# Questions tagged [iid]

iid is an acronym for independent and identically distributed. Many statistical methods assume that the data are iid; that is, that each observation comes from the same distribution and is independent of other observations.

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### What the i.i.d. assumption of the errors in linear regression implies for the response variable y?

In the linear regression model we assume that the errors $ε_i$ are independent and identically distributed (i.i.d.) random variables. I am trying to understand what this assumption implies regarding ...
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### AR/ARMA model - test residual for independence or lack of correlation

Shumway and Stoffer (2017), a great book that I highly recommend, define an AR(p) model as $x_t=\phi_1 x_{t-1}+\phi_2 x_{t-2}+...+\phi_p x_{t-p}+w_t$, where $w_t$~$wn(0,\sigma_w^2)$; $w_t$ is not ...
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### What is the meaning of these subscripts in iid random variables? [duplicate]

I've been studying statistics on my own and I'm having a hard time understanding some notations. On this page: http://scipp.ucsc.edu/~haber/ph116C/iid.pdf, specifically on the second paragraph, the ...
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### How to calculate Maximum Likelihood Estimator

I have samples of a noisy real vector with constant phase y¯(2) = a¯ . e^jθ + w where θ is a real scalar, and the entries of w¯ are complex normal i.i.d, where W i,real, W i,image ∼ N(0,σ^2) for i = 1,...
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### MGF of sample mean of poisson distribution

Let $X_1,X_2,\dots,X_n\stackrel{iid}{\sim}Poiss(\lambda)$ Let mgf of $X_1$ is given by $M_X(t)=e^{\lambda(e^t-1)}$ and let $\bar{X_n}=\frac{1}{n}(X_1+X_2+\dots+X_n)$ Then, by Weak Law of Large Numbers ...
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### Clarifications on I.I.D. assumption in machine learning

In this question, it was stated that the assumption of i.i.d. for data comes in the form of $$(X_i,y_i)∼P(X,y),∀i=1,...,N \\(X_i,y_i) \;independent\; of \;(X_j,y_j),\;∀i≠j∈{1,...,N}$$ I am clear with ...
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### Confusion in definition of independent and identically distributed random variables [duplicate]

From what I learnt, a random variable is a function which assigns real values to outcome space, and the probability distribution is a function that assigns probability to different values produced by ...
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### Why is MAP and ML widely accepted? [closed]

(ML as in Maximum Likelihood and MAP as in Maximum A-posteriori) I'm going trough a course book on my own, and without really having peers to talk to I'm turning to stack exchange with these rather ...
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### Non IID data and SVM Classifier

I am training an SVM model to predict the trend of stock prices (one-day ahead predictions. Classification task). It Had completely slipped from my mind that SVMs assume IID data until I had a ...
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### Difference of independent random variables that is not unimodal

This paywalled article shows that the difference of two i.i.d. random variables is unimodal and symmetric if the distribution of the random variables is unimodal. Is there a non-unimodal distribution ...
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### Posterior distribution of two i.i.d. uniform r.v. given their difference with graphical intuition

I have two i.i.d. random variables, $\theta_1$ and $\theta_2$ which are uniformly distributed on the unit square. I need to compute the joint posterior distribution of these two variables, given their ...
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### Probability with two IID random variables

Assume $X$ and $Y$ are two IID random variables with infinite support, I am interested in $P(X>a , X>Y+b)$ where $a$ and $b$ are two constants. Is there any family of distribution for X and Y ...
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### Confounding variables VS i.i.d assumption

I made up an example so as to illustrate my question with some more context. Say there are two national parks, and a ranger is interested in finding out how the number of rabbits (Y) varies with the ...
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### How to compute ESS (Effective Sample Size)?

I implemented the ESS calculation according to this manual like this: ...
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### What if my samples are not IIDs? [closed]

I'm testing my system and getting some results over time (Queues size, wating time, ecc.). When I plot the correlograms they exhibit a high degree of autocorrelation, even for high lags. Now, what are ...
### What exactly is $p(x,y)$ in the context of iid assumption in machine learning?
The i.i.d. assumption states: We are given a data set, $\{(x_i,y_i)\}_{i = 1, \ldots, n}$, each data $(x_i,y_i)$ is generated in an independent and identically distributed fashion. To me, ...