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Frequentist Statistical Inference
Frequentist inference is a type of statistical inference based in frequentist probability, which treats “probability” in equivalent terms to “frequency” and draws conclusions from sample-data by means of emphasizing the frequency or proportion of findings in the data. Frequentist inference underlies frequentist statistics, in which the well-established methodologies of statistical hypothesis testing and confidence intervals are founded. History of frequentist statistics Frequentism is based on the presumption that statistics represent probabilistic frequencies. This view was primarily developed by Ronald Fisher and the team of Jerzy Neyman and Egon Pearson. Ronald Fisher contributed to frequentist statistics by developing the frequentist concept of "significance testing", which is the study of the significance of a measure of a statistic when compared to the hypothesis. Neyman-Pearson extended Fisher's ideas to apply to multiple hypotheses. They posed that the ratio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Inference
Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population. In machine learning, the term ''inference'' is sometimes used instead to mean "make a prediction, by evaluating an already trained model"; in this context inferring properties of the model is referred to as ''training'' or ''learning'' (rather than ''inference''), and using a model for prediction is referred to as ''inference'' (instead of ''prediction''); se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Design Of Experiments
The design of experiments (DOE), also known as experiment design 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. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation. In its simplest form, an experiment aims at predicting the outcome by introducing a change of the preconditions, which is represented by one or more independent variables, also referred to as "input variables" or "predictor variables." The change in one or more independent variables is generally hypothesized to result in a change in one or more dependent variables, also referred to as "output variables" or "response variables." The experimental design may also identify ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German Tank Problem
German(s) may refer to: * Germany, the country of the Germans and German things **Germania (Roman era) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizenship in Germany, see also German nationality law **Germanic peoples (Roman era) * German diaspora * German language * German cuisine, traditional foods of Germany People * German (given name) * German (surname) * Germán, a Spanish name Places * German (parish), Isle of Man * German, Albania, or Gërmej * German, Bulgaria * German, Iran * German, North Macedonia * German, New York, U.S. * Agios Germanos, Greece Other uses * German (mythology), a South Slavic mythological being * Germans (band), a Canadian rock band * "German" (song), a 2019 song by No Money Enterprise * ''The German'', a 2008 short film * "The Germans", an episode of ''Fawlty Towers'' * ''The German'', a nickname for Congolese rebel André Kisase Ngandu See also * Germanic (di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intuitive Statistics
Intuitive statistics, or folk statistics, is the cognitive phenomenon where organisms use data to make generalizations and predictions about the world. This can be a small amount of sample data or training instances, which in turn contribute to inductive inferences about either population-level properties, future data, or both. Inferences can involve revising hypotheses, or beliefs, in light of probabilistic data that inform and motivate future predictions. The informal tendency for cognitive animals to intuitively generate statistical inferences, when formalized with certain axioms of probability theory, constitutes statistics as an academic discipline. Because this capacity can accommodate a broad range of informational domains, the subject matter is similarly broad and overlaps substantially with other cognitive phenomena. Indeed, some have argued that "cognition as an intuitive statistician" is an apt companion metaphor to the computer metaphor of cognition. Others appeal to a v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Significance Test
A statistical hypothesis test is a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a critical value or equivalently by evaluating a ''p''-value computed from the test statistic. Roughly 100 specialized statistical tests are in use and noteworthy. History While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see . Choice of null hypothesis Paul Meehl has argued that the epistemological importance of the choice of null hypothesis has gone largely unacknowledged. When the null hypothesis is predicted by theory, a more precise experiment will be a more severe test of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical description of a Randomness, random phenomenon in terms of its sample space and the Probability, probabilities of Event (probability theory), events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that fair coin, the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random values. Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions with special properties or for especially important applications are given specific names. Introduction A prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Variate
In probability and statistics, a random variate or simply variate is a particular outcome or ''realization'' of a random variable; the random variates which are other outcomes of the same random variable might have different values ( random numbers). A random deviate or simply deviate is the difference of a random variate with respect to the distribution central location (e.g., mean), often divided by the standard deviation of the distribution (i.e., as a standard score). Random variates are used when simulating processes driven by random influences (stochastic processes). In modern applications, such simulations would derive random variates corresponding to any given probability distribution from computer procedures designed to create random variates corresponding to a uniform distribution, where these procedures would actually provide values chosen from a uniform distribution of pseudorandom numbers. Procedures to generate random variates corresponding to a given distribut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. ''Parameter'' has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition. In addition to its technical uses, there are also extended uses, especially in non-scientific contexts, where it is used to mean defining characteristics or boundaries, as in the phrases 'test parameters' or 'game play parameters'. Modelization When a system theory, system is modeled by equations, the values that describe the system are called ''parameters''. For example, in mechanics, the masses, the dimensions and shapes (for solid bodies), the densities and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency Probability
Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability (the ''long-run probability'') as the limit of a sequence, limit of its Empirical probability, relative frequency in infinitely many Experiment (probability theory), trials. Probabilities can be found (in principle) by a repeatable objective process, as in repeated sampling (statistics), sampling from the same population (statistics), population, and are thus ideally devoid of subjectivity. The continued use of frequentist methods in scientific inference, however, has been called into question. The development of the frequentist account was motivated by the problems and paradoxes of the previously dominant viewpoint, the Classical definition of probability, classical interpretation. In the classical interpretation, probability was defined in terms of the principle of indifference, based on the natural symmetry of a problem, so, for example, the probabilities of dice game ... [...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] |
Bayesian Probability
Bayesian probability ( or ) is an interpretation of the concept of probability, in which, instead of frequency or 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 hypotheses; that is, with propositions whose 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, relevant data (evidence). The Bayesian interpretation provides a standard set of procedur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Decision
An optimal decision is a decision that leads to at least as good a known or expected outcome as all other available decision options. It is an important concept in decision theory. In order to compare the different decision outcomes, one commonly assigns a utility value to each of them. If there is uncertainty as to what the outcome will be but one has knowledge about the distribution of the uncertainty, then under the von Neumann–Morgenstern axioms the optimal decision maximizes the expected utility (a probability– weighted average of utility over all possible outcomes of a decision). Sometimes, the equivalent problem of minimizing the expected value of loss is considered, where loss is (–1) times utility. Another equivalent problem is minimizing expected regret. "Utility" is only an arbitrary term for quantifying the desirability of a particular decision outcome and not necessarily related to "usefulness." For example, it may well be the optimal decision for someone to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
