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If all 1,000 take the test, 82 of those with the disease will get a true positive result (sensitivity of 90.1%), 9 of those with the disease will get a false negative result (false negative rate of 9.9%), 827 of those without the disease will get a true negative result (specificity of 91.0%), and 82 of those without the disease will get a false ...
In other words, if X and Y are random variables that take different values with probability zero, then the expectation of X will equal the expectation of Y. If X = c {\displaystyle X=c} (a.s.) for some real number c , then E [ X ] = c . {\displaystyle \operatorname {E} [X]=c.}
Consider the estimator of θ based on binomial sample x~b(θ,n) where θ denotes the probability for success. Assuming θ is distributed according to the conjugate prior, which in this case is the Beta distribution B(a,b), the posterior distribution is known to be B(a+x,b+n-x). Thus, the Bayes estimator under MSE is
A consistent estimator is an estimator whose sequence of estimates converge in probability to the quantity being estimated as the index (usually the sample size) grows without bound. In other words, increasing the sample size increases the probability of the estimator being close to the population parameter.
Having done so, it is then desired to predict the accident rate of each customer in the sample. As above, one may use the conditional expected value of the accident rate Θ given the observed number of accidents during the baseline period. Thus, if a customer suffers six accidents during the baseline period, that customer's estimated accident ...
An efficient estimator is an estimator that estimates the quantity of interest in some “best possible” manner. The notion of “best possible” relies upon the choice of a particular loss function — the function which quantifies the relative degree of undesirability of estimation errors of different magnitudes.
where is the instance, [] the expectation value, is a class into which an instance is classified, (|) is the conditional probability of label for instance , and () is the 0–1 loss function: L ( x , y ) = 1 − δ x , y = { 0 if x = y 1 if x ≠ y {\displaystyle L(x,y)=1-\delta _{x,y}={\begin{cases}0&{\text{if }}x=y\\1&{\text{if }}x\neq y\end ...
In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...