Bayesian reasoning

Bayesian reasoning, also called Bayesian inference or probabilistic reasoning, is a means of assessing probability in order to incorporate new information with the most accuracy. It encourages assessing confidence in a hypothesis as a matter of degree that may be adjusted depending on the reliability of new information that tends either to confirm or refute the hypothesis.

Bayes Theorum
Bayesian reasoning is derived from Bayes Theorum.

Use in medicine
Bayesian reasoning comes up in medicine and scientific research with regard to the correct interpretation of test results, particularly in accurately accounting for the possibility of a false positive or false negative. Clinicians and patients alike frequently show difficulty accurately incorporating those possibilities to predict how reliable a given test result is.

To illustrate the difference Bayesian reasoning can make in a health care setting, artificial intelligence researcher Eliezer S. Yudkowsky offers the following hypothetical. Imagine if it were the case that:"'1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening.  What is the probability that she actually has breast cancer?'"Yudkowsky cites studies in the 1970s through the 1990s in which only 15% doctors got the type of question right. Most estimated that the woman had a 70 or 80% chance of having breast cancer in light of the positive mammogram. In fact, the odds the hypothetical woman has breast cancer is 7.8%. This is because of the large number of false positives: since 99% of women in the age group do not have breast cancer and of them, 9.6% still test positive (a false negative), testing a group of 10,000 women would produce 950 false positives. Meanwhile, only 100 women (1% of the 10,000 women in the data sample) would have breast cancer, and the mammogram would detect it 80% of the time, producing 80 true positives. Thus only 80 of 1030 positive mammograms, or 7.8%, actually reflected the presence of cancer in this hypothetical.

This example emphasizes the necessity of exercising caution when revising a belief based on new information. Prior to the mammogram, a woman in this hypothetical would have expected to have a 1% chance of having breast cancer. The positive mammogram result changes the prediction, but by far less than one might estimate. Bayesian reason encourages careful attention to how much new evidence should weigh on the revision of a hypothesis.

Criticism
As Bayesian reasoning gained popularity, some critics have pointed out that it is only as useful as the evidence incorporated. They warn that Bayesian reasoning could offer legitimacy to dangerously false conclusions if based on poor evidence.

Learn more

 * Bayes' rule: Guide from Arbital.com
 * Berry, DA. "A case for Bayesianism in clinical trials." Stat Med. 1993 Aug;12(15-16):1377-93; discussion 1395-404.
 * Hornberger, J. "Introduction to Bayesian reasoning." Int J Technol Assess Health Care. 2001 Winter;17(1):9-16.