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Expected value of a random variable given that certain conditions are known to occur
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated
Conditional_expectation
Proposition in probability theory
of total expectation, the law of iterated expectations (LIE), Adam's law, the tower rule, and the smoothing property of conditional expectation, among other
Law_of_total_expectation
Theorem in probability theory
varies around its conditional mean E [ Y ∣ X ] . {\displaystyle \operatorname {E} [Y\mid X].} Taking the expectation of this conditional variance across
Law_of_total_variance
Probability distribution
_{k}^{\infty }x\,f_{X}(x)\,dx.} Alternatively, by using the definition of conditional expectation, it can be written as g ( k ) = E [ X ∣ X > k ] Pr ( X > k )
Log-normal_distribution
Risk measure estimating the average loss in the worst tail of the distribution
is also called conditional value at risk (CVaR), average value at risk (AVaR), tail value at risk (TVaR), conditional tail expectation (CTE), expected
Expected_shortfall
Generalization of the one-dimensional normal distribution to higher dimensions
(X_{1}\mid X_{2}=x_{2})=1-\rho ^{2};} thus the conditional variance does not depend on x2. The conditional expectation of X1 given that X2 is smaller/bigger than
Multivariate normal distribution
Multivariate_normal_distribution
quantity used in place of the true conditional probability (or conditional expectation) underlying the proof. Raghavan gives this description: We first
Method of conditional probabilities
Method_of_conditional_probabilities
Probability theory and statistics concept
{\mathcal {G}})\;} An expectation of a random variable with respect to a regular conditional probability is equal to its conditional expectation. Consider the
Conditional probability distribution
Conditional_probability_distribution
Generalization of conditional expectation
In mathematics, non-commutative conditional expectation is a generalization of the notion of conditional expectation in classical probability. The space
Non-commutative conditional expectation
Non-commutative_conditional_expectation
Measure giving the average loss beyond a specified Value-at-Risk level
tail value at risk (TVaR), also known as tail conditional expectation (TCE) or conditional tail expectation (CTE), is a risk measure associated with the
Tail_value_at_risk
Set of statistical processes for estimating the relationships among variables
linear regression), this allows the researcher to estimate the conditional expectation (or population average value) of the dependent variable when the
Regression_analysis
Model in probability theory
observations, is equal to the most recent value. In other words, the conditional expectation of the next value, given the past, is equal to the present value
Martingale (probability theory)
Martingale_(probability_theory)
Set of quantities in probability theory
derivative identity can be established between the conditional cumulant and the conditional expectation. For example, suppose that Y = X + Z where Z is standard
Cumulant
Variance of a random variable given value of other variables
X ) {\displaystyle \operatorname {E} (Y\mid X)} stands for the conditional expectation of Y given X, which we may recall, is a random variable itself
Conditional_variance
Average value of a random variable
{\hat {A}}\rangle ^{2}} . Arithmetic mean Central tendency Conditional expectation Expectation (epistemic) Expectile – related to expectations in a way
Expected_value
Concept in probability theory
is the conditional density of Y given X. This result can be extended to measure theoretical conditional expectation using the regular conditional probability
Regular conditional probability
Regular_conditional_probability
Iterative method for finding maximum likelihood estimates in statistical models
the imputed complete data". Expectation conditional maximization (ECM) replaces each M step with a sequence of conditional maximization (CM) steps in which
Expectation–maximization algorithm
Expectation–maximization_algorithm
Operator for offsetting time series elements
{\displaystyle E[X_{t+j}|\Omega _{t}]=E_{t}[X_{t+j}].} With these time-dependent conditional expectations, there is the need to distinguish between the backshift
