the supremum of all lower bounds ... The frame condition is a generalization of Parseval's identity that maintains norm equivalence between ...