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Confusion Of The Inverse
Confusion of the inverse, also called the conditional probability fallacy or the inverse fallacy, is a logical fallacy whereupon a conditional probability is equated with its inverse; that is, given two events ''A'' and ''B'', the probability of ''A'' happening given that ''B'' has happened is assumed to be about the same as the probability of ''B'' given ''A'', when there is actually no evidence for this assumption. More formally, ''P''(''A'', ''B'') is assumed to be approximately equal to ''P''(''B'', ''A''). Examples Example 1 In one study, physicians were asked to give the chances of malignancy with a 1% prior probability of occurring. A test can detect 80% of malignancies and has a 10% false positive rate. What is the probability of malignancy given a positive test result? Approximately 95 out of 100 physicians responded the probability of malignancy would be about 75%, apparently because the physicians believed that the chances of malignancy given a positive test result were ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Informal Fallacy
Informal fallacies are a type of incorrect argument in natural language. The source of the error is not just due to the ''form'' of the argument, as is the case for formal fallacies, but can also be due to their ''content'' and ''context''. Fallacies, despite being incorrect, usually ''appear'' to be correct and thereby can seduce people into accepting and using them. These misleading appearances are often connected to various aspects of natural language, such as ambiguous or vague expressions, or the assumption of implicit premises instead of making them explicit. Traditionally, a great number of informal fallacies have been identified, including the fallacy of equivocation, the fallacy of amphiboly, the fallacies of composition and division, the false dilemma, the fallacy of begging the question, the ad hominem fallacy and the appeal to ignorance. There is no general agreement as to how the various fallacies are to be grouped into categories. One approach sometimes found in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Probability
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is and the event is known or assumed to have occurred, "the conditional probability of given ", or "the probability of under the condition ", is usually written as or occasionally . This can also be understood as the fraction of probability B that intersects with A: P(A \mid B) = \frac. For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing. For example, the conditional probability that someone unwell (sick) is coughing might be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prior Probability
In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable. Bayes' theorem calculates the renormalized pointwise product of the prior and the likelihood function, to produce the ''posterior probability distribution'', which is the conditional distribution of the uncertain quantity given the data. Similarly, the prior probability of a random event or an uncertain proposition is the unconditional probability that is assigned before any relevant evidence is taken into account. Priors can be created using a num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayes' Theorem
In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately (by conditioning it on their age) than simply assuming that the individual is typical of the population as a whole. One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference. When applied, the probabilities involved in the theorem may have different probability interpretations. With Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to Bayesia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marijuana
Cannabis, also known as marijuana among other names, is a psychoactive drug from the cannabis plant. Native to Central or South Asia, the cannabis plant has been used as a drug for both recreational and entheogenic purposes and in various traditional medicines for centuries. Tetrahydrocannabinol (THC) is the main psychoactive component of cannabis, which is one of the 483 known compounds in the plant, including at least 65 other cannabinoids, such as cannabidiol (CBD). Cannabis can be used by smoking, vaporizing, within food, or as an extract. Cannabis has various mental and physical effects, which include euphoria, altered states of mind and sense of time, difficulty concentrating, impaired short-term memory, impaired body movement (balance and fine psychomotor control), relaxation, and an increase in appetite. Onset of effects is felt within minutes when smoked, but may take up to 90 minutes when eaten. The effects last for two to six hours, depending on the amount us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slashdot
''Slashdot'' (sometimes abbreviated as ''/.'') is a social news website that originally advertised itself as "News for Nerds. Stuff that Matters". It features news stories concerning science, technology, and politics that are submitted and evaluated by site users and editors. Each story has a comments section attached to it where users can add online comments. The website was founded in 1997 by Hope College students Rob Malda, also known as "CmdrTaco", and classmate Jeff Bates, also known as "Hemos". In 2012, they sold it to DHI Group, Inc. (i.e., Dice Holdings International, which created the Dice.com website for tech job seekers). In January 2016, BIZX acquired both slashdot.org and SourceForge. In December 2019, BIZX rebranded to Slashdot Media. Summaries of stories and hyperlinks to news articles are submitted by Slashdot's own users, and each story becomes the topic of a threaded discussion among users. Discussion is moderated by a user-based moderation system. Randomly sele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monty Hall Problem
