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Pairwise error probability is the error probability that for a transmitted signal ( X {\displaystyle X} ) its corresponding but distorted version ( X
Pairwise_error_probability
When the occurrence of one event does not affect the likelihood of another
Mutual independence implies pairwise independence, but not the other way around. In the standard literature of probability theory, statistics, and stochastic
Independence (probability theory)
Independence_(probability_theory)
Chance of wrongly rejecting the null hypothesis
positive ratio (also known as fall-out or false alarm rate ) is the probability of falsely rejecting the null hypothesis for a particular test. The false
False_positive_rate
Branch of mathematics concerning probability
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations
Probability_theory
Probability of making type I errors when performing multiple hypotheses tests
Family-wise error rate (FWER) is a term from statistics for the probability of making one or more false discoveries, or type I errors when performing
Family-wise_error_rate
Machine learning problem
application of the pairwise coupling algorithm by Hastie and Tibshirani. A method used to assign scores to pairs of predicted probabilities and actual discrete
Probabilistic_classification
Probability of an event occurring, given that another event has already occurred
Joint probability distribution Monty Hall problem Pairwise independent distribution Posterior probability Postselection Regular conditional probability Gut
Conditional_probability
Topics referred to by the same term
refer to: Packetized Ensemble Protocol, used by Telebit modems Pairwise error probability, in digital communications Peak envelope power of a transmitter
PEP
Statistical measure of how far values spread from their average
In probability theory and statistics, variance is a measure of dispersion, meaning it is a measure of how far a set of numbers are spread out from their
Variance
condition than pairwise independence. nonparametric regression nonparametric statistics non-sampling error normal distribution normal probability plot null
Glossary of probability and statistics
Glossary_of_probability_and_statistics
Process of comparing two entities to determine preference
Pairwise comparison generally is any process of comparing entities in pairs to judge which of each entity is preferred, or has a greater amount of some
Pairwise comparison (psychology)
Pairwise_comparison_(psychology)
Diagnostic plot of binary classifier ability
area under the probability distribution from − ∞ {\displaystyle -\infty } to the discrimination threshold) of the detection probability in the y-axis versus
Receiver operating characteristic
Receiver_operating_characteristic
Formula on random variables
be simplified if X 1 , … , X n {\displaystyle X_{1},\ldots ,X_{n}} are pairwise independent or just uncorrelated, integrable random variables, each with
Bienaymé's_identity
Non-parametric method for testing whether samples originate from the same distribution
analyzing the specific sample pairs for stochastic dominance, Dunn's test, pairwise Mann–Whitney tests with Bonferroni correction, or the more powerful but
Kruskal–Wallis_test
(disambiguation) Probability integral transform Probability interpretations Probability mass function Probability matching Probability metric Probability of error Probability
List_of_statistics_articles
Sets with no element in common
is pairwise disjoint. A Helly family is a system of sets within which the only subfamilies with empty intersections are the ones that are pairwise disjoint
Disjoint_sets
Ambiguous term in statistics
into class membership probabilities in the case with classes count greater than two: Reduction to binary tasks and subsequent pairwise coupling, see Hastie
Calibration_(statistics)
Fundamental theorem in probability theory and statistics
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample
Central_limit_theorem
Post-hoc statistical test for pairwise comparisons
increases. For four or more groups, the probability of at least one Type I error occurring among the pairwise comparisons can exceed the nominal α {\displaystyle
Fisher's least significant difference
Fisher's_least_significant_difference
Statistical measure used in survey research
analysis. When the selection probabilities may be different, the sample size is random, and the pairwise selection probabilities are independent, we call
Design_effect
Reasoning for mathematical statements
are pairwise equivalent. In order to prove that the statements φ 1 , … , φ n {\displaystyle \varphi _{1},\ldots ,\varphi _{n}} are each pairwise equivalent
Mathematical_proof
variation distance in probability theory / (2:R) Coupling / (2:BRG) Lévy–Prokhorov metric / (2:G) Wasserstein metric / (2:G) Pairwise independence / (3:B)
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Multiple comparison procedure
family-wise error rate. See Criticism Section for further details. Duncan (1965) also gave the first Bayesian multiple comparison procedure, for the pairwise comparisons
Duncan's new multiple range test
Duncan's_new_multiple_range_test
Inequality applying to probability spaces
principle Schuette–Nesbitt formula Boole–Fréchet inequalities Probability of the union of pairwise independent events Boole, George (1847). The Mathematical
Boole's_inequality
Nonparametric test of the null hypothesis