Lag_operator
Lemma in measure theory
infinity. The conditional expectation of the limit inferior might not be well defined on this set, because the conditional expectation of the negative
Fatou's_lemma
Technique in statistics
kernel regression is a non-parametric technique to estimate the conditional expectation of a random variable. The objective is to find a non-linear relation
Kernel_regression
Probability theory concept
hypothesis. It is the opposite of conditional dependence. Conditional independence is usually formulated in terms of conditional probability, as a special case
Conditional_independence
Statistical theorem
estimator of a parameter θ {\displaystyle \theta } , then the conditional expectation of δ ( X ) {\displaystyle \delta (X)} given T ( X ) {\displaystyle
Rao–Blackwell_theorem
the conditional probability of failure is at most the conditional expectation of F {\displaystyle F} . Next we calculate the conditional expectation of
Randomized_rounding
Theorized increase of longevity with age
{E} [T-t\mid T>t]=p\cdot t.} Here the left hand side denotes the conditional expectation of the remaining lifetime T − t {\displaystyle T-t} , given that
Lindy_effect
Probability theory term
irrespective of other possible values of X. Given that X = 1, the conditional expectation of the random variable Y is E ( Y | X = 1 ) = 3 10 {\displaystyle
Conditioning_(probability)
Statistical measure of how far values spread from their average
[X\mid Y])+\operatorname {Var} (\operatorname {E} [X\mid Y]).} The conditional expectation E ( X ∣ Y ) {\displaystyle \operatorname {E} (X\mid Y)} of X
Variance
Type of vector space in math
random variable 1), and so this kernel is a closed subspace. The conditional expectation has a natural interpretation in the Hilbert space. Suppose that
Hilbert_space
Theorem in measure theory
Conditional expectation – Expected value of a random variable given that certain conditions are known to occur Borel–Kolmogorov paradox – Conditional
Disintegration_theorem
Concept in probability theory
a)} is larger than or equal to a {\displaystyle a} because the conditional expectation only takes into account of values larger than or equal to a {\displaystyle
Markov's_inequality
Concept in probability theory
theorem – Conditional independence of exchangeable observations Conditional expectation – Expected value of a random variable given that certain conditions
Conditional_dependence
the notion of a quasi‐conditional expectation—a completely positive map that generalizes the classical conditional expectation to the noncommutative setting—which
Quantum_Markov_chain
American mathematician and statistician (1919–2010)
1954. In 1947, while at Howard, Blackwell published the paper "Conditional Expectation and Unbiased Sequential Estimation", which outlined a technique
David_Blackwell
Statistical techniques analyzing facts to make predictions about unknown events
is used in order to create the conditional expectation and, similar to the ARIMA method, the conditional expectation is then compared to the account
Predictive_analytics
Statement in probability theory
generated by the other. The lemma plays an important role in the conditional expectation in probability theory, where it allows replacement of the conditioning
Doob–Dynkin_lemma
Inequality between integrals in Lp spaces
non-negative random variable Z has infinite expected value, then its conditional expectation is defined by E [ Z | G ] = sup n ∈ N E [ min { Z , n } | G ] a
Hölder's_inequality
Formula relating stochastic processes to partial differential equations
Feynman–Kac formula expresses u ( x , t ) {\displaystyle u(x,t)} as a conditional expectation of a certain random variable: u ( x , t ) = E [ e − ∫ t T V ( X
Feynman–Kac_formula
Statistical technique correcting sampling bias
observation (the so-called selection equation) together with the conditional expectation of the dependent variable (the so-called outcome equation). The
Heckman_correction
Puzzle in logic and mathematics
'paradoxical' if for any given first-envelope amount x, the expectation of the other envelope conditional on x is greater than x. The literature contains dozens
Two_envelopes_problem