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show ''Let's Make a Deal'' and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the ''American Statistician'' in 1975. It became famous as a question from reader Craig F. Whitaker's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in ''Parade'' magazine in 1990: Vos Savant's response was that the contestant should switch to the other door. Under the standard assumptions, the switching strategy has a probability of winning the car, while the strategy that remains with the initial choice has only a probability. When the player first makes their choice, there is a chance that the car is behind one of the doors not chosen. This probability does not change after the host reveals a goat behind one of the unchosen doors. When the host provides information about the 2 unchosen do ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Base Rate Fallacy
The base rate fallacy, also called base rate neglect or base rate bias, is a type of fallacy in which people tend to ignore the base rate (i.e., general prevalence) in favor of the individuating information (i.e., information pertaining only to a specific case). Base rate neglect is a specific form of the more general extension neglect. False positive paradox An example of the base rate fallacy is the false positive paradox. This paradox describes situations where there are more false positive test results than true positives. For example, if a facial recognition camera can identify wanted criminals 99% accurately, but analyzes 10,000 people a day, the high accuracy is outweighed by the number of tests, and the program's list of criminals will likely have far more false positives than true. The probability of a positive test result is determined not only by the accuracy of the test but also by the characteristics of the sampled population. When the prevalence, the proportion of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Illicit Conversion
Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "If the lamp were broken, then the room would be dark"), and invalidly inferring its converse ("The room is dark, so the lamp is broken"), even though that statement may not be true. This arises when a consequent ("the room would be dark") has other possible antecedents (for example, "the lamp is in working order, but is switched off" or "there is no lamp in the room"). Converse errors are common in everyday thinking and communication and can result from, among other causes, communication issues, misconceptions about logic, and failure to consider other causes. The opposite statement, denying the consequent, ''is'' a valid form of argument (modus tollens). Formal description Affirming the consequent is the action of taking a true statement P \to Q and invalidly concluding its converse Q \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sensitivity And Specificity
''Sensitivity'' and ''specificity'' mathematically describe the accuracy of a test which reports the presence or absence of a condition. Individuals for which the condition is satisfied are considered "positive" and those for which it is not are considered "negative". *Sensitivity (true positive rate) refers to the probability of a positive test, conditioned on truly being positive. *Specificity (true negative rate) refers to the probability of a negative test, conditioned on truly being negative. If the true condition can not be known, a " gold standard test" is assumed to be correct. In a diagnostic test, sensitivity is a measure of how well a test can identify true positives and specificity is a measure of how well a test can identify true negatives. For all testing, both diagnostic and screening, there is usually a trade-off between sensitivity and specificity, such that higher sensitivities will mean lower specificities and vice versa. If the goal is to return the ratio at w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Converse (logic)
In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication ''P'' → ''Q'', the converse is ''Q'' → ''P''. For the categorical proposition ''All S are P'', the converse is ''All P are S''. Either way, the truth of the converse is generally independent from that of the original statement.Robert Audi, ed. (1999), ''The Cambridge Dictionary of Philosophy'', 2nd ed., Cambridge University Press: "converse". Implicational converse Let ''S'' be a statement of the form ''P implies Q'' (''P'' → ''Q''). Then the converse of ''S'' is the statement ''Q implies P'' (''Q'' → ''P''). In general, the truth of ''S'' says nothing about the truth of its converse, unless the antecedent ''P'' and the consequent ''Q'' are logically equivalent. For example, consider the true statement "If I am a human, then I am mortal." The converse of that statement is "If I am mortal, then I am ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prosecutor's Fallacy
The prosecutor's fallacy is a fallacy of statistical reasoning involving a test for an occurrence, such as a DNA match. A positive result in the test may paradoxically be more likely to be an erroneous result than an actual occurrence, even if the test is very accurate. The fallacy is named because it is typically used by a prosecutor to exaggerate the probability of a criminal defendant's guilt. The fallacy can be used to support other claims as well – including the innocence of a defendant. For instance, if a perpetrator were known to have the same blood type as a given defendant and 10% of the population to share that blood type, then one version of the prosecutor's fallacy would be to claim that, on that basis alone, the probability that the defendant is guilty is 90%. However, this conclusion is only close to correct if the defendant was selected as the main suspect based on robust evidence discovered prior to the blood test and unrelated to it (the blood match may th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
