|
Reference Class Problem
In statistics, the reference class problem is the problem of deciding what class to use when calculating the probability applicable to a particular case. For example, to estimate the probability of an aircraft crashing, we could refer to the frequency of crashes among various different sets of aircraft: all aircraft, this make of aircraft, aircraft flown by this company in the last ten years, etc. In this example, the aircraft for which we wish to calculate the probability of a crash is a member of many different classes, in which the frequency of crashes differs. It is not obvious which class we should refer to for this aircraft. In general, any case is a member of very many classes among which the frequency of the attribute of interest differs. The reference class problem discusses which class is the most appropriate to use. More formally, many arguments in statistics take the form of a statistical syllogism: #X proportion of F are G #I is an F #Therefore, the chance that I is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Shonubi
Charles is a masculine given name predominantly found in English and French speaking countries. It is from the French form ''Charles'' of the Proto-Germanic name (in runic alphabet) or ''*karilaz'' (in Latin alphabet), whose meaning was "free man". The Old English descendant of this word was '' Ċearl'' or ''Ċeorl'', as the name of King Cearl of Mercia, that disappeared after the Norman conquest of England. The name was notably borne by Charlemagne (Charles the Great), and was at the time Latinized as ''Karolus'' (as in ''Vita Karoli Magni''), later also as '' Carolus''. Some Germanic languages, for example Dutch and German, have retained the word in two separate senses. In the particular case of Dutch, ''Karel'' refers to the given name, whereas the noun ''kerel'' means "a bloke, fellow, man". Etymology The name's etymology is a Common Germanic noun ''*karilaz'' meaning "free man", which survives in English as churl (< Old English ''ċeorl''), which developed its depr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectrum Bias
In biostatistics, spectrum bias refers to the phenomenon that the performance of a diagnostic test may vary in different clinical settings because each setting has a different mix of patients. Because the performance may be dependent on the mix of patients, performance at one clinic may not be predictive of performance at another clinic. These differences are interpreted as a kind of ''bias''. Mathematically, the spectrum bias is a sampling bias and not a traditional statistical bias; this has led some authors to refer to the phenomenon as ''spectrum effects'', whilst others maintain it is a bias if the true performance of the test differs from that which is 'expected'. Usually the performance of a diagnostic test is measured in terms of its sensitivity and specificity and it is changes in these that are considered when referring to spectrum bias. However, other performance measures such as the likelihood ratios may also be affected by spectrum bias. Generally spectrum bias is co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reference Class Forecasting
Reference class forecasting or comparison class forecasting is a method of predicting the future by looking at similar past situations and their outcomes. The theories behind reference class forecasting were developed by Daniel Kahneman and Amos Tversky. The theoretical work helped Kahneman win the Nobel Prize in Economics. Reference class forecasting is so named as it predicts the outcome of a planned action based on actual outcomes in a reference class of similar actions to that being forecast. Discussion of which reference class to use when forecasting a given situation is known as the reference class problem. Overview Kahneman and Tversky Decision Research Technical Report PTR-1042-77-6. In found that human judgment is generally optimistic due to overconfidence and insufficient consideration of distributional information about outcomes. People tend to underestimate the costs, completion times, and risks of planned actions, whereas they tend to overestimate the benefits of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Syllogism
A statistical syllogism (or proportional syllogism or direct inference) is a non-deductive syllogism. It argues, using inductive reasoning, from a generalization true for the most part to a particular case. Introduction Statistical syllogisms may use qualifying words like "most", "frequently", "almost never", "rarely", etc., or may have a statistical generalization as one or both of their premises. ''For example:'' #Almost all people are taller than 26 inches #Gareth is a person #Therefore, Gareth is taller than 26 inches Premise 1 (the major premise) is a generalization, and the argument attempts to draw a conclusion from that generalization. In contrast to a deductive syllogism, the premises logically support or confirm the conclusion rather than strictly implying it: it is possible for the premises to be true and the conclusion false, but it is not likely. ''General form:'' #X proportion of F are G #I is an F #I is a G In the abstract form above, F is called the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariance
In probability theory and statistics, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values (that is, the variables tend to show similar behavior), the covariance is positive. In the opposite case, when the greater values of one variable mainly correspond to the lesser values of the other, (that is, the variables tend to show opposite behavior), the covariance is negative. The sign of the covariance therefore shows the tendency in the linear relationship between the variables. The magnitude of the covariance is not easy to interpret because it is not normalized and hence depends on the magnitudes of the variables. The normalized version of the covariance, the correlation coefficient, however, shows by its magnitude the strength of the linear relation. A distinction must be made between (1) the covariance of two random ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heroin
Heroin, also known as diacetylmorphine and diamorphine among other names, is a potent opioid mainly used as a recreational drug for its euphoric effects. Medical grade diamorphine is used as a pure hydrochloride salt. Various white and brown powders sold illegally around the world as heroin have variable "cuts". Black tar heroin is a variable admixture of morphine derivatives—predominantly 6-MAM (6-monoacetylmorphine), which is the result of crude acetylation during clandestine production of street heroin. Heroin is used medically in several countries to relieve pain, such as during childbirth or a heart attack, as well as in opioid replacement therapy. It is typically injected, usually into a vein, but it can also be smoked, snorted, or inhaled. In a clinical context, the route of administration is most commonly intravenous injection; it may also be given by intramuscular or subcutaneous injection, as well as orally in the form of tablets. The onset of effects is usuall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
JFK Airport
John F. Kennedy International Airport (colloquially referred to as JFK Airport, Kennedy Airport, New York-JFK, or simply JFK) is the main international airport serving New York City. The airport is the busiest of the seven airports in the Aviation in the New York metropolitan area, New York airport system, the List of the busiest airports in the United States, 13th-busiest airport in the United States, and the List of busiest airports by international passenger traffic#2018 statistics, busiest international air passenger gateway into North America. Over 90 airlines operate from the airport, with nonstop or direct flights to destinations in all six inhabited continents. JFK is located in the Jamaica, Queens, Jamaica neighborhood of Queens, southeast of Midtown Manhattan. The airport features six passenger terminals and four runways. It is primarily accessible via car, bus, shuttle, or other vehicle transit via the JFK Expressway or Interstate 678 (Van Wyck Expressway), or via t ... [...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] |
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Likelihood Function
The likelihood function (often simply called the likelihood) represents the probability of random variable realizations conditional on particular values of the statistical parameters. Thus, when evaluated on a given sample, the likelihood function indicates which parameter values are more ''likely'' than others, in the sense that they would have made the observed data more probable. Consequently, the likelihood is often written as \mathcal(\theta\mid X) instead of P(X \mid \theta), to emphasize that it is to be understood as a function of the parameters \theta instead of the random variable X. In maximum likelihood estimation, the arg max of the likelihood function serves as a point estimate for \theta, while local curvature (approximated by the likelihood's Hessian matrix) indicates the estimate's precision. Meanwhile in Bayesian statistics, parameter estimates are derived from the converse of the likelihood, the so-called posterior probability, which is calculated via Bayes' r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Probability
Bayesian probability is an Probability interpretations, interpretation of the concept of probability, in which, instead of frequentist probability, frequency or propensity probability, propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with Hypothesis, hypotheses; that is, with propositions whose truth value, truth or falsity is unknown. In the Bayesian view, a probability is assigned to a hypothesis, whereas under frequentist inference, a hypothesis is typically tested without being assigned a probability. Bayesian probability belongs to the category of evidential probabilities; to evaluate the probability of a hypothesis, the Bayesian probabilist specifies a prior probability. This, in turn, is then updated to a posterior probability in the light of new, re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> Probability")