of the sizes of the two samples being compared. This measure is the probability that the value of a random observation from the higher group will be
Mann–Whitney_U_test
The probability of superiority or common language effect size is the probability that, when sampling a pair of observations from two groups, the observation
Probability_of_superiority
Statistical procedure
discussion of multiple-comparison procedures is the question of the probability of Type I errors. Most differences among alternative techniques result from different
Dunnett's_test
Statistical test for multiple comparisons
factors: α {\displaystyle \ \alpha ~\quad } the Type I error rate, or the probability of rejecting a true null hypothesis; k {\displaystyle \
Tukey's_range_test
Uncertainty Statistical dispersion Observational error Equiprobable Equipossible Average Probability interpretations Markovian Statistical regularity
List_of_probability_topics
Machine learning technique
converting them into pairwise comparisons for prediction purposes. In the online scenario, when human feedback is collected through pairwise comparisons under
Reinforcement learning from human feedback
Reinforcement_learning_from_human_feedback
Square root of the mean square
are compared, the RMS of the pairwise differences of the two data sets can serve as a measure of how far on average the error is from 0. The mean of the
Root_mean_square
Probabilistic data structure in computer science
functions must be pairwise independent. The parameters w and d can be chosen by setting w = ⌈e/ε⌉ and d = ⌈ln 1/δ⌉, where the error in answering a query
Count–min_sketch
Basic circuit in quantum computing
also with n qubits initialized to | 0 ⟩ {\displaystyle |0\rangle } and pairwise CNOT its qubits with the qubits in register A, such that for each p the
Quantum_logic_gate
Variable representing a random phenomenon
may also represent uncertainty, such as measurement error. However, the interpretation of probability is philosophically complicated, and even in specific
Random_variable
Statistical hypothesis test
comparisons"/ "planned comparisons"- a particular set of comparisons "pairwise comparisons"-all possible comparisons i.e. Fisher's least significant difference
F-test
Collection of statistical models
units. These include graphical methods based on limiting the probability of false negative errors, graphical methods based on an expected variation increase
Analysis_of_variance
Algorithm that employs a degree of randomness as part of its logic or procedure
function the input size and its parameter k, but allows a small probability of error. Observe that any Las Vegas algorithm can be converted into a Monte
Randomized_algorithm
Technique to reduce dimensionality of points in Euclidean space
space in a way which approximately preserves pairwise distances between the points with high probability. In random projection, the original d {\displaystyle
Random_projection
Misuse of data analysis
variable. Conventional tests of statistical significance are based on the probability that a particular result would arise if chance alone were at work, and
Data_dredging
Multiple comparison method in statistics
estimates of all possible contrasts among the factor level means, not just the pairwise differences considered by the Tukey–Kramer method. It works on similar
Scheffé's_method
Statistical modeling method
performed when the distribution of the error terms is known to belong to a certain parametric family ƒθ of probability distributions. When fθ is a normal
Linear_regression
Alignment of more than two molecular sequences
Multiple sequence alignments require more sophisticated methodologies than pairwise alignments, as they are more computationally complex. Most multiple sequence
Multiple_sequence_alignment
Use of machine learning to rank items
of three approaches: pointwise (where individual documents are ranked), pairwise (where pairs of documents are ranked into a relative order), and listwise
Learning_to_rank
Statistical test for multiple comparisons
Because the number of means within a range changes with each successive pairwise comparison, the critical value of the q statistic also changes with each
Newman–Keuls_method
mutual information in the pairwise marginal distribution. More recently, the exponential rate of convergence of the error probability was provided. The obvious
Chow–Liu_tree
Stochastic process generalizing Brownian motion
maximum of the function w are a dense countable set; the maximum values are pairwise different; each local maximum is sharp in the following sense: if w has
Wiener_process
Grammar model in linguistics
interactions, pairwise structure and other nested structures. However, pseudoknots can not be modeled. PCFGs extend CFG by assigning probabilities to each production
Probabilistic context-free grammar
Probabilistic_context-free_grammar
Measure of consensus in ratings given by multiple observers
Kendall's τ, or Spearman's ρ {\displaystyle \rho } can be used to measure pairwise correlation among raters using a scale that is ordered. Pearson assumes
Inter-rater_reliability
Economic model of personal preferences
the probabilities of agents' mistakes in pairwise comparisons are independent and identically distributed: all mistakes have the same probability p. This
Random_utility_model
Simultaneous observation and analysis of more than one outcome variable
algorithms to determine a set of synthetic variables that best represent the pairwise distances between records. The original method is principal coordinates
