Table of Contents
53 relations: Andrey Kolmogorov, Base rate fallacy, Bayes' theorem, Bayesian epistemology, Bayesian probability, Begging the question, Borel–Kolmogorov paradox, Bruno de Finetti, Chain rule (probability), Conditional event algebra, Conditional expectation, Conditional independence, Conditional probability distribution, Conditional probability table, Conditioning (probability), Conservatism (belief revision), Dengue fever, Dice, Disintegration theorem, Elementary event, Event (probability theory), False positives and false negatives, Franz Thomas Bruss, Independence (probability theory), Σ-algebra, Joint probability distribution, L'Hôpital's rule, Law of total probability, Leibniz integral rule, Limit (mathematics), Marginal distribution, Monty Hall problem, Morse code, Mutual exclusivity, Pairwise independence, Partition of a set, Posterior probability, Postselection, Probabilistic classification, Probability, Probability axioms, Probability distribution, Probability interpretations, Probability measure, Probability theory, Quotient, Radical probabilism, Regular conditional probability, Sample space, Selection bias, ... Expand index (3 more) »
- Mathematical fallacies
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov (a, 25 April 1903 – 20 October 1987) was a Soviet mathematician who contributed to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.
See Conditional probability and Andrey Kolmogorov
Base rate fallacy
The base rate fallacy, also called base rate neglect or base rate bias, is a type of fallacy in which people tend to ignore the base rate (e.g., general prevalence) in favor of the individuating information (i.e., information pertaining only to a specific case).
See Conditional probability and Base rate fallacy
Bayes' theorem
Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting conditional probabilities, allowing us to find the probability of a cause given its effect.
See Conditional probability and Bayes' theorem
Bayesian epistemology
Bayesian epistemology is a formal approach to various topics in epistemology that has its roots in Thomas Bayes' work in the field of probability theory.
See Conditional probability and Bayesian epistemology
Bayesian probability
Bayesian probability 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.
See Conditional probability and Bayesian probability
Begging the question
In classical rhetoric and logic, begging the question or assuming the conclusion (Latin: petītiō principiī) is an informal fallacy that occurs when an argument's premises assume the truth of the conclusion.
See Conditional probability and Begging the question
Borel–Kolmogorov paradox
In probability theory, the Borel–Kolmogorov paradox (sometimes known as Borel's paradox) is a paradox relating to conditional probability with respect to an event of probability zero (also known as a null set).
See Conditional probability and Borel–Kolmogorov paradox
Bruno de Finetti
Bruno de Finetti (13 June 1906 – 20 July 1985) was an Italian probabilist statistician and actuary, noted for the "operational subjective" conception of probability.
See Conditional probability and Bruno de Finetti
Chain rule (probability)
In probability theory, the chain rule (also called the general product rule) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities.
See Conditional probability and Chain rule (probability)
Conditional event algebra
A standard, Boolean algebra of events is a set of events related to one another by the familiar operations and, or, and not.
See Conditional probability and Conditional event algebra
Conditional expectation
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution.
See Conditional probability and Conditional expectation
Conditional independence
In probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of a hypothesis.
See Conditional probability and Conditional independence
Conditional probability distribution
In probability theory and statistics, the conditional probability distribution is a probability distribution that describes the probability of an outcome given the occurrence of a particular event.
See Conditional probability and Conditional probability distribution
Conditional probability table
In statistics, the conditional probability table (CPT) is defined for a set of discrete and mutually dependent random variables to display conditional probabilities of a single variable with respect to the others (i.e., the probability of each possible value of one variable if we know the values taken on by the other variables).
See Conditional probability and Conditional probability table
Conditioning (probability)
Beliefs depend on the available information.
See Conditional probability and Conditioning (probability)
Conservatism (belief revision)
In cognitive psychology and decision science, conservatism or conservatism bias is a bias which refers to the tendency to revise one's belief insufficiently when presented with new evidence.
See Conditional probability and Conservatism (belief revision)
Dengue fever
Dengue fever is a mosquito-borne disease caused by dengue virus, prevalent in tropical and subtropical areas.
See Conditional probability and Dengue fever
Dice
Dice (die or dice) are small, throwable objects with marked sides that can rest in multiple positions.
See Conditional probability and Dice
Disintegration theorem
In mathematics, the disintegration theorem is a result in measure theory and probability theory.
See Conditional probability and Disintegration theorem
Elementary event
In probability theory, an elementary event, also called an atomic event or sample point, is an event which contains only a single outcome in the sample space.
See Conditional probability and Elementary event
Event (probability theory)
In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.
See Conditional probability and Event (probability theory)
False positives and false negatives
A false positive is an error in binary classification in which a test result incorrectly indicates the presence of a condition (such as a disease when the disease is not present), while a false negative is the opposite error, where the test result incorrectly indicates the absence of a condition when it is actually present.
