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concept of a martingale[citation needed]. A (time) sequence of random variables is weakly dependent if distinct portions of the sequence have a covariance that
Weakly dependent random variables
Weakly_dependent_random_variables
Technique in statistics
that affect both the dependent and explanatory variables, or the covariates are subject to measurement error. Explanatory variables that suffer from one
Instrumental_variables
Concept in statistics
In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely
Exchangeable_random_variables
Method in probability theory
between the distribution of a sum of m {\displaystyle m} -dependent sequence of random variables and a standard normal distribution in the Kolmogorov (uniform)
Stein's_method
Inequalities in probability theory
also proved generalizations of the inequalities above to weakly dependent random variables. For example, inequality (2) can be extended as follows. Let
Bernstein inequalities (probability theory)
Bernstein_inequalities_(probability_theory)
French probability theorist
interests focus on dependent and weakly dependent random variables, including Bernstein inequalities and central limit theorems for these variables. She is a professor
Florence_Merlevède
Type of signal in signal processing
serially uncorrelated random variables with a mean of zero and a finite variance; a single realization of white noise is a random shock. In some contexts
White_noise
Fundamental theorem in probability theory and statistics
needed] 2√3/n − 1. Theorem—Let random variables X1, X2, ... ∈ L2(Ω) be such that Xn → 0 weakly in L2(Ω) and X n → 1 weakly in L1(Ω). Then there exist integers
Central_limit_theorem
Average value of a random variable
{E} [XY]=\operatorname {E} [X]\operatorname {E} [Y].} If the random variables are dependent, then generally E [ X Y ] ≠ E [ X ] E [ Y ] , {\displaystyle
Expected_value
Statistical modeling method
response (dependent variable) and one or more explanatory variables (regressor or independent variable). A model with exactly one explanatory variable is a
Linear_regression
of independent random variables ( X 1 ⊥ X 2 {\displaystyle X_{1}\perp X_{2}} ) and the weak assumption of uncorrelated random variables ( Cov ( X 1
Mean_dependence
Set of statistical processes for estimating the relationships among variables
a dependent variable (often called the outcome or response variable, or a label in machine learning parlance) and one or more independent variables (often
Regression_analysis
Type of random mathematical object
technique originally developed for approximating random variables such as Gaussian and Poisson variables, which has also been applied to point processes
Poisson_point_process
Type of stochastic process
Keep in mind that a weakly white noise is not necessarily strictly stationary. Let ω {\displaystyle \omega } be a random variable uniformly distributed
Stationary_process
Statistical model
understanding the relationship between an independent variable and a dependent variable when these variables do not have an obvious direct connection. In 1986
Mediation_(statistics)
Creating sequence of numbers that cannot be predicted
List of random number generators PP (complexity) Procedural generation Random password generator Random variable, contains a chance-dependent value Randomized
Random_number_generation
Representation of a type of random process
of random process. It can be used to describe time-varying processes from many natural and artificial sources. The model specifies output variables that
Autoregressive_model
Regression for more than two discrete outcomes
possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued
Multinomial logistic regression
Multinomial_logistic_regression
Statistical relationship
statistics, correlation is a type of statistical relationship between two random variables or bivariate data. It usually refers to the extent to which a pair
Correlation
Generalized method of moments estimator in econometrics
for a subset of the variables. When the exogeneity assumptions are violated and correlation pattern between time varying variables and errors may be complicated
Arellano–Bond_estimator
Statistical phenomenon
random variable is extreme, the next sampling of the same random variable is likely to be closer to its mean. Furthermore, when many random variables
Regression_toward_the_mean
Method for estimating the unknown parameters in a linear regression model
predictor variables x can be treated as fixed values, rather than random variables. This stronger form means, for example, that the predictor variables are
Ordinary_least_squares
Type of time series model
estimates the speed at which a dependent variable returns to equilibrium following changes in other explanatory variables. Yule (1926) and Granger and Newbold
Error_correction_model
Probability theory concept
discrete random variables X {\displaystyle X} and Y {\displaystyle Y} are conditionally independent given a third discrete random variable Z {\displaystyle
Conditional_independence
Nonparametric measure of rank correlation
dependence between the rankings of two variables). It assesses how well the relationship between two variables can be described using a monotonic function
