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List Of Probability Topics
This is a list of probability topics. It overlaps with the (alphabetical) list of statistical topics. There are also the outline of probability and catalog of articles in probability theory. For distributions, see List of probability distributions. For journals, see list of probability journals. For contributors to the field, see list of mathematical probabilists and list of statisticians. General aspects * Probability * Randomness, Pseudorandomness, Quasirandomness * Randomization, hardware random number generator * Random number generation * Random sequence * Uncertainty * Statistical dispersion * Observational error * Equiprobable ** Equipossible * Average * Probability interpretations * Markovian (other), Markovian * Statistical regularity * Central tendency * Bean machine * Relative frequency * Frequency probability * Maximum likelihood * Bayesian probability * Principle of indifference * Credal set * Cox's theorem * Principle of maximum entropy * Information entropy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Statistical Topics
0–9 * 1.96 *2SLS (two-stage least squares) redirects to instrumental variable *3SLS – see three-stage least squares * 68–95–99.7 rule *100-year flood A *A priori probability *Abductive reasoning *Absolute deviation *Absolute risk reduction * Absorbing Markov chain *ABX test * Accelerated failure time model * Acceptable quality limit *Acceptance sampling * Accidental sampling *Accuracy and precision * Accuracy paradox * Acquiescence bias *Actuarial science *Adapted process * Adaptive estimator * Additive Markov chain *Additive model *Additive smoothing *Additive white Gaussian noise *Adjusted Rand index – see Rand index (subsection) * ADMB software *Admissible decision rule *Age adjustment * Age-standardized mortality rate *Age stratification *Aggregate data * Aggregate pattern *Akaike information criterion *Algebra of random variables * Algebraic statistics *Algorithmic inference *Algorithms for calculating variance *All models are wrong *All-pairs testing *Allan va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Observational Error
Observational error (or measurement error) is the difference between a measured value of a quantity and its unknown true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. Such errors are inherent in the measurement process; for example lengths measured with a ruler calibrated in whole centimeters will have a measurement error of several millimeters. The error or uncertainty of a measurement can be estimated, and is specified with the measurement as, for example, 32.3 ± 0.5 cm. Scientific observations are marred by two distinct types of errors, systematic errors on the one hand, and random, on the other hand. The effects of random errors can be mitigated by the repeated measurements. Constant or systematic errors on the contrary must be carefully avoided, because they arise from one or more causes which constantly act in the same way, and have the effect of always altering the result of the experiment in the same direction. They therefore alter the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Indifference
The principle of indifference (also called principle of insufficient reason) is a rule for assigning epistemic probabilities. The principle of indifference states that in the absence of any relevant evidence, agents should distribute their credence (or "degrees of belief") equally among all the possible outcomes under consideration. In Bayesian probability, this is the simplest non-informative prior. Examples The textbook examples for the application of the principle of indifference are coins, dice, and cards. In a macroscopic system, at least, it must be assumed that the physical laws that govern the system are not known well enough to predict the outcome. As observed some centuries ago by John Arbuthnot (in the preface of ''Of the Laws of Chance'', 1692), :It is impossible for a Die, with such determin'd force and direction, not to fall on such determin'd side, only I don't know the force and direction which makes it fall on such determin'd side, and therefore I call it ... [...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] |
Maximum Likelihood
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when the random errors are assumed to have normal distributions with the same variance. From the perspective of Bayesian inference, ML ... [...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] |
Relative Frequency
In probability theory and statistics, the empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, i.e. by means not of a theoretical sample space but of an actual experiment. More generally, empirical probability estimates probabilities from experience and observation. Given an event in a sample space, the relative frequency of is the ratio being the number of outcomes in which the event occurs, and being the total number of outcomes of the experiment. In statistical terms, the empirical probability is an ''estimator'' or ''estimate'' of a probability. In simple cases, where the result of a trial only determines whether or not the specified event has occurred, modelling using a binomial distribution might be appropriate and then the empirical estimate is the maximum likelihood estimate. It is the Bayesian estimate for the same case if certain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bean Machine
The Galton board, also known as the Galton box or quincunx or bean machine (or incorrectly Dalton board), is a device invented by Francis Galton to demonstrate the central limit theorem, in particular that with sufficient sample size the binomial distribution approximates a normal distribution. Galton designed it to illustrate his idea of Regression toward the mean, regression to the mean, which he called "reversion to mediocrity" and made part of his Eugenics, eugenist ideology. Description The Galton board consists of a vertical board with interleaved rows of pegs. Beads are dropped from the top and, when the device is level, bounce either left or right as they hit the pegs. Eventually they are collected into bins at the bottom, where the height of bead columns accumulated in the bins approximate a normal distribution, bell curve. Overlaying Pascal's triangle onto the pins shows the number of different paths that can be taken to get to each bin. Large-scale working models of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Tendency
In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution.Weisberg H.F (1992) ''Central Tendency and Variability'', Sage University Paper Series on Quantitative Applications in the Social Sciences, p.2 Colloquially, measures of central tendency are often called '' averages.'' The term ''central tendency'' dates from the late 1920s. The most common measures of central tendency are the arithmetic mean, the median, and the mode. A middle tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution. Occasionally authors use central tendency to denote "the tendency of quantitative data to cluster around some central value."Upton, G.; Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP (entry for "central tendency")Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP for International Statistical Institute. (entry for "cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Regularity
Statistical regularity is a notion in statistics and probability theory that random events exhibit regularity when repeated enough times or that enough sufficiently similar random events exhibit regularity. It is an umbrella term that covers the law of large numbers, all central limit theorems and ergodic theorems. If one throws a dice once, it is difficult to predict the outcome, but if one repeats this experiment many times, one will see that the number of times each result occurs divided by the number of throws will eventually stabilize towards a specific value. Repeating a series of trials will produce similar, but not identical, results for each series: the average, the standard deviation and other distributional characteristics will be around the same for each series of trials. The notion is used in games of chance, demographic statistics, quality control of a manufacturing process, and in many other parts of our lives. Observations of this phenomenon provided the initial m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markovian (other) (surname)
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Markovian is an adjective that may describe: * In probability theory and statistics, subjects named for Andrey Markov: ** A Markov chain or Markov process, a stochastic model describing a sequence of possible events ** The Markov property, the memoryless property of a stochastic process * The Markovians, an extinct god-like species in Jack L. Chalker's ''Well World'' series of novels * Markovian Parallax Denigrate, references a mysterious series of Usenet messages See also * Markov Markov ( Bulgarian, ), Markova, and Markoff are common surnames used in Russia and Bulgaria. Notable people with the name include: Academics * Ivana Markova (1938–2024), Czechoslovak-British emeritus professor of psychology at the University of S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Interpretations
The word "probability" has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical, tendency of something to occur, or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory. There are two broad categories of probability interpretations which can be called "physical" and "evidential" probabilities. Physical probabilities, which are also called objective or frequency probability, frequency probabilities, are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms. In such systems, a given type of event (such as a yielding a six) tends to occur at a persistent rate, or "relative frequency", in a long run of trials. Physical probabilities either explain, or are invoked to explain, these stable frequencies. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
