What is Bayes' sentence?
Bayes' sentence, sometimes called the Bayes government or the principle of inverse probability, is a mathematical sentence that stems very quickly from the axioms of probability theory. In practice, it is used to calculate an updated probability of a target phenomenon or hypothesis H due to the new Empirical data X and some basic information or previous probabilities.
The previous probability of a certain hypothesis is usually represented by a certain percentage between 0% and 100%, or a certain number between 0 and 1. This probability is often called degree of trust , and is different from the observer to the observer, observer, observer, observer to observer, observer, observer, observer, observer, observer, observer, observer The observer, observer, observer, because no, because there is no same experience and therefore differ for the hypotheses. Bayes' sentence in a scientific context is called Bayesian inference, which is quantitativeThe formalization of the scientific method. Allows optimal revision of the theoretical probability distribution due to experimentul results.
Bayes' Theore in the Context of Scientific Inference Says the Following: "The New Probability of Some Hypothesis H Being True (Called Posterior) Observatory This Evidence x Given That H is Actually True (Called Conditional Probability, Or Likeliiod), Times The Prior Probability of H Being True, All Divided by the Probability of X. "
Common revision of the above in terms of the result of the test contributes to the probability that the patient has cancer can be shown as the following:
p (positive | cancer)*p (cancer)
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p (positive | cancer)*p (cancer) + p (positive | ~ cancer)*p (~ cancer)
The vertical bar means "given". The probability that the patient has cancer after a positive result in a certain cancer test is equivalent to the probability of positive results due to cancer (derived from past results) times of previous probability that each person has cancer (relatively low) divided by the same number, plus the probability of false times of previous probability.
It sounds complicated, but the above equation can be used to determine the updated probability of any hypothesis due to any quantifiable experimental result.