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Empirical interventional study
to identify the variables. The quasi-independent variable is the variable that is manipulated in order to affect a dependent variable. In a time series
Quasi-experiment
Form of causal modeling that fit networks of constructs to data
latent variables (variables thought to exist but which can't be directly observed). Additional causal connections link those latent variables to observed
Structural_equation_modeling
Statistical model
process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal
Gaussian_process
Graphical tool in probability
T.J.; Cooke, R.M. (2002). "Vines — a new graphical model for dependent random variables". Annals of Statistics. 30 (4): 1031–1068. CiteSeerX 10.1.1.26
Vine_copula
Differential equations involving stochastic processes
differential equation with the right hand side perturbed by a term dependent on a white noise variable. In most cases, SDEs are understood as continuous time limit
Stochastic differential equation
Stochastic_differential_equation
Statistical technique correcting sampling bias
technique to correct bias from non-randomly selected samples or otherwise incidentally truncated dependent variables, a pervasive issue in quantitative
Heckman_correction
Statistical test of variance
in a model with two independent variables, if only one variable exerts a significant effect on the dependent variable and the other does not, then the
Omnibus_test
Concept in probability and statistics
estimation (as an application example) Hsu, Hwei (1997). Probability, random variables, and random processes. McGraw-Hill. ISBN 978-0-07-030644-8. Lapidoth, Amos
Autocovariance
Estimator in statistics and econometrics
terms follows a random walk. The estimator requires data on a dependent variable, y i t {\displaystyle y_{it}} , and independent variables, x i t {\displaystyle
First-difference_estimator
Instantaneous rate of change (mathematics)
independent and dependent variables. It can be calculated in terms of the partial derivatives with respect to the independent variables. For a real-valued
Derivative
Statistical method
all continuous random variables, and D [ 0 , 1 ] {\displaystyle D[0,1]} contains the distribution functions for all random variables. Statements about
Bootstrapping_(statistics)
Computer simulation with random inputs
system that has variables that can change stochastically (randomly) with individual probabilities. Realizations of these random variables are generated
Stochastic_simulation
In-depth, detailed examination of a particular case
determining which of many intervening variables truly links the independent variable with a dependent variable. The primary problem is that qualitative
Case_study
Statistical modeling technique
expresses the conditional quantiles of a dependent variable as a linear function of the explanatory variables. Crucial to the practicality of quantile
Quantile_regression
Method in machine learning
attempts to draw observed connections between statistical variables in a dataset. This makes random forests particularly useful in such fields as banking
Bootstrap_aggregating
Advanced method of process control
dependent variables of the modeled system that will be caused by changes in the independent variables. In a chemical process, independent variables that
Model_predictive_control
Statistical concept
optimal e-variables for small blocks of outcomes and these are then multiplied to obtain e-variables for larger samples - these e-variables work well
E-values
Dependence of the state of a system on its history
equilibrium of a system can not be predicted solely based on environmental variables, but also requires knowledge of the system's past history. Notable examples
Hysteresis
Dynamical system
(lattices or networks), and real (number or vector), local, continuous state variables. Studied systems include populations, chemical reactions, convection,
Coupled_map_lattice
Mathematical theorem
Kolmogorov in 1929. Let {Yn} be independent, identically distributed random variables with zero means and unit variances. Let Sn = Y1 + ... + Yn. Then lim sup
Law_of_the_iterated_logarithm
Fundamental Buddhist teaching
प्रतीत्यसमुत्पाद, Pāli: paṭiccasamuppāda), commonly translated as dependent origination, or dependent arising, is a key doctrine in Buddhism shared by all schools
Pratītyasamutpāda
Statistical technique to use observational data for causal analysis
treatment (i.e., an explanatory variable or an independent variable) on an outcome (i.e., a response variable or dependent variable) by comparing the average
Difference_in_differences
Subset of artificial intelligence
a process of reducing the number of random variables under consideration by obtaining a set of principal variables. In other words, it is a process of
Machine_learning
Description of a quantum-mechanical system
appreciated in a single dimension. In canonical quantization, the classical variables x {\displaystyle x} and p {\displaystyle p} are promoted to self-adjoint
Schrödinger_equation
Method of data analysis
analysis creates variables that are linear combinations of the original variables. The new variables have the property that the variables are all orthogonal
Principal_component_analysis
