###### Self-Sufficient

- This forum will explore state policy strategies that can strengthen supports for Ohio learners and jobseekers, thereby increasing the likelihood that Ohioans with low incomes will find better employment opportunities and eventually become self-sufficient. (constantcontact.com)

###### displaystyle

- Roughly, given a set X {\displaystyle \mathbf {X} } of independent identically distributed data conditioned on an unknown parameter θ {\displaystyle \theta } , a sufficient statistic is a function T ( X ) {\displaystyle T(\mathbf {X} )} whose value contains all the information needed to compute any estimate of the parameter (e.g. a maximum likelihood estimate). (wikipedia.org)
- In other words, no information about the regression is lost in reducing the dimension of x {\displaystyle {\textbf {x}}} if the reduction is sufficient. (wikipedia.org)
- However, if there exists a sufficient dimension reduction R ( x ) {\displaystyle R({\textbf {x}})} with small enough dimension, a sufficient summary plot of y {\displaystyle y} versus R ( x ) {\displaystyle R({\textbf {x}})} may be constructed and visually interpreted with relative ease. (wikipedia.org)
- A^{T}{\textbf {x}}} , and the plot of y {\displaystyle y} versus A T x {\displaystyle A^{T}{\textbf {x}}} is a sufficient summary plot. (wikipedia.org)
- If S {\displaystyle {\mathcal {S}}} has basis η {\displaystyle \eta } and is a minimum DRS, then a plot of y versus η T x {\displaystyle \eta ^{T}{\textbf {x}}} is a minimal sufficient summary plot, and it is (d + 1)-dimensional. (wikipedia.org)

###### mean

- However, just because you eat a lot of red meat does not mean that you are getting sufficient amounts of B-12 in your system. (hubpages.com)
- But what should sufficient completeness mean for a rewrite theory \(\mathcal{R} = (\Sigma,E,R)\) with equations E and non-equational rules R describing concurrent transitions in a system? (springer.com)
- For example, for a Gaussian distribution with unknown mean and variance, the jointly sufficient statistic, from which maximum likelihood estimates of both parameters can be estimated, consists of two functions, the sum of all data points and the sum of all squared data points (or equivalently, the sample mean and sample variance). (wikipedia.org)
- As an example, the sample mean is sufficient for the mean (μ) of a normal distribution with known variance. (wikipedia.org)
- On the other hand, for an arbitrary distribution the median is not sufficient for the mean: even if the median of the sample is known, knowing the sample itself would provide further information about the population mean. (wikipedia.org)

###### conditions

- We give simple sufficient conditions on sample sizes that ensure existence of ε -optimal treatment rules when there are multiple treatments and outcomes are bounded. (pnas.org)
- Sufficient conditions are given allowing the automatic checking of sufficient completeness, deadlock freedom, and other related properties, by propositional tree automata modulo equational axioms such as associativity, commutativity, and identity. (springer.com)

###### summary

- A scatter plot that contains all available regression information is called a sufficient summary plot. (wikipedia.org)

###### given

- A statistic t = T(X) is sufficient for underlying parameter θ precisely if the conditional probability distribution of the data X, given the statistic t = T(X), does not depend on the parameter θ, i.e. (wikipedia.org)
- and that the conditional probability of the parameter θ given the sufficient statistic t and the conditional probability of the data x given the sufficient statistic t are statistically independent. (wikipedia.org)

###### sample

- In particular, a statistic is sufficient for a family of probability distributions if the sample from which it is calculated gives no additional information than does the statistic, as to which of those probability distributions is that of the population from which the sample was taken. (wikipedia.org)

###### statistics

- In statistics, sufficient dimension reduction (SDR) is a paradigm for analyzing data that combines the ideas of dimension reduction with the concept of sufficiency. (wikipedia.org)

###### distribution

- The concept, due to Ronald Fisher, is equivalent to the statement that, conditional on the value of a sufficient statistic for a parameter, the joint probability distribution of the data does not depend on that parameter. (wikipedia.org)