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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).
In frequentist inference, the likelihood ratio is the basis for a test statistic, the so-called likelihood-ratio test. By the Neyman–Pearson lemma, this is the most powerful test for comparing two simple hypotheses at a given significance level. Numerous other tests can be viewed as likelihood-ratio tests or approximations thereof. [15]
Probabilistic risk assessment (PRA) is a systematic and comprehensive methodology to evaluate risks associated with a complex engineered technological entity (such as an airliner or a nuclear power plant) or the effects of stressors on the environment (probabilistic environmental risk assessment, or PERA).
The likelihood-ratio test, also known as Wilks test, [2] is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. [3] In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent.
Pre-test probability: For example, if about 2 out of every 5 patients with abdominal distension have ascites, then the pretest probability is 40%. Likelihood Ratio: An example "test" is that the physical exam finding of bulging flanks has a positive likelihood ratio of 2.0 for ascites.
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.
The Cox partial likelihood, shown below, is obtained by using Breslow's estimate of the baseline hazard function, plugging it into the full likelihood and then observing that the result is a product of two factors. The first factor is the partial likelihood shown below, in which the baseline hazard has "canceled out".
Qualitative risk analysis is a technique used to quantify risk associated with a particular hazard. Risk assessment is used for uncertain events that could have many outcomes and for which there could be significant consequences. Risk is a function of probability of an event (a particular hazard occurring) and the consequences given the event ...