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In
probability Probability is the branch of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained ...

probability
and
statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...

statistics
, base rate generally refers to the (base) class probabilities unconditioned on featural evidence, frequently also known as prior probabilities. For example, if it were the case that 1% of the public were "medical professionals", and 99% of the public were ''not'' "medical professionals", then the base rate of medical professionals is simply 1%. In the
sciences Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is something that is truth, true. The usual test for a statement of ...

sciences
, including
medicine Medicine is the science Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity, awareness, or understanding of someone or something, such as facts ( descriptive knowledge), skills (proced ...

medicine
, the base rate is critical for comparison. It may at first seem impressive that 1,000 people beat their winter cold while using 'Treatment X', until we look at the entire 'Treatment X' population and find that the base rate of success is only 1/100 (i.e. 100,000 people tried the treatment, but the other 99,000 people never really beat their winter cold). The treatment's effectiveness is clearer when such base rate information (i.e. "1,000 people... out of how many?") is available. Note that controls may likewise offer further information for comparison; maybe the
control group In the design of experiments The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation ...

control group
s, who were using no treatment at all, had their own base rate success of 5/100. Controls thus indicate that 'Treatment X' makes things worse, despite that initial proud claim about 1,000 people. The normative method for integrating base rates ( prior probabilities) and featural evidence (
likelihood In statistics, the likelihood function (often simply called the likelihood) measures the goodness of fit of a statistical model to a Sample (statistics), sample of data for given values of the unknown Statistical parameter, parameters. It is formed ...
s) is given by
Bayes' rule In probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expr ...
.


The base rate fallacy

A large number of psychological studies have examined a phenomenon called base-rate neglect'' or ''
base rate fallacy The base rate fallacy, also called base rate neglect or base rate bias, is a type of fallacy A fallacy is the use of Validity (logic), invalid or otherwise faulty reasoning, or "wrong moves" in the construction of an argument. A fallacious argument ...
in which category base rates are not integrated with featural evidence in the normative manner. Mathematician
Keith Devlin Keith J. Devlin (born 16 March 1947) is a British mathematician and popular science Popular science (also called pop-science or popsci) is an interpretation of science Science (from the Latin word ''scientia'', meaning "knowledge") is a ...
provides an illustration of the risks of this: He asks us to imagine that there is a type of cancer that afflicts 1% of all people. A doctor then says there is a test for that cancer which is about 80%
reliable Reliability, reliable, or unreliable may refer to: Science, technology, and mathematics Computing * Data reliability (disambiguation), Data reliability, a property of some disk arrays in computer storage * High availability * Reliability (computer ...
. He also says that the test provides a positive result for 100% of people who have the cancer, but it also results in a 'false positive' for 20% of people - who do not have the cancer. Now, if we test positive, we may be tempted to think it is 80% likely that we have the cancer. Devlin explains that, in fact, our odds are less than 5%. What is missing from the jumble of statistics is the most relevant base rate information. We should ask the doctor, ''"Out of the number of people who test positive (this is the base rate group that we care about), how many have the cancer?"'' In assessing the probability that a given individual is a member of a particular class, we must account for other information besides the base rate. In particular, we must account for featural evidence. For example, when we see a person wearing a white doctor's coat and
stethoscope The stethoscope is an acoustic medical Medicine is the science and Praxis (process) , practice of caring for a patient, managing the diagnosis, prognosis, Preventive medicine, prevention, therapy, treatment, Palliative care , palliation o ...

stethoscope
, and prescribing medication, we have evidence which may allow us to conclude that the probability of this ''particular'' individual being a "medical professional" is considerably greater than the category base rate of 1%.


References

{{Reflist Epidemiology Psychometrics
Bayesian statistics {{JEL code, C11 Statistical theory Conditional probability Mathematical and quantitative methods (economics) ...
Machine learning