Georgian mathematician who developed a kernel regression method
estimator along with Geoffrey Watson, which proposes estimating the conditional expectation of a random variable as a locally weighted average using a kernel
Èlizbar_Nadaraya
Sentences of the form "if x, then y"
headings zero conditional, first conditional (or conditional I), second conditional (or conditional II), third conditional (or conditional III) and mixed
English_conditional_sentences
Bound on probability of a random variable being far from its mean
^{2}}}={\frac {1}{k^{2}}}.} It can also be proved directly using conditional expectation: σ 2 = E [ ( X − μ ) 2 ] = E [ ( X − μ ) 2 | k σ ≤ | X − μ | ]
Chebyshev's_inequality
Mathematical rule for inverting probabilities
P_{X}^{y}(A)=E(1_{A}(X)|Y=y)} Existence and uniqueness of the needed conditional expectation is a consequence of the Radon–Nikodym theorem. Andrey Kolmogorov
Bayes'_theorem
Type of probability space
setup, the conditional probability is another probability measure, and the conditional expectation may be treated as the (usual) expectation with respect
Standard_probability_space
Estimated potential loss for an investment under a given set of conditions
capital, backtesting, stress testing, expected shortfall, and tail conditional expectation. Common parameters for VaR are 1% and 5% probabilities and one
Value_at_risk
Concept in statistics
variables' density functions, or in kernel regression to estimate the conditional expectation of a random variable. Kernels are also used in time series, in
Kernel_(statistics)
Theorem in probability theory
(b) The stopping time τ {\displaystyle \tau } has finite expectation and the conditional expectations of the absolute value of the martingale increments
Optional_stopping_theorem
Theorem in probability theory
Hoeffding's lemma handles the total expectation, but it also holds for the case when the expectation is conditional expectation and the bounds are measurable
Azuma's_inequality
Concept in econometrics
assumption which requires that the error term has a zero conditional expectation conditional on the complete set of regressors, including past, present
Endogeneity_(econometrics)
Overview of and topical guide to probability
zero–one law Conditional probability Conditioning (probability) Conditional expectation Conditional probability distribution Regular conditional probability
Outline_of_probability
Topics referred to by the same term
Martingale (probability theory), a stochastic process in which the conditional expectation of the next value, given the current and preceding values, is the
Martingale
Waiting time property of certain probability distributions
ISBN 978-0-387-94594-1. Nagel, Werner; Steyer, Rolf (2017-04-04). Probability and Conditional Expectation: Fundamentals for the Empirical Sciences. Wiley Series in Probability
Memorylessness
Set of methods for supervised statistical learning
For the square-loss, the target function is the conditional expectation function, f s q ( x ) = E [ y x ] {\displaystyle f_{sq}(x)=\mathbb
Support_vector_machine
Method of statistical inference
P_{X}^{y}(A)=E(1_{A}(X)|Y=y)} Existence and uniqueness of the needed conditional expectation is a consequence of the Radon–Nikodym theorem. This was formulated
Bayesian_inference
Statistical property
distribution is a member of the linear exponential family and the conditional expectation function is correctly specified). Yet, in the context of binary
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
first, second or third conditional; there also exist "zero conditional" and mixed conditional sentences. A "first conditional" sentence expresses a future
Uses_of_English_verb_forms
Theorem of convex functions
in the y variable, and the following well-known property of the conditional expectation: E [ ( E [ X ∣ G ] ) ∣ G ] = E [ X ∣ G ] . {\displaystyle
Jensen's_inequality
Notion in measure theory
Conditional expectation – Expected value of a random variable given that certain conditions are known to occur Borel–Kolmogorov paradox – Conditional
Lifting_theory
Theorem in measure theory
Cambridge University Press. ISBN 0-521-40605-6. Zitkovic, Gordan (Fall 2013). "Lecture10: Conditional Expectation" (PDF). Retrieved December 25, 2020.