Generalized function whose value is zero everywhere except at zero
used to represent the resulting probability density function of a random variable that is transformed by continuously differentiable function. If Y =
Dirac_delta_function
Cryptographic attack
queries. How much this information can help an attacker depends on many variables such as cryptographic system design, the CPU running the system, the algorithms
Timing_attack
Principle used in linear cryptanalysis
more naturally when the random variables take values in { − 1 , 1 } {\displaystyle \{-1,1\}} . If we introduce variables χ i = 1 − 2 X i = ( − 1 )
Piling-up_lemma
Philosophical view that events are determined by prior events
hidden variables really existed. Many experiments have verified the quantum predictions. Bell's theorem only applies to local hidden variables. Quantum
Determinism
Statistical hypothesis test
of additional explanatory variables that are associated with the response. Including such additional explanatory variables using regression or anova reduces
Student's_t-test
Scripting language created in 1994
PHP variables are declared and initialized. <?php $name = 'John'; // variable of string type being declared and initialized $age = 18; // variable of integer
PHP
Unpredictable phenomenon in complex systems
needed] Bedau notes that weak emergence is not a universal metaphysical solvent, as the hypothesis that consciousness is weakly emergent would not resolve
Emergence
Computer network management and monitoring protocol
manager-to-agent request to retrieve the value of a variable or list of variables. Desired variables are specified in variable bindings (the value field is not used)
Simple Network Management Protocol
Simple_Network_Management_Protocol
When a system's behavior depends on timing of uncontrollable events
software, or other system where the system's substantive behavior is dependent on the sequence or timing of uncontrollable events, leading to unexpected
Race_condition
Experiments to test Bell's theorem in quantum mechanics
hidden variables. Furthermore, Einstein argued that the hidden variables should obey the condition of locality: Whatever the hidden variables actually
Bell_test
Object or module in concurrent programming
condition variable, with a unique mutex for each condition variable. With nonblocking condition variables (also called "Mesa style" condition variables or "signal
Monitor_(synchronization)
Ability of the brain to continuously change
exhibits a higher degree of plasticity than the adult brain. Activity-dependent plasticity can have significant implications for healthy development,
Neuroplasticity
Statistical method for handling multiple comparisons
numbers of variables being measured per sample (e.g. thousands of gene expression levels). In these datasets, too few of the measured variables showed statistical
False_discovery_rate
Mathematical problem involving optimal stopping theory
{\displaystyle n>2} , the answer is yes: Alice can choose random numbers (which are dependent random variables) in such a way that Bob cannot play better than using
Secretary_problem
Change in the heritable traits of populations
the random fluctuation of allele frequencies within a population from one generation to the next. When selective forces are absent or relatively weak, allele
Evolution
Probability of making type I errors when performing multiple hypotheses tests
true null hypotheses, R is an observable random variable, and S, T, U, and V are unobservable random variables. The FWER is the probability of making at
Family-wise_error_rate
Context dependence in quantum measurements
being jointly distributed for random variables is equivalent to being measurable functions of one and the same random variable (this generalizes Arthur Fine's
Quantum_contextuality
Overall strategy utilized to carry out research
researcher randomly assigns participants to different conditions, measures the variables of interest, and tries to control for confounding variables. Therefore
Research_design
Type of pseudorandom number generation algorithm
than others. They are built from the following components: RR: A random (input-dependent) rotation, with output half the size of input. Given a 2b-bit input
Permuted congruential generator
Permuted_congruential_generator
Information-carrying connections between people
that B and C are linked to each other: That is, if we consider any two randomly selected individuals, such as A and B, from the set S = A, B, C, D, E,
Interpersonal_ties
Type of cipher
64-bit block size and a variable key length from 1 bit up to 448 bits. It is a 16-round Feistel cipher and uses large key-dependent S-boxes. Notable features
Block_cipher
Tasks in machine learning
training data set to determine, or learn, the optimal combinations of variables that will generate a good predictive model. The goal is to produce a trained
Training, validation, and test data sets
Training,_validation,_and_test_data_sets
Statistical interpretation with many tests
true null hypotheses, R is an observable random variable, and S, T, U, and V are unobservable random variables. P(at least 1 H_0 is wrongly rejected)00
Multiple_comparisons_problem
Family of statistical methods based on sampling of available data
