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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: ', "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. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...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''. Etymology The name's etymology is a Common Germanic noun ''*karilaz'' meaning "free man", which survives in English as churl (James (< Latin ''-us'', see Spanish/ Portuguese ''Carlos''). According to Julius Pokorny, the historical linguist and Indo-European studies, Indo-Europeanist, the root meaning of Charles is "old man", from Proto-Indo-European language, Indo-European *wikt:Appendix:Proto-Indo-E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simpson's Paradox
Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science statistics, and is particularly problematic when frequency data are unduly given causal interpretations. Judea Pearl. ''Causality: Models, Reasoning, and Inference'', Cambridge University Press (2000, 2nd edition 2009). . The paradox can be resolved when confounding variables and causal relations are appropriately addressed in the statistical modeling (e.g., through cluster analysis). Simpson's paradox has been used to illustrate the kind of misleading results that the misuse of statistics can generate. Edward H. Simpson first described this phenomenon in a technical paper in 1951; the statisticians Karl Pearson (in 1899) and Udny Yule (in 1903) had mentioned similar effects earlier. The name ''Simpson's paradox'' was introduced by Col ... [...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 benefi ... [...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. The sign of the covariance, therefore, shows the tendency in the linear relationship between the variables. If greater values of one variable mainly correspond with greater values of the other variable, and the same holds for lesser values (that is, the variables tend to show similar behavior), the covariance is positive. In the opposite case, when greater values of one variable mainly correspond to lesser values of the other (that is, the variables tend to show opposite behavior), the covariance is negative. The magnitude of the covariance is the geometric mean of the variances that are in common for the two random variables. The Pearson product-moment correlation coefficient, correlation coefficient normalizes the covariance by dividing by the geometric mean of the total variances for the two random variables. A distinction must be made between (1) the covariance of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heroin
Heroin, also known as diacetylmorphine and diamorphine among other names, is a morphinan opioid substance synthesized from the Opium, dried latex of the Papaver somniferum, opium poppy; it is mainly used as a recreational drug for its euphoric effects. Heroin is used medically in several countries to Pain reliever, relieve pain, such as during childbirth or a heart attack, as well as in opioid replacement therapy. Medical-grade diamorphine is used as a pure Hydrochloride, hydrochloride salt. Various white and brown powders sold illegally around the world as ''heroin'' are routinely diluted with cutting agents. 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 typically Drug injection, injected, usually into a vein, but it can also be snorted, smoked, or inhaled. In a clinical context, the route of administration is mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
JFK Airport
John F. Kennedy International Airport is a major international airport serving New York City and its metropolitan area. JFK Airport is located on the southwestern shore of Long Island, in Queens, New York City, bordering Jamaica Bay. It is the busiest of the seven airports in the New York airport system, the sixth-busiest airport in the United States, and the busiest international commercial airport in North America. The airport, which covers , is the largest in the New York metropolitan area. Over 90 airlines operate from JFK Airport, with nonstop or direct flights to destinations on all six inhabited continents. JFK Airport is located in the Jamaica neighborhood of Queens, southeast of Midtown Manhattan. The airport features five 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 by train. JFK is a hub for American Airlines and Delta Air Li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayes' Theorem
Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting Conditional probability, conditional probabilities, allowing one to find the probability of a cause given its effect. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to someone of a known age to be assessed more accurately by conditioning it relative to their age, rather than assuming that the person is typical of the population as a whole. Based on Bayes' law, both the prevalence of a disease in a given population and the error rate of an infectious disease test must be taken into account to evaluate the meaning of a positive test result and avoid the ''base-rate fallacy''. One of Bayes' theorem's many applications is Bayesian inference, an approach to statistical inference, where it is used to invert the probability of Realization (probability), observations given a model configuration (i.e., th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."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, . This number is often expressed as a percentage (%), ranging from 0% to 100%. 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 as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Likelihood Function
A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability of seeing that data under different parameter values of the model. It is constructed from the joint probability distribution of the random variable that (presumably) generated the observations. When evaluated on the actual data points, it becomes a function solely of the model parameters. In maximum likelihood estimation, the argument that maximizes the likelihood function serves as a point estimate for the unknown parameter, while the Fisher information (often approximated by the likelihood's Hessian matrix at the maximum) gives an indication of the estimate's precision. In contrast, in Bayesian statistics, the estimate of interest is the ''converse'' of the likelihood, the so-called posterior probability of the parameter given the observed data, which is calculated via Bayes' rule. Definition The likelihood function, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
