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Risk is the lack of certainty about the outcome of making a particular choice. Statistically, the level of downside risk can be calculated as the product of the probability that harm occurs (e.g., that an accident happens) multiplied by the severity of that harm (i.e., the average amount of harm or more conservatively the maximum credible amount of harm).
The log-likelihood function being plotted is used in the computation of the score (the gradient of the log-likelihood) and Fisher information (the curvature of the log-likelihood). Thus, the graph has a direct interpretation in the context of maximum likelihood estimation and likelihood-ratio tests .
This makes testing feasible when the unconstrained maximum likelihood estimate is a boundary point in the parameter space. [citation needed] Further, because the score test only requires the estimation of the likelihood function under the null hypothesis, it is less specific than the likelihood ratio test about the alternative hypothesis. [5]
If the likelihood ratio for a test in a population is not clearly better than one, the test will not provide good evidence: the post-test probability will not be meaningfully different from the pretest probability. Knowing or estimating the likelihood ratio for a test in a population allows a clinician to better interpret the result. [7]
This is consistent with the conclusions stated in the original report that published the PSI/PORT score: [1] "The prediction rule we describe accurately identifies the patients with community-acquired pneumonia who are at low risk for death and other adverse outcomes. This prediction rule may help physicians make more rational decisions about ...
When used as part of an aviation hazard analysis, a "Likelihood" is a specific probability. It is the joint probability of a hazard occurring, that hazard causing or contributing to an aircraft accident or incident, and the resulting degree of loss or harm falling within one of the defined severity categories.
For example, a risk of 9 out of 10 will usually be considered as "high risk", but a risk of 7 out of 10 can be considered either "high risk" or "medium risk" depending on context. The definition of the intervals is on right open-ended intervals but can be equivalently defined using left open-ended intervals ( τ j − 1 , τ j ] {\displaystyle ...
Risk assessment determines possible mishaps, their likelihood and consequences, and the tolerances for such events. [1] [2] The results of this process may be expressed in a quantitative or qualitative fashion. Risk assessment is an inherent part of a broader risk management strategy to help reduce any potential risk-related consequences. [1] [3]