Bayes law
Bayes law
Scientists are increasingly relying on genetics to improve their understanding of risk factors for patients. A patient prone to type II diabetes, for example, may live a longer healthier life by being very cautious of sugary and fatty foods. Scientists often apply bayes rule in these situations to help understand the statistical probability of one event given the occurrence of another event. In mathematics this is written as a manipulation of P(A) (the probability of event a) and P(B) )(the probability of event B). Thus Bayes law is written as P(A | B) (the probability of event a occurring given event B.
The National Library of Medicine’s National Center for Bio Technology Information explains in their article entitled Bayesian Analysis and Risk Assessment in Genetic Counseling and Testing how scientists apply Bayes law to discover the statistical likelyhood of a disease developing given the presence of a certain gene. Scientists start with two mutually exclusive hypotheses and conduct tests to conclude the probability of each respective hypothesis as well as both hypothesis. In a person this may look like them having DNA strand X as hypothesis A and having Lung Cancer as hypothesis B. Scientists would test different patients to identify what the probability of a certain patient having DNA X P(X) is, what the probability of a patient having Lung Cancer P(LC) is, and what the probability of a patient having both DNA X and lung Cancer is. Age and other factors of course need to be controlled for but using this information scientists may use Bayes law to determine someone’s predisposition to develop lung cancer.
Lets say, for example I’m 35 and my doctor identifies that I have DNA strand X. In research they studied over 1000 people aged 70 and above and discovered that P(X) = 0.05, P(LC) = 0.01 and P(X & LC) = 0.006 thus by using the equation P(A | B) = P(A & B) / P(B) = P(LC | X) = P(X & LC) / P(X) = 0.006/0.05 = 0.12 we know that the probability that I develop Lung Cancer by age 70 is 0.12. This figure is twelve times higher than the average test subject without control for DNA strand X and thus would inform me that smoking cigarettes would be a very bad idea for me.
This science is vastly improving the health of people across the Globe and relies heavily on Bayes law and Bayesian reasoning.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1867463/
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