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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.
The results of this test must be interpreted carefully. The person's medical risk factors determine at which increment (5 mm, 10 mm, or 15 mm) of induration the result is considered positive. [12] A positive result indicates TB exposure. 5 mm or more is positive in An HIV-positive person; Persons with recent contacts with a TB patient
The medical history includes obtaining the symptoms of pulmonary TB: productive, prolonged cough of three or more weeks, chest pain, and hemoptysis. Systemic symptoms include low grade remittent fever, chills, night sweats, appetite loss, weight loss, easy fatiguability, and production of sputum that starts out mucoid but changes to purulent. [1]
Aspergilloma in an old tuberculosis cavity; healed, calcified tuberculous lesions are also present towards the right of the image Healed tuberculous cavity, where the entire left lung is destroyed. Post-tuberculosis lung disease (PTLD) is ongoing lung disease that is caused by tuberculosis (TB) but persists after the infection is cured. [1]
In clinical practice, post-test probabilities are often just estimated or even guessed. This is usually acceptable in the finding of a pathognomonic sign or symptom, in which case it is almost certain that the target condition is present; or in the absence of finding a sine qua non sign or symptom, in which case it is almost certain that the target condition is absent.
Posterior probability is a conditional probability conditioned on randomly observed data. Hence it is a random variable. For a random variable, it is important to summarize its amount of uncertainty. One way to achieve this goal is to provide a credible interval of the posterior probability. [11]
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.
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".