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[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.
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.
Variational Bayesian methods are a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning.They are typically used in complex statistical models consisting of observed variables (usually termed "data") as well as unknown parameters and latent variables, with various sorts of relationships among the three types of random variables, as ...
The Cramér–Rao bound [9] [10] states that the inverse of the Fisher information is a lower bound on the variance of any unbiased estimator of θ. Van Trees (1968) and Frieden (2004) provide the following method of deriving the Cramér–Rao bound, a result which describes use of the Fisher information.
The Cramér–Rao lower bound is a lower bound of the variance of an unbiased estimator, representing the "best" an unbiased estimator can be. An efficient estimator is also the minimum variance unbiased estimator (MVUE). This is because an efficient estimator maintains equality on the Cramér–Rao inequality for all parameter values, which ...
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.
For the lower bound one first shows, using some algebra, that it is the largest term in the summation. ... Machine learning techniques arise largely from statistics ...
In statistics, the Chapman–Robbins bound or Hammersley–Chapman–Robbins bound is a lower bound on the variance of estimators of a deterministic parameter. It is a generalization of the Cramér–Rao bound; compared to the Cramér–Rao bound, it is both tighter and applicable to a wider range of problems. However, it is usually more ...