List Of Probability Topics
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List Of Probability Topics
This is a list of probability topics, by Wikipedia page. 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 * 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 * Urn ...
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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 varia ...
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Observational Error
Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics, an error is not necessarily a " mistake". Variability is an inherent part of the results of measurements and of the measurement process. Measurement errors can be divided into two components: ''random'' and ''systematic''. Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by repeatable processes inherent to the system. Systematic error may also refer to an error with a non-zero mean, the effect of which is not reduced when observations are averaged. Measurement errors can be summarized in terms of accuracy and precision. Measurement error should not be confused with measurement unce ...
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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. The principle of indifference is meaningless under the frequency interpretation of probability, in which probabilities are relative frequencies rather than degrees of belief in uncertain propositions, conditional upon state information. 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 ...
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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 ...
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Maximum Likelihood
In statistics, maximum likelihood estimation (MLE) is a method of estimation theory, estimating the Statistical parameter, parameters of an assumed probability distribution, given some observed data. This is achieved by Mathematical optimization, maximizing a likelihood function so that, under the assumed statistical model, the Realization (probability), observed data is most probable. The point estimate, 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 function, 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 ...
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Frequency Probability
Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability as the limit of a sequence, limit of its relative Frequency_(statistics), frequency in many trials (the long-run probability). Probabilities can be found (in principle) by a repeatable objective process (and are thus ideally devoid of opinion). 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, ''e.g.'' the probabilities of dice games arise from the natural symmetric 6-sidedness of the cube. This classical interpretation stumbled at any statistical problem that has no natural symmetr ...
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Relative Frequency
In statistics, the frequency (or absolute frequency) of an event i is the number n_i of times the observation has occurred/recorded in an experiment or study. These frequencies are often depicted graphically or in tabular form. Types The cumulative frequency is the total of the absolute frequencies of all events at or below a certain point in an ordered list of events. The (or empirical probability) of an event is the absolute frequency normalized by the total number of events: : f_i = \frac = \frac. The values of f_i for all events i can be plotted to produce a frequency distribution. In the case when n_i = 0 for certain i, pseudocounts can be added. Depicting frequency distributions A frequency distribution shows us a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data notably to show results of an election, income of people for a certain region, sales of a product within ...
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