observed sample. Resampling methods are: Permutation tests (also re-randomization tests) for generating counterfactual samples Bootstrapping Cross validation
Resampling_(statistics)
Turbulence that concerns the regimes of magnetofluid flow at high Reynolds number
{\displaystyle z^{\pm }} variables: where τ ± {\displaystyle \tau ^{\pm }} are the interaction time scales of z ± {\displaystyle z^{\pm }} variables. Iroshnikov and
Magnetohydrodynamic turbulence
Magnetohydrodynamic_turbulence
Academic field
represent a random graph Y ∈ Y {\displaystyle Y\in {\mathcal {Y}}} via a set of n {\displaystyle n} nodes and a collection of tie variables { Y i j : i
Network_science
Law of electrical current and voltage
sometimes also referred to as Ohm's law, having variables that are closely related to the V, I, and R scalar variables of Ohm's law, but which are each functions
Ohm's_law
Structure of a speech community
measured. The independent variables for this study were age, sex and location. These linguistic variables made up the dependent variable of the study, and were
Social network (sociolinguistics)
Social_network_(sociolinguistics)
Theorem in probability theory
New York: Wiley. Azuma, K. (1967). "Weighted Sums of Certain Dependent Random Variables" (PDF). Tôhoku Mathematical Journal. 19 (3): 357–367. doi:10.2748/tmj/1178243286
Azuma's_inequality
Block cipher
security needs and time considerations. Beyond the variables used above, the following variables are used in this algorithm: A, B - The two words composing
RC5
Limiting set in dynamical systems
they may be separate variables such as the inflation rate and the unemployment rate.[not verified in body] If the evolving variable is two- or three-dimensional
Attractor
Data type for values having two types
\tau } may depend on the term variable x {\displaystyle x} . In particular, if a term M {\displaystyle M} has the dependent intersection type ( x : σ )
Intersection_type
Paradigm in machine learning that uses no classification labels
latent variable models. Latent variable models are statistical models where in addition to the observed variables, a set of latent variables also exists
Unsupervised_learning
Machine instruction code that executes properly regardless of where in memory it resides
memory location. The latter terms are sometimes referred to as position-dependent code. Generating position-independent code is often the default behavior
Position-independent_code
Equations of motion for viscous fluids
need not be constant – in general, they depend on two thermodynamics variables if the fluid contains a single chemical species, say for example, pressure
Navier–Stokes_equations
Energy contained within a system
linearly homogeneous function of the three variables (that is, it is extensive in these variables), and that it is weakly convex. Knowing temperature and pressure
Internal_energy
Network protocol
store the MD5-hash of the password (strictly speaking of HMAC's internal variables i_key_pad and o_key_pad). Such implementations leverage that for computing
CRAM-MD5
Random process independent of past history
X_{n-1}=\ell ,m,p} state. A discrete-time Markov chain is a sequence of random variables X1, X2, X3, ... with the Markov property, namely that the probability
Markov_chain
Stochastic volatility model used in derivatives markets
F} and σ {\displaystyle \sigma } are represented by stochastic state variables whose time evolution is given by the following system of stochastic differential
SABR_volatility_model
American mathematician (1942–2026)
1972, with his dissertation Limit Theorems for Sums of Strongly Dependent Random Variables supervised by Benoit Mandelbrot. Between 1972 and 1974 Taqqu lectured
Murad_Taqqu
Family of stochastic processes
the prior knowledge about the distribution of random variables—how likely it is that the random variables are distributed according to one or another particular
Dirichlet_process
System for rating game players
regression, where the games results are dependent variables, the players' ratings are independent variables, and the model relating both is probabilistic:
Elo_rating_system
Loop that increases an initial effect
to the originating process can be direct, or it can be via other state variables. Such systems can give rich qualitative behaviors, but whether the feedback
Positive_feedback
Bilateral trade flow model
the dependent variable in place of the level of bilateral trade flows. In applied work, the gravity model is often extended by including variables to account
Gravity_model_of_trade
Differentiation under the integral sign formula
transform, which can be differentiated to generate the moments of a random variable. Whether Leibniz's integral rule applies is essentially a question
Leibniz_integral_rule
different scales on a dimension. Because stochastic processes are random variables with a time and a space component, their self-similarity properties
Self-similar_process
Group of endocrine diseases characterized by high blood sugar levels
terms, including childhood-onset diabetes, juvenile diabetes, and insulin-dependent diabetes mellitus. Likewise, the term "type 2 diabetes" has replaced several
Diabetes
executed by a virtual machine. SPL supports both standard variables assigned with = and "hot" variables assigned with :=. For example, the statement A = 1.
