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In Bayesian statistics, the posterior predictive distribution is the distribution of possible unobserved values conditional on the observed values. [1] [2]Given a set of N i.i.d. observations = {, …,}, a new value ~ will be drawn from a distribution that depends on a parameter , where is the parameter space.
In the context of Bayesian statistics, the posterior probability distribution usually describes the epistemic uncertainty about statistical parameters conditional on a collection of observed data. From a given posterior distribution, various point and interval estimates can be derived, such as the maximum a posteriori (MAP) or the highest ...
For example, the incidence of breast cancer in a woman in the United Kingdom at age 55 to 59 is estimated at 280 cases per 100.000 per year, [6] and the risk factor of having been exposed to high-dose ionizing radiation to the chest (for example, as treatments for other cancers) confers a relative risk of breast cancer between 2.1 and 4.0, [7 ...
Credible intervals are typically used to characterize posterior probability distributions or predictive probability distributions. [1] Their generalization to disconnected or multivariate sets is called credible region. Credible intervals are a Bayesian analog to confidence intervals in frequentist statistics. [2]
Predictive power is a Bayesian power. A parameter in Bayesian setting is a random variable. Predictive power is a function of a parameter(s), therefore predictive power is also a variable. Both conditional power and predictive power use statistical significance as success criteria. However statistical significance is often not enough to define ...
Beyond that, cross-validation techniques [51] and predictive checks [52] [53] represent promising future strategies to evaluate the stability and out-of-sample predictive validity of ABC inferences. This is particularly important when modeling large data sets, because then the posterior support of a particular model can appear overwhelmingly ...
The positive predictive value (PPV), or precision, is defined as = + = where a "true positive" is the event that the test makes a positive prediction, and the subject has a positive result under the gold standard, and a "false positive" is the event that the test makes a positive prediction, and the subject has a negative result under the gold standard.
Staging of breast cancer is one aspect of breast cancer classification that assists in making appropriate treatment choices, when considered along with other classification aspects such as estrogen receptor and progesterone receptor levels in the cancer tissue, the human epidermal growth factor receptor 2 status, menopausal status, and the ...