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Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
The above expression makes clear that the uncertainty coefficient is a normalised mutual information I(X;Y). In particular, the uncertainty coefficient ranges in [0, 1] as I(X;Y) < H(X) and both I(X,Y) and H(X) are positive or null. Note that the value of U (but not H!) is independent of the base of the log since all logarithms are proportional.
In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a quantity measured on an interval or ratio scale.. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation.
= env([0,0], [0.1, 0.25]) = [0, 0.25] where env([x 1,x 2], [y 1,y 2]) is [min(x 1,y 1), max(x 2,y 2)]. Likewise, the probability of the disjunction is surely in the interval P(A v B) = a + b − a × b = 1 − (1 − a) × (1 − b) = 1 − (1 − [0.2, 0.25]) × (1 − [0.1, 0.3]) = 1 − [0.75, 0.8] × [0.7, 0.9] = 1 − [0.525, 0.72] = [0.28 ...
Entropy Η(X) (i.e. the expected surprisal) of a coin flip, measured in bits, graphed versus the bias of the coin Pr(X = 1), where X = 1 represents a result of heads. [ 10 ] : 14–15 Here, the entropy is at most 1 bit, and to communicate the outcome of a coin flip (2 possible values) will require an average of at most 1 bit (exactly 1 bit for ...
Given some experimental measurements of a system and some computer simulation results from its mathematical model, inverse uncertainty quantification estimates the discrepancy between the experiment and the mathematical model (which is called bias correction), and estimates the values of unknown parameters in the model if there are any (which ...
(1) The Type I bias equations 1.1 and 1.2 are not affected by the sample size n. (2) Eq(1.4) is a re-arrangement of the second term in Eq(1.3). (3) The Type II bias and the variance and standard deviation all decrease with increasing sample size, and they also decrease, for a given sample size, when x's standard deviation σ becomes small ...
Note that the values at 0 and 1 are given by the limit := + = (by L'Hôpital's rule); and that "binary" refers to two possible values for the variable, not the units of information. When p = 1 / 2 {\displaystyle p=1/2} , the binary entropy function attains its maximum value, 1 shannon (1 binary unit of information); this is the case of ...