Dominated_convergence_theorem
Set of machine learning methods
log-likelihood empirical loss and group LASSO regularization with conditional expectation consensus on unlabeled data for image categorization. We can define
Multiple_kernel_learning
Branch of mathematics that studies dynamical systems
} where E ( f | C ) {\displaystyle E(f|{\mathcal {C}})} is the conditional expectation given the σ-algebra C {\displaystyle {\mathcal {C}}} of invariant
Ergodic_theory
Estimation method that minimizes the mean square error
}(y)=\operatorname {E} \{x\mid y\}.} In other words, the MMSE estimator is the conditional expectation of x {\displaystyle x} given the known observed value of the measurements
Minimum mean square error estimator
Minimum_mean_square_error_estimator
0. A conditional expectation is the expected value of the truncated distribution (mean of the tail), MT, computed with respect to its conditional probability
Datar–Mathews method for real option valuation
Datar–Mathews_method_for_real_option_valuation
Open-source data analysis software
In 2022, Orange extended the Explain add-on with an Individual Conditional Expectation plot and the Permutation Feature Importance technique. In 2023
Orange_(software)
Concept in probability theory
⋅ , B ) {\displaystyle \kappa (\cdot ,B)} is a version of the conditional expectation E [ 1 { X ∈ B } ∣ G ] {\displaystyle \mathbb {E} [\mathbf {1} _{\{X\in
Markov_kernel
Concept in information theory
)}\leq {\sqrt {I(X;Y\mid Y')\,2\log 2}},} relating the conditional expectation to the conditional mutual information. This is a simple consequence of Pinsker's
Inequalities in information theory
Inequalities_in_information_theory
Bayesian statistical inference method
this without knowledge of G. Under squared error loss (SEL), the conditional expectation E(θi | Yi = yi) is a reasonable quantity to use for prediction
Empirical_Bayes_method
dividends are reinvested Risk measure Distortion risk measure Tail conditional expectation Value at risk Convex risk measure Entropic risk measure Coherent
List of financial performance measures
List_of_financial_performance_measures
Statistics concept
In this model, for each unit increase in the value of x, the conditional expectation of y increases by β1 units. In many settings, such a linear relationship
Polynomial_regression
Formula in probability theory
Similar comments apply to the conditional covariance. The law of total covariance can be proved using the law of total expectation: First, cov ( X , Y ) =
Law_of_total_covariance
Random field Conditional random field Borel–Cantelli lemma Wick product Conditioning (probability) Conditional expectation Conditional probability distribution
List_of_probability_topics
Mathematical function, in linear algebra
and E [ a X ] = a E [ X ] {\displaystyle E[aX]=aE[X]} . The conditional expectation is as well. But the variance of a random variable is not linear
Linear_map
Probability distribution
ISBN 978-0-471-27246-5. Nagel, Werner; Steyer, Rolf (2017-04-04). Probability and Conditional Expectation: Fundamentals for the Empirical Sciences. Wiley Series in Probability
Geometric_distribution
on the probability P [ y > 0 ] {\displaystyle P[y>0]} and the conditional expectation: E [ y ∣ x , y > 0 ] {\displaystyle \operatorname {E} [y\mid
Truncated_normal_hurdle_model
Type of stochastic process
latter does not depend on n. The same argument applies to the conditional expectation.[vague] Øksendal, Bernt K. (2003). Stochastic Differential Equations:
Local_martingale
Mathematical set with some added structure
standard probability space a conditional expectation may be treated as the integral over the conditional measure (regular conditional probabilities, see also
Space_(mathematics)
Framework for modeling optimization problems that involve uncertainty
T − 1 ] ] {\displaystyle E[U(W_{T})|\xi _{[T-1]}]} denotes the conditional expectation of U ( W T ) {\displaystyle U(W_{T})} given ξ [ T − 1 ] {\displaystyle
Stochastic_programming
Concept in financial mathematics
Superposed risk measures Entropic value at risk Drawdown Tail conditional expectation Entropic risk measure Superhedging price Expectile Variance (or
Risk_measure
Arminian religious doctrine
The conditional preservation of the saints, or conditional perseverance of the saints, or commonly conditional security, is the Arminian Christian belief
Conditional preservation of the saints