DADiSP
Facts provided or learned about something or someone
if, given its state variables for some initial period, the theory logically determines a unique set of values for those variables for any other period
Information
Methods employed to reduce error in science tests
variables. A confounder is an extraneous variable that is related to both the independent variable (treatment or exposure) and the dependent variable
Scientific_control
WEAKLY DEPENDENT-RANDOM-VARIABLES
WEAKLY DEPENDENT-RANDOM-VARIABLES
Surname or Lastname
English
English : probably a variant of Crandon, a habitational name from Crandon in Somerset or Crandean in Falmer, Sussex. Compare Grandin.
Girl/Female
Hindu
Independent, Submissive, Willing, Dependent
Girl/Female
Tamil
Independent, Submissive, Willing, Dependent
Surname or Lastname
English
English : variant spelling of Weekley.
Surname or Lastname
English
English : variant of Ransom.
Surname or Lastname
English
English : unexplained; perhaps a variant of Francom.
Surname or Lastname
English
English : variant spelling of Randall.Americanized spelling of Randel.
Girl/Female
Hindu
Independent, Submissive, Willing, Dependent
Male
Scandinavian
 Scandinavian form of Old Norse Randolfr, RANDOLF means "shield-wolf." Compare with another form of Randolf.
Surname or Lastname
English
English : variant of Rand 1, from the Old French oblique case.
Surname or Lastname
English
English : variant of Brandon.
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Boy/Male
English American
Son of Rand.
Girl/Female
Tamil
Independent, Submissive, Willing, Dependent
Female
English
Variant spelling of English Randy, RANDI means "worthy of admiration."
Surname or Lastname
English
English : variant spelling of Weekley.
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : patronymic from the Middle English personal name Rand(e) (see Rand 1).
Boy/Male
English
Son of Rand.
Male
English
 Variant spelling of Middle English Randulf, RANDOLF means "shield-wolf." Compare with other forms of Randolf.
Surname or Lastname
English
English : variant of Weekley.
WEAKLY DEPENDENT-RANDOM-VARIABLES
WEAKLY DEPENDENT-RANDOM-VARIABLES
Girl/Female
Arabic, Muslim
Spring
Surname or Lastname
English
English : variant of Bean.Probably a translation of German Bohne, which while singular in standard German is also a dialect plural (the singular form being Bohn), or an Americanized spelling of Binz.
Boy/Male
English American
When a nineteenth-century American named Maverick refused to brand his calves as other ranchers...
Boy/Male
Arabic, Muslim
Single; Unique; Another Name for God; Unequalled
Girl/Female
Hindu
Ear, Veda
Girl/Female
Indian
Sharp, Fem of rahif
Boy/Male
Tamil
Mokshgna | மோகà¯à®·à¯à®•à®¨à®¾
Boy/Male
Tamil
Saikalateeta | ஸாஈ கலாதீதா
Beyond time limitations
Girl/Female
British, English, Greek, Irish
Pure
Girl/Female
Indian
The Vine of Happiness; The Stem of Happiness
WEAKLY DEPENDENT-RANDOM-VARIABLES
WEAKLY DEPENDENT-RANDOM-VARIABLES
WEAKLY DEPENDENT-RANDOM-VARIABLES
WEAKLY DEPENDENT-RANDOM-VARIABLES
WEAKLY DEPENDENT-RANDOM-VARIABLES
a.
Supported from above; suspended; depending; pendulous; hanging; as, a pendent leaf.
adv.
In a dependent manner.
a.
Not dependent; free; not subject to control by others; not relying on others; not subordinate; as, few men are wholly independent.
a.
Depending on itself; independent.
n.
The act or state of depending; state of being dependent; a hanging down or from; suspension from a support.
adv.
In a random manner.
superl.
Not strong of constitution; infirm; feeble; as, a weakly woman; a man of a weakly constitution.
n.
A dependency; a dependent territory.
n.
One who depends; a dependent.
a.
Going at random or by chance; done or made at hazard, or without settled direction, aim, or purpose; hazarded without previous calculation; left to chance; haphazard; as, a random guess.
n.
Random.
n.
State of being dependent; dependence; state of being subordinate; subordination; concatenation; connection; reliance; trust.
n.
A roving motion; course without definite direction; want of direction, rule, or method; hazard; chance; -- commonly used in the phrase at random, that is, without a settled point of direction; at hazard.
a.
Hanging down; as, a dependent bough or leaf.
v. i.
To go or stray at random.
n.
To exact a ransom for, or a payment on.
v. t.
A deponent verb.
n.
Distance to which a missile is cast; range; reach; as, the random of a rifle ball.
n.
See Dependent, Dependence, Dependency.
a.
Dependent on one's self; self-depending; self-reliant.