Term, with Synonyms and Cross-References Definition Notes and Comments

confidence interval
Synonym: interval
A range of values [a, b] determined from a sample, using a predetermined rule chosen such that, in repeated random samples from the same population, the fraction α of computed ranges will include the true value of an unknown parameter. The values a and b are called confidence limits; α is called the confidence coefficient (commonly chosen to be .95 or .99); and 1 - α is called the confidence level. (Adapted from SRA Glossary.)a Confidence intervals should not be interpreted as implying that the parameter itself has a range of values; it has only one value. For any given sample the confidence limits a and b define a random range within which the parameter of interest will lie with probability a (provided that the actual population satisfies the initial hypothesis).
constrained uncertainty See also Bayesian approach. Uncertainty about a parameter, prediction, or other entity that has been reduced by incorporating additional information, such as new physical observations. For most of the examples in this report, uncertainty is constrained using the Bayesian approach, conditioning on physical observations, producing a posterior distribution for parameters and predictions.
continuous random variable
See also cumulative distribution function, probability density function.
A random variable, X, is continuous if it has an absolutely continuous cumulative distribution function.d  
cumulative distribution function
Synonyms: cumulative distribution, cdf, distribution function
See also probability density function,
The probability that a random variable X will be less than or equal to a value x; written as P{Xx}.f,g The cdf always exists for any random variable; it is monotonic nondecreasing in x, and (being a probability 0 ≤ P{Xx} ≤ 1. If P{Xx} is absolutely continuous
probability distribution.   in x, then X is called a continuous random variable; if it is discontinuous at a finite or countably infinite number of values of x, and constant otherwise, X is called a discrete random variable.
data assimilation A recursive process for producing predictions with uncertainty regarding some process, commonly used in weather forecasting and other fields of geoscience. At a given iteration, new physical observations are combined with model-based predictions to produce updated predictions and updated estimates of the current state of the system. The combination method is usually based on Bayesian inference. The Kalman filter, the ensemble Kalman filter, and particle filters are examples of approaches with which data assimilation is carried out.
data verification and validation The process of verifying the internal consistency and correctness of data and validating that they represent real-world entities appropriate for their intended purpose or an expected range of purposes.h  
discrete random variable
See also cumulative distribution function.
A random variable that has a nonzero probability for only a finite, or countably infinite, set of values.b  

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