Conditional_preservation_of_the_saints
Z_{t}} is an m × d {\displaystyle m\times d} matrix. In fact the conditional expectation is given by E g [ X ∣ F t ] := Y t {\displaystyle \mathbb {E} ^{g}[X\mid
G-expectation
Financial model
where E t ( r s ) {\displaystyle \mathbb {E} _{t}(r_{s})} is the conditional expectation of the short rate and TP ( τ ) {\displaystyle {\text{TP}}(\tau
Affine_term_structure_model
{p(y)}{p(x,y)}}.} This uses the conditional expectation from probability theory. A basic property of the conditional entropy is that: H ( X | Y ) = H
Quantities_of_information
Partial differential equations describing diffusion
{\displaystyle F} solves the PDE, the first integral is zero. Taking conditional expectation and using the martingale property of the Itô integral gives E [
Kolmogorov backward equations (diffusion)
Kolmogorov_backward_equations_(diffusion)
Technique for the generative modeling of a continuous probability distribution
improve class-conditional generation by using a classifier. The original publication used CLIP text encoders to improve text-conditional image generation
Diffusion_model
Natural-language "if" sentences about what may be the case
three-valued or random-variable-like object whose expectation equals P(B|A); another (Bradley) represents conditionals via ordered pairs/tuples of worlds encoding
Indicative_conditional
Family of iterative methods
( X n ) n ≥ 0 {\displaystyle (X_{n})_{n\geq 0}} , in which the conditional expectation of X n {\displaystyle X_{n}} given θ n {\displaystyle \theta _{n}}
Stochastic_approximation
Algebraic structure of set algebra
_{n\to \infty }A_{n}.} In much of probability, especially when conditional expectation is involved, one is concerned with sets that represent only part
Σ-algebra
Hypothetical self-improving program
∣ ⋅ ] {\displaystyle E_{\mu }[\cdot \mid \cdot ]} denotes the conditional expectation operator with respect to some possibly unknown distribution μ {\displaystyle
Gödel_machine
of the Cuntz algebra 𝒪2 with the property that there exists a conditional expectation from 𝒪2 to B. The commutative unital C* algebra of (real or complex-valued)
Nuclear_C*-algebra
Technique for improving the efficiency of estimators in conditional moment models
conditional moment models, a class of semiparametric models that generate conditional expectation functions. To estimate parameters of a conditional moment
Optimal_instruments
Statistical concept
The correctness of the above algorithm is a perfect exercise of conditional expectation. We now analyze the expected number of coinflips. Given the bias
Fair_coin
Class of statistical modeling methods
Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured
Conditional_random_field
Method for estimating the unknown parameters in a linear regression model
relation between these variables suggests that the linearity of the conditional mean function may not hold. Different levels of variability in the residuals
Ordinary_least_squares
Concept in probability theory
Correlation, item 17. Bain, Lee; Engelhardt, Max (1992). "Chapter 5.5 Conditional Expectation". Introduction to Probability and Mathematical Statistics (2nd ed
Uncorrelatedness (probability theory)
Uncorrelatedness_(probability_theory)
Information theory
In probability theory, particularly information theory, the conditional mutual information is, in its most basic form, the expected value of the mutual
Conditional mutual information
Conditional_mutual_information
Study of uncertainty in the output of a mathematical model or system
through an equation similar to variance-based indices replacing the conditional expectation with a distance, as ξ i = E [ d ( P Y , P Y | X i ) ] {\displaystyle
Sensitivity_analysis
Theorem in probability theory
\quad n\in {\mathbb {N} }_{0}.} Assumption (11) implies that the conditional expectation of Xn given Fn–1 equals E[Xn] almost surely for every n ∈ N {\displaystyle
Wald's_equation
Collection of random variables
the current value and all the past values of the process, the conditional expectation of every future value is equal to the current value. In discrete
Stochastic_process
Mathematical model used for classification or regression
referred to as conditional models, are a class of models frequently used for classification. In machine learning, it typically models the conditional distribution
Discriminative_model
Statistical model