See Conditional probability and False positives and false negatives
Franz Thomas Bruss
Franz Thomas Bruss (born 27. September 1949 in Kleinblittersdorf (Saarland)) is Emeritus Professor of Mathematics at the Université Libre de Bruxelles, where he had been director of "Mathématiques Générales" and co-director of the probability chair, and where he continues his research as invited professor.
See Conditional probability and Franz Thomas Bruss
Independence (probability theory)
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.
See Conditional probability and Independence (probability theory)
Σ-algebra
In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections.
See Conditional probability and Σ-algebra
Joint probability distribution
Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs.
See Conditional probability and Joint probability distribution
L'Hôpital's rule
L'Hôpital's rule or L'Hospital's rule, also known as Bernoulli's rule, is a mathematical theorem that allows evaluating limits of indeterminate forms using derivatives.
See Conditional probability and L'Hôpital's rule
Law of total probability
In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities.
See Conditional probability and Law of total probability
Leibniz integral rule
In calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form \int_^ f(x,t)\,dt, where -\infty and the integrands are functions dependent on x, the derivative of this integral is expressible as \begin & \frac \left (\int_^ f(x,t)\,dt \right) \\ &.
See Conditional probability and Leibniz integral rule
Limit (mathematics)
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value.
See Conditional probability and Limit (mathematics)
Marginal distribution
In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset.
See Conditional probability and Marginal distribution
Monty Hall problem
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall.
See Conditional probability and Monty Hall problem
Morse code
Morse code is a telecommunications method which encodes text characters as standardized sequences of two different signal durations, called dots and dashes, or dits and dahs.
See Conditional probability and Morse code
Mutual exclusivity
In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time.
See Conditional probability and Mutual exclusivity
Pairwise independence
In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent.
See Conditional probability and Pairwise independence
Partition of a set
In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset.
See Conditional probability and Partition of a set
Posterior probability
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood via an application of Bayes' rule.
See Conditional probability and Posterior probability
Postselection
In probability theory, to postselect is to condition a probability space upon the occurrence of a given event.
See Conditional probability and Postselection
Probabilistic classification
In machine learning, a probabilistic classifier is a classifier that is able to predict, given an observation of an input, a probability distribution over a set of classes, rather than only outputting the most likely class that the observation should belong to.
See Conditional probability and Probabilistic classification
Probability
Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur.
See Conditional probability and Probability
Probability axioms
The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933.
See Conditional probability and Probability axioms
Probability distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment.
See Conditional probability and Probability distribution
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.
See Conditional probability and Probability interpretations
Probability measure
In mathematics, a probability measure is a real-valued function defined on a set of events in a σ-algebra that satisfies measure properties such as countable additivity.
See Conditional probability and Probability measure
Probability theory
Probability theory or probability calculus is the branch of mathematics concerned with probability.
See Conditional probability and Probability theory
Quotient
In arithmetic, a quotient (from quotiens 'how many times', pronounced) is a quantity produced by the division of two numbers.
See Conditional probability and Quotient
Radical probabilism
Radical probabilism is a hypothesis in philosophy, in particular epistemology, and probability theory that holds that no facts are known for certain.
See Conditional probability and Radical probabilism
Regular conditional probability
In probability theory, regular conditional probability is a concept that formalizes the notion of conditioning on the outcome of a random variable.
See Conditional probability and Regular conditional probability
Sample space
In probability theory, the sample space (also called sample description space, possibility space, or outcome space) of an experiment or random trial is the set of all possible outcomes or results of that experiment.
See Conditional probability and Sample space
Selection bias
Selection bias is the bias introduced by the selection of individuals, groups, or data for analysis in such a way that proper randomization is not achieved, thereby failing to ensure that the sample obtained is representative of the population intended to be analyzed.
See Conditional probability and Selection bias
Sequela
A sequela (usually used in the plural, sequelae) is a pathological condition resulting from a disease, injury, therapy, or other trauma.
See Conditional probability and Sequela
Statistical inference
Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.
See Conditional probability and Statistical inference
Undefined (mathematics)
In mathematics, the term undefined is often used to refer to an expression which is not assigned an interpretation or a value (such as an indeterminate form, which has the possibility of assuming different values).
See Conditional probability and Undefined (mathematics)
See also
Mathematical fallacies
- Conditional probability
- Division by infinity
- Division by zero
- Freshman's dream
- List of incomplete or incorrect mathematical proofs
- Mathematical fallacy
References
Also known as A given b, Absolute probability, Conditional fallacy, Conditional probabilities, Conditional probability fallacy, Conditional probablility, Partition rule, Unconditional probability.