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Computerized adaptive testing (CAT) is a form of computer-based test that adapts to the examinee's ability level. For this reason, it has also been called tailored testing . In other words, it is a form of computer-administered test in which the next item or set of items selected to be administered depends on the correctness of the test taker's ...
The Dirac delta function, although not strictly a probability distribution, is a limiting form of many continuous probability functions. It represents a discrete probability distribution concentrated at 0 — a degenerate distribution — it is a Distribution (mathematics) in the generalized function sense; but the notation treats it as if it ...
The posterior distribution in general describes the parameter in question, and in this case the parameter itself is a discrete probability distribution, i.e. the actual categorical distribution that generated the data. For example, if 3 categories in the ratio 40:5:55 are in the observed data, then ignoring the effect of the prior distribution ...
At the same time, the probability that the sequence contains a particular subsequence (such as the word MONKEY, or the 12th through 999th digits of pi, or a version of the King James Bible) increases as the total string increases. This probability approaches 1 as the total string approaches infinity, and thus the original theorem is correct.
There are many longstanding unsolved problems in mathematics for which a solution has still not yet been found. The notable unsolved problems in statistics are generally of a different flavor; according to John Tukey, [1] "difficulties in identifying problems have delayed statistics far more than difficulties in solving problems."
Calibrated probability assessments are subjective probabilities assigned by individuals who have been trained to assess probabilities in a way that historically represents their uncertainty. [ 1 ] [ 2 ] For example, when a person has calibrated a situation and says they are "80% confident" in each of 100 predictions they made, they will get ...
For the case of a single parameter and data that can be summarised in a single sufficient statistic, it can be shown that the credible interval and the confidence interval coincide if the unknown parameter is a location parameter (i.e. the forward probability function has the form (|) = ()), with a prior that is a uniform flat distribution; [6 ...
Some state departments of insurance allow insurers to use cat modeling in their rate filings to help determine how much premium their policyholders are charged in catastrophe-prone areas. Insurance rating agencies such as A. M. Best and Standard & Poor's use cat modeling to assess the financial strength of insurers that take on catastrophe risk.