In statistics, a maximum-entropy Markov model (MEMM), or conditional Markov model (CMM), is a graphical model for sequence labeling that combines features
Maximum-entropy_Markov_model
validity Conditional change model Conditional distribution – see Conditional probability distribution Conditional dependence Conditional expectation Conditional
List_of_statistics_articles
CONDITIONAL EXPECTATION
CONDITIONAL EXPECTATION
Girl/Female
Tamil
Circumstance, Period of life, Wick, Condition, Degree
Boy/Male
African, Arabic, Australian, French, Indian, Muslim, Sindhi
Sacrifice; Unconditional Love; Love
Boy/Male
Arabic
State; Condition
Boy/Male
Tamil
Hope, Expectation, Pre-eminence
Girl/Female
Tamil
Good or Happy condition, Solution
Boy/Male
Tamil
Can travel in all climatic conditions
Girl/Female
Indian
Circumstance, Period of life, Wick, Condition, Degree
Boy/Male
African, Arabic, Australian, Greek, Swahili
Unique; Graceful; Kind; Sweet; The Beautiful Ocean; Loving; Forgiving; Content; Delighted; Beauty; Perfect; State; Handsome; Condition; The Sea
Boy/Male
Tamil
Hope, Expectation, Pre-eminence
Girl/Female
Hindu
Good or Happy condition, Solution, Fortune
Girl/Female
Hindu
Good or Happy condition, Solution
Girl/Female
Tamil
Niriksha | நிரீகà¯à®·à®¾
Unseen, Expectation, Hope
Niriksha | நிரீகà¯à®·à®¾
Girl/Female
Tamil
Good or Happy condition, Solution, Fortune
Girl/Female
Tamil
Expectation
Boy/Male
Bengali, Indian
Sleepless; Condition of Being Awake; One who Conquers Sleep
Boy/Male
Indian
Can Travel in All Climatic Conditions
Girl/Female
Tamil
Asha Rani | ஆஷா ராணீ Â
Hope, Aspiration, Expectation
Asha Rani | ஆஷா ராணீ Â
Girl/Female
Tamil
Apekshaa | அபேகà¯à®·à®¾
Expected, Expectation
Apekshaa | அபேகà¯à®·à®¾
Girl/Female
Tamil
Ashavathi | அஷாவதீ
Hope, Aspiration, Expectation
Ashavathi | அஷாவதீ
Girl/Female
Tamil
Apeksha | அபேகà¯à®·à®¾
Expected, Expectation
CONDITIONAL EXPECTATION
CONDITIONAL EXPECTATION
Girl/Female
American, Australian, Celtic, Chinese, Indian, Irish
Little King; Descendant of Rian
Boy/Male
Gujarati, Hindu, Indian, Punjabi, Sikh, Thai
Prayer; Repetition
Surname or Lastname
Irish
Irish : variant of Curley.English : habitational name from Corley in Warwickshire or Coreley in Shropshire, both named with Old English corna, a metathesized form of crona, genitive plural of cron, cran ‘crane’ + lēah ‘woodland clearing’.
Boy/Male
American, Australian, British, English
From the Bull Pasture; Meadow of the Sheep
Girl/Female
Hindu, Indian, Kannada, Marathi
Summer Season
Boy/Male
Hindu, Indian
One who Always have Power
Girl/Female
Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Miracle
Boy/Male
Tamil
A sage
Girl/Female
Hindu
Fragrant, Jasmine, Gardener, Another name for Durga and the ganges, A garland maker
Boy/Male
Bengali, Hebrew, Hindu, Indian, Sanskrit
Loved
CONDITIONAL EXPECTATION
CONDITIONAL EXPECTATION
CONDITIONAL EXPECTATION
CONDITIONAL EXPECTATION
CONDITIONAL EXPECTATION
adv.
In a conditional manner; subject to a condition or conditions; not absolutely or positively.
v. t.
To qualify by conditions; to regulate.
a.
Containing, implying, or depending on, a condition or conditions; not absolute; made or granted on certain terms; as, a conditional promise.
adv.
Conditionally.
a.
Unconditional.
v. i.
To impose upon an object those relations or conditions without which knowledge and thought are alleged to be impossible.
a.
Having, or known under or by, conditions or relations; not independent; not absolute.
a.
Of the nature of a proviso; containing a proviso or condition; conditional; as, a provisory clause.
a.
Surrounded; circumstanced; in a certain state or condition, as of property or health; as, a well conditioned man.
n.
A limitation.
a.
Not conditional limited, or conditioned; made without condition; absolute; unreserved; as, an unconditional surrender.
n.
train; acclimate.
imp. & p. p.
of Condition
v. t.
Conditional.
n.
A conditional word, mode, or proposition.
n.
To invest with, or limit by, conditions; to burden or qualify by a condition; to impose or be imposed as the condition of.
v. t.
To put under conditions; to render conditional.
a.
Not conditioned or subject to conditions; unconditional.
n.
To put under conditions; to require to pass a new examination or to make up a specified study, as a condition of remaining in one's class or in college; as, to condition a student who has failed in some branch of study.
a.
Expressing a condition or supposition; as, a conditional word, mode, or tense.