uncorrelated

WordNet

not varying together

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2014/02/05 10:56:00」(JST)

wiki en

In probability theory and statistics, two real-valued random variables, X,Y, are said to be uncorrelated if their covariance, E(XY) - E(X)E(Y), is zero. A set of two or more random variables is called uncorrelated if each pair of them are uncorrelated. If two variables are uncorrelated, there is no linear relationship between them.

Uncorrelated random variables have a Pearson correlation coefficient of zero, except in the trivial case when either variable has zero variance (is a constant). In this case the correlation is undefined.

In general, uncorrelatedness is not the same as orthogonality, except in the special case where either X or Y has an expected value of 0. In this case, the covariance is the expectation of the product, and X and Y are uncorrelated if and only if E(XY) = 0.

If X and Y are independent, then they are uncorrelated. However, not all uncorrelated variables are independent. For example, if X is a continuous random variable uniformly distributed on [−1, 1] and Y = X², then X and Y are uncorrelated even though X determines Y and a particular value of Y can be produced by only one or two values of X.

Example Of Dependence Without Correlation[edit]

Uncorrelated random variables are not necessarily independent

Let X be a random variable that takes the value 0 with probability 1/2, and takes the value 1 with probability 1/2.
Let Z be a random variable that takes the value -1 with probability 1/2, and takes the value 1 with probability 1/2.
Let U be a random variable constructed as U=XZ.

The claim is that U and X have zero covariance (and thus are uncorrelated), but are not independent.

Proof:

First note:

Now, by definition

Therefore

A necessary condition for showing that U and X are independent is showing that for any number a and b, . We prove that this is not true. PIck a=1 and b=0.

Thus so U and X are not independent.

Q.E.D.

When uncorrelatedness implies independence[edit]

There are cases in which uncorrelatedness does imply independence. One of these cases is the one in which both random variables are two-valued (so each can be linearly transformed to have a binomial distribution with n=1).^[1] Further, two jointly normally distributed random variables are independent if they are uncorrelated,^[2] although this does not hold for variables whose marginal distributions are normal and uncorrelated but whose joint distribution is not joint normal (see Normally distributed and uncorrelated does not imply independent).

References[edit]

^ Virtual Laboratories in Probability and Statistics: Covariance and Correlation, item 17.
^ Bain, Lee; Engelhardt, Max (1992). "Chapter 5.5 Conditional Expectation". Introduction to Probability and Mathematical Statistics (2nd ed.). pp. 185–186. ISBN 0534929303.

English Journal

Sulindac sulfide inhibits sarcoendoplasmic reticulum Ca(2+) ATPase, induces endoplasmic reticulum stress response, and exerts toxicity in glioma cells: Relevant similarities to and important differences from celecoxib.

White MC, Johnson GG, Zhang W, Hobrath JV, Piazza GA, Grimaldi M.SourceLaboratory of Neuropharmacology, Medicinal Chemistry Department, Drug Discovery Division, Southern Research Institute, Birmingham, Alabama.
Journal of neuroscience research.J Neurosci Res.2013 Mar;91(3):393-406. doi: 10.1002/jnr.23169. Epub 2012 Dec 30.
Malignant gliomas have low survival expectations regardless of current treatments. Nonsteroidal anti-inflammatory drugs (NSAIDs) prevent cell transformation and slow cancer cell growth by mechanisms independent of cyclooxygenase (COX) inhibition. Certain NSAIDs trigger the endoplasmic reticulum stre
PMID 23280445

Predictive accuracy of risk factors and markers: a simulation study of the effect of novel markers on different performance measures for logistic regression models.

Austin PC, Steyerberg EW.SourceInstitute for Clinical Evaluative Sciences, Toronto, ON, Canada; Department of Health Management, Policy and Evaluation, University of Toronto, Toronto, ON, Canada; Dalla Lana School of Public Health, University of Toronto, Toronto, ON, Canada.
Statistics in medicine.Stat Med.2013 Feb 20;32(4):661-72. doi: 10.1002/sim.5598. Epub 2012 Sep 10.
The change in c-statistic is frequently used to summarize the change in predictive accuracy when a novel risk factor is added to an existing logistic regression model. We explored the relationship between the absolute change in the c-statistic, Brier score, generalized R(2) , and the discrimination
PMID 22961910

Hybrid biasing approaches for global variance reduction.

Wu Z, Abdel-Khalik HS.SourceDepartment of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695, United States.
Applied radiation and isotopes : including data, instrumentation and methods for use in agriculture, industry and medicine.Appl Radiat Isot.2013 Feb;72:83-8. doi: 10.1016/j.apradiso.2012.09.026. Epub 2012 Oct 17.
A new variant of Monte Carlo-deterministic (DT) hybrid variance reduction approach based on Gaussian process theory is presented for accelerating convergence of Monte Carlo simulation and compared with Forward-Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) approach implemented in
PMID 23208236

Japanese Journal

B-5-6 ターボ復号における無相関外部LLRの交換に関する一検討(B-5.無線通信システムA(移動通信))

飯田剛基,衣斐信介,三瓶政一
電子情報通信学会総合大会講演論文集 2015年_通信(1), 361, 2015-02-24
NAID 110009927457

中年女性における被養育体験・内的作業モデルと摂食障害傾向との関連性についての研究

黒浜翔太,野添新一,原田彩
心身医学 55(2), 146-155, 2015-02-01
最近,中年女性の摂食障害が多く報告されている.本研究では,30〜59歳の一般中年女性369名を対象として,質問紙調査を行い,彼女らの被養育体験や心的表象である内的作業モデルと現在の摂食障害傾向との関連を明らかにすることを目的とした.調査の結果,彼女らの内的作業モデルから分類した恐れ・回避型は,他の型に比して高い摂食障害傾向を示した.また,内的作業モデルの不安定な部分は,摂食障害傾向に影響していた. …
NAID 110009908941

意識調査からみたてんかん医療の現状と今後のあり方について　I―てんかんを抱える人の受診行動、医療施設ならびに主治医との関係―

山内俊雄,川窪美英子
てんかん研究 33(1), 37-49, 2015
てんかんを抱える人たちの現状を明らかにし、より質の高い医療を行うための示唆を得るべく、様態も多様な成人てんかん患者男女300名に対し、WEB調査を行った。本論文では、患者の受診行動や求めていることについて検討した。通院施設や診療科の選択とてんかんの様態に関連はなく、最初の受診先で治療を継続している人が約4割、決まった主治医がいる人は9割以上であった。主治医は、ある程度の専門性があれば、てんかん専門 …
NAID 130005092332

Related Pictures

The effect of task duration correlations on project schedules – a study using Monte Coherence, plasmons, and me! | Skulls in the Stars Cryptocurrencies: an Uncorrelated Asset Class - Cantech Letter uncorrelated - definition - What is ? Lecture Notes: Reduction of Uncorrelated Noise - ppt download Investing In Private Placements - Cranson Capital Pthr Magazines Ultra High Resolution Seismic Method: Uncorrelated Chirp - Baradello Luca