Multivariate_statistics
applications of pairwise distance statistical PMFs usually lack two necessary features to make them fully rigorous: the use of a proper probability distribution
Statistical_potential
Concept in genealogy and genetics
population-based linkage analyses including a method for pairwise IBD segment detection Relate: estimates the probability of IBD between pairs of individuals at a specific
Identity_by_descent
Counting technique in combinatorics
Include the cardinalities of the sets. Exclude the cardinalities of the pairwise intersections. Include the cardinalities of the triple-wise intersections
Inclusion–exclusion_principle
Theory of stochastic processes
where Zk are pairwise uncorrelated random variables and the functions ek are continuous real-valued functions on [a, b] that are pairwise orthogonal in
Kosambi–Karhunen–Loève theorem
Kosambi–Karhunen–Loève_theorem
1868 U.S. court case
Robinson v. Mandell, Charles Sanders Peirce testified that he had made pairwise comparisons of 42 examples of Howland's signature, overlaying them and
Howland_will_forgery_trial
"Highly entangled" quantum state of 3 or more qubits
of the coordinate system, each orientation will be observed with 50% probability. However the result of all three measurements on the state gives the
Greenberger–Horne–Zeilinger state
Greenberger–Horne–Zeilinger_state
Generalization of the one-dimensional normal distribution to higher dimensions
In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization
Multivariate normal distribution
Multivariate_normal_distribution
Method of protein structure prediction using other known proteins
available. The simplest method of template identification relies on serial pairwise sequence alignments aided by database search techniques such as FASTA and
Homology_modeling
Area of discrete mathematics
is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices
Graph_theory
Process of replacing missing data with substituted values
missing data include: hot deck and cold deck imputation; listwise and pairwise deletion; mean imputation; non-negative matrix factorization; regression
Imputation_(statistics)
alignment software is a compilation of software tools and web portals used in pairwise sequence alignment and multiple sequence alignment. See structural alignment
List of sequence alignment software
List_of_sequence_alignment_software
Statistical test of variance
a pairwise MCP, such as that of the most disparate means in Tukey's test, is a form of omnibus test all by itself, controlling the family-wise error rate
Omnibus_test
Data mining technique
set can be computed in linear time on the size of the set, so when many pairwise similarities need to be estimated this method can lead to a substantial
MinHash
Statistical method in data analysis
criterion, which specifies the dissimilarity of sets as a function of the pairwise distances of observations in the sets. The choice of metric as well as
Hierarchical_clustering
Classical problem in combinatorics
Safra, Shmuel (1997), "A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP", STOC '97:
Set_cover_problem
Criterion of fair item allocation
{MMS} _{v_{i}}^{1{\text{-out-of-}}n}(C)} . An allocation is a vector of n pairwise-disjoint subsets of C {\displaystyle C} -- one subset per agent. An allocation
Maximin_share
Clustering algorithm minimizing the sum of distances to k representatives
usage: import kmedoids from sklearn.metrics import pairwise_distances dissimilarity_matrix = pairwise_distances(X, metric="euclidean") fp = kmedoids
K-medoids
Branch of discrete mathematics
problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas
Combinatorics
Non-parametric statistical test
Eisinga, Heskes, Pelzer and Te Grotenhuis (2017) provide an exact test for pairwise comparison of Friedman rank sums, implemented in R. The Eisinga c.s. exact
Friedman_test
Single-winner electoral system
The Kemeny method is an electoral system that uses ranked ballots and pairwise comparison counts to identify the most popular choices in an election. It
Kemeny_method
Model of quantum computing
small probability of error by majority sampling, for a sufficiently large sample size. Specifically, take k independent samples from the probability distribution
Quantum_circuit
Method of a dimension reduction
h i {\displaystyle h_{i}} and s i {\displaystyle s_{i}} are chosen be pairwise independent. 2. For each item q i {\displaystyle q_{i}} in the stream,
Count_sketch
System for rating game players
1750-and-under tournament, they would now have a rating floor of 1800. Pairwise comparisons form the basis of the Elo rating methodology. Elo made references
Elo_rating_system
Measure of dependence between two variables
In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two
Mutual_information
Mathematical principles
property. One variant - the pairwise PM - is satisfied exclusively by divisor methods. That is, an apportionment method is pairwise PM if-and-only-if it is
Mathematics_of_apportionment
Set of methods for supervised statistical learning
classification using the kernel trick, representing the data only through a set of pairwise similarity comparisons between the original data points using a kernel
Support_vector_machine
Index of articles associated with the same name
known in probability. However, the Smith set, a generalization of the Condorcet criteria that is the smallest set of candidates that are pairwise unbeaten
Voting_criteria
Class of statistics in estimation theory
{\displaystyle f(x_{1},x_{2})=|x_{1}-x_{2}|} , the U-statistic is the mean pairwise deviation f n ( x 1 , … , x n ) = 2 / ( n ( n − 1 ) ) ∑ i > j | x i − x
U-statistic
Fewest edge crossings in drawing of a graph
also called k-planar. Other variants of the crossing number include the pairwise crossing number (the minimum number of pairs of edges that cross in any
Crossing number (graph theory)
Crossing_number_(graph_theory)
Analysis of sets of categorical sequences
different states (overall state distribution) and their standard errors Transition probabilities between states. State sequences can nicely be rendered graphically
Sequence analysis in social sciences
Sequence_analysis_in_social_sciences
Nonparametric measure of rank correlation
are incorporated). Stata implementation: spearman varlist calculates all pairwise correlation coefficients for all variables in varlist. MATLAB implementation:
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Class of transformations that quantum systems and processes can undergo
}\lambda \operatorname {E} _{A}(\lambda )} where EA(λ) is a family of pairwise orthogonal projections, each onto the respective eigenspace of A associated
Quantum_operation
1957 technique for modelling problems of decision making under uncertainty
by $ b {\displaystyle b} ; with probability 0.6, she loses the bet amount $ b {\displaystyle b} ; all plays are pairwise independent. On any play of the
Stochastic dynamic programming
Stochastic_dynamic_programming
Biological theory
PMC 310895. PMID 10899151. Roach JC, Boysen C, Wang K, Hood L (1995). "Pairwise end sequencing: a unified approach to genomic mapping and sequencing".
DNA_sequencing_theory
Filling in missing entries of a matrix
M} (as measured by the root mean square error (RMSE)) with high probability. In particular, with probability 1 − 1 n 3 {\displaystyle 1-{\frac {1}{n^{3}}}}
Matrix_completion
Probability distribution
Toby (2011). Evaluation of the suitability of a Zipfian gap model for pairwise sequence alignment (PDF). International Conference on Bioinformatics Computational
Zipf's_law
Type of location test in statistical analysis
making it a conservative test in the sense that its actual type I error probability will be lower than the nominal level, with a corresponding loss of
Paired_difference_test
Mathematical ways to group elements of a set
P)\;A\neq B\implies A\cap B=\emptyset } ). The elements of P are said to be pairwise disjoint or mutually exclusive. See also mutual exclusivity. The sets in
Partition_of_a_set
Causal or moderating relationship between statistical variables
variables, several interaction variables are constructed, with pairwise-products representing pairwise-interactions and higher order products representing higher
Interaction_(statistics)
Objects maximally similar to other objects in a dataset
set X {\displaystyle {\mathcal {X}}} can be computed after computing all pairwise distances between points in the ensemble. This would take O ( n 2 ) {\textstyle
Medoid
Complexity class
expressed as a sum of pairwise products of these terms. Intuitively, we want to design a machine whose acceptance probability is something like 1 2 (
PostBQP
Method used in statistics, pattern recognition, and other fields
inequality for product probability spaces). Data separability by classical linear discriminants simplifies the problem of error correction for artificial
Linear_discriminant_analysis
Method of data analysis
matrix (that is, PX is a random vector with all its distinct components pairwise uncorrelated). A quick computation assuming P {\displaystyle P} were unitary
Principal_component_analysis
Single-winner electoral system
various pivot probabilities are for pairwise ties. In each of the scenarios summarized below, all voters share a common set of pivot probabilities. In the first
Approval_voting
Rate at which mutations occur during some unit of time
1999). "Estimation of past demographic parameters from the distribution of pairwise differences when the mutation rates vary among sites: application to human
Mutation_rate
Hypothetical reconstruction of information from the brain
to 20 ms), the Ising model is able to effectively capture the present pairwise correlations, and is given by: P ( r | s ) = 1 Z ( s ) e x p ( ∑ i h i
Neural_decoding
Message encoded with more bits than needed
by the joint state and not any simpler collection of sources. The above pairwise redundancy measure can be generalized to a set of n variables. R e d u
Redundancy (information theory)
Redundancy_(information_theory)
Comparative politics for electoral systems
highest probability of being the best candidate. However, Condorcet's model is based on the extremely strong assumption of independent errors, i.e. voters
Comparison of electoral systems
Comparison_of_electoral_systems
List of concepts in artificial intelligence
theory The study of graphs, which are mathematical structures used to model pairwise relations between objects. graph traversal The process of visiting (checking
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Ecological concept
theory of molecular evolution, an idealised diploid population will have a pairwise nucleotide diversity equal to 4 μ {\displaystyle \mu } Ne, where μ {\displaystyle
Effective_population_size
PAIRWISE ERROR-PROBABILITY
PAIRWISE ERROR-PROBABILITY
Girl/Female
Australian, British, English, Gaelic, Irish
Terror; Lovers
Boy/Male
Anglo Saxon
Terror.
Male
Swiss
, axe, or, terror.
Male
English
Scottish surname transferred to forename use, from a place name possibly ERROL means "to wander."Â
Boy/Male
Christian & English(British/American/Australian)
Wanderering Noble
Female
Arthurian
, error for Nineve (q.v.).
Girl/Female
Hindu, Indian
Without Error
Boy/Male
Anglo Saxon
Terror.
Male
Swiss
, axe, or, terror.
Boy/Male
Anglo Saxon
Terror.
Girl/Female
Muslim/Islamic
Fountain of paridise
Boy/Male
Tamil
King of terror
Boy/Male
English American German Latin Scottish
Army commander. Army, weald power. Also can be a, meaning nobleman. Famous bearer: Australian...
Boy/Male
American, Anglo, Australian, British, Chinese, Christian, English, French, Indian, Scottish, Teutonic
Maker of Arrows; Arror Featherer
Boy/Male
Arabic, Hindu, Indian, Muslim, Tamil
Terror; Kings; Royal
Boy/Male
Anglo Saxon
Terror.
Boy/Male
American, Anglo, British, Christian, Danish, English, German, Jamaican, Latin, Scottish
To Wander; Nobleman; Leader; Earl; Wanderer
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Error-less
Girl/Female
Arabic
Highest Garden in Paridise; Heaven
Boy/Male
Hindu
King of terror
PAIRWISE ERROR-PROBABILITY
PAIRWISE ERROR-PROBABILITY
Boy/Male
Gujarati, Indian, Kannada
Moon; Lotus; Conch Shell
Girl/Female
Indian
Hibiscus Flower
Girl/Female
Biblical
Desirable.
Boy/Male
Indian, Punjabi, Sikh
Lamp of the Lord Sun
Boy/Male
Tamil
Heart, Love
Boy/Male
Tamil
Calm, Tranquil, Stedy, Quiet
Girl/Female
Muslim
Praiseworthy
Boy/Male
Arabic, Muslim
Another Name for Prophet Muhammad
Girl/Female
Hindu
Boy/Male
American, Anglo, British, English
Spearman
PAIRWISE ERROR-PROBABILITY
PAIRWISE ERROR-PROBABILITY
PAIRWISE ERROR-PROBABILITY
PAIRWISE ERROR-PROBABILITY
PAIRWISE ERROR-PROBABILITY
n.
The difference between the approximate result and the true result; -- used particularly in the rule of double position.
n.
Liability to error.
n.
Alt. of Parvise
adv.
In the manner of a pale or pales; by perpendicular lines or divisions; as, to divide an escutcheon palewise.
n.
An error; a mistake.
a.
Full of error; wrong.
n.
Exemption from error.
n.
A mistake in the proceedings of a court of record in matters of law or of fact.
n.
Misguidance; error.
n.
The difference between the observed value of a quantity and that which is taken or computed to be the true value; -- sometimes called residual error.
n.
The difference between an observed value and the true value of a quantity.
n.
A wandering; a roving or irregular course.
n.
Mistake; error; fault.
n.
A moral offense; violation of duty; a sin or transgression; iniquity; fault.
a.
Liable to error; fallible.
n.
A departing or deviation from the truth; falsity; false notion; wrong opinion; mistake; misapprehension.
n.
A fault of a player of the side in the field which results in failure to put out a player on the other side, or gives him an unearned base.
n.
An error in pleading.
n.
A wandering or deviation from the right course or standard; irregularity; mistake; inaccuracy; something made wrong or left wrong; as, an error in writing or in printing; a clerical error.
n.
One who encourages and propagates error